Question
Exercise 1:
Input: Directed graph G=(V,E)
Write a pseudo-code algorithm that uses DFS (Depth-first search) that decides if a given graph has an unique topological order (topological sort).
What is the running time? Why does it work?

Exercise 2:
Input: Undirected Graph, G=(V,E) and an edge (U,V) ∈ E.
Write a pseudo-code algorithm that decide if a given edge is inside some circle in G but not in ALL the circles in G.
What is the running time? Why does it work?

Exercise 3:
Input: Directed graph G=(V,E) , it is known that E is NOT an empty set.
Write two pseudo-code algorithm:
A) That checks if G is a acyclic graph. If truth, find the minimal set of vertices that form a directed path which can reach all the vertices in the graph.
B) Find the minimal set of vertices that form a directed path which can reach every vertex in the graph.
What is the running time? Why does it work? For A and B.
Solution Preview

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references.
Students may use these solutions for personal skill-building and practice.
Unethical use is strictly forbidden.

Exercise 1:
Input: Directed graph G=(V,E)
Write a pseudo-code algorithm that uses DFS (Depth-first search) that decides if a given graph has an unique topological order(topological sort).
What is the running time? Why does it work?
• Pseduo-code

Boolean isHamiltonPath(v, ADJ, L, stack_size)
If stack_size == size of ADJ then
Return true
For i in range 0 to size of ADJ
If there is a edge from ADJ[v] to ADJ[i] and L[i] == false then
L[i] = true
If isHamiltonPath(i, ADJ, L, stack_size + 1) == true
Return true
L[i] = fasle
Return false

Boolean hasHamiltonPath(G)
L <- empty list of boolean value
Put all vertex in G to an array named ADJ
For i in range of 0 to number of vertex in G
Push false to L
For i in range 0 to size of ADJ
L[i] = true
If isHamiltonPath(i, ADJ, L, 1) == true then
Return true
L[i] = false
This is only a preview of the solution.
Please use the purchase button to see the entire solution.
By purchasing this solution you'll be able to access the following files:
Solution.docx
Purchase Solution
$125.00
Google Pay
Amazon
Paypal
Mastercard
Visacard
Discover
Amex
View Available Computer Science Tutors 529 tutors matched
Ionut
(ionut)
Hi! MSc Applied Informatics & Computer Science Engineer. Practical experience in many CS & IT branches.Research work & homework
5/5 (5,654+ sessions)
2 hours avg response
Leo
(Leo)
Hi! I have been a professor in New York and taught in a math department and in an applied math department.
4.9/5 (5,652+ sessions)
2 hours avg response
Pranay
(math1983)
Ph.D. in mathematics and working as an Assistant Professor in University. I can provide help in mathematics, statistics and allied areas.
4.6/5 (5,512+ sessions)
1 hour avg response

Similar Homework Solutions

8.1.0PHP Version410msRequest Duration45MBMemory UsageGET college-homework-library/{category}/{subject}/{id}Route
    • Booting (275ms)time
    • Application (135ms)time
    • 1 x Booting (67.11%)
      275ms
      1 x Application (32.89%)
      135ms
      • Illuminate\Routing\Events\Routing (1.36ms)
      • Illuminate\Routing\Events\RouteMatched (550μs)
      • Illuminate\Foundation\Events\LocaleUpdated (4.31ms)
      • eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (187μs)
      • eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (168μs)
      • Illuminate\Database\Events\ConnectionEstablished (970μs)
      • Illuminate\Database\Events\StatementPrepared (9.73ms)
      • Illuminate\Database\Events\QueryExecuted (1.11ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (107μs)
      • eloquent.booting: App\Models\Subject (106μs)
      • eloquent.booted: App\Models\Subject (42μs)
      • Illuminate\Database\Events\StatementPrepared (1.67ms)
      • Illuminate\Database\Events\QueryExecuted (896μs)
      • eloquent.retrieved: App\Models\Subject (102μs)
      • eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (119μs)
      • eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (42μs)
      • Illuminate\Database\Events\StatementPrepared (633μs)
      • Illuminate\Database\Events\QueryExecuted (723μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (74μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (15μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (9μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (6μs)
      • eloquent.booting: App\Models\SubjectCat (292μs)
      • eloquent.booted: App\Models\SubjectCat (40μs)
      • Illuminate\Database\Events\StatementPrepared (687μs)
      • Illuminate\Database\Events\QueryExecuted (1.17ms)
      • eloquent.retrieved: App\Models\SubjectCat (96μs)
      • Illuminate\Cache\Events\CacheHit (10.91ms)
      • Illuminate\Cache\Events\CacheMissed (228μs)
      • Illuminate\Database\Events\StatementPrepared (956μs)
      • Illuminate\Database\Events\QueryExecuted (2.84ms)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (85μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (16μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (8μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (7μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (7μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (6μs)
      • Illuminate\Database\Events\StatementPrepared (1.01ms)
      • Illuminate\Database\Events\QueryExecuted (1.06ms)
      • eloquent.retrieved: App\Models\Subject (103μs)
      • Illuminate\Cache\Events\KeyWritten (828μs)
      • Illuminate\Database\Events\StatementPrepared (1.88ms)
      • Illuminate\Database\Events\QueryExecuted (1.13ms)
      • Illuminate\Database\Events\StatementPrepared (730μs)
      • Illuminate\Database\Events\QueryExecuted (867μs)
      • Illuminate\Database\Events\StatementPrepared (619μs)
      • Illuminate\Database\Events\QueryExecuted (756μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (50μs)
      • Illuminate\Cache\Events\CacheHit (816μs)
      • creating: homework.show (300μs)
      • composing: homework.show (120μs)
      • creating: components.breadcrumbs (275μs)
      • composing: components.breadcrumbs (125μs)
      • Illuminate\Database\Events\StatementPrepared (1.05ms)
      • Illuminate\Database\Events\QueryExecuted (801μs)
      • eloquent.retrieved: App\Models\SubjectCat (72μs)
      • Illuminate\Cache\Events\CacheMissed (4.65ms)
      • Illuminate\Database\Events\StatementPrepared (675μs)
      • Illuminate\Database\Events\QueryExecuted (864μs)
      • eloquent.retrieved: App\Models\SubjectCat (65μs)
      • Illuminate\Cache\Events\KeyWritten (341μs)
      • Illuminate\Cache\Events\CacheHit (223μs)
      • Illuminate\Cache\Events\CacheHit (154μs)
      • Illuminate\Cache\Events\CacheHit (113μs)
      • Illuminate\Cache\Events\CacheHit (140μs)
      • Illuminate\Cache\Events\CacheHit (119μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (108μs)
      • Illuminate\Cache\Events\CacheHit (118μs)
      • Illuminate\Cache\Events\CacheHit (102μs)
      • Illuminate\Cache\Events\CacheHit (117μs)
      • Illuminate\Cache\Events\CacheHit (101μs)
      • Illuminate\Cache\Events\CacheHit (114μs)
      • Illuminate\Cache\Events\CacheHit (98μs)
      • Illuminate\Cache\Events\CacheMissed (200μs)
      • Illuminate\Database\Events\StatementPrepared (755μs)
      • Illuminate\Database\Events\QueryExecuted (864μs)
      • eloquent.retrieved: App\Models\SubjectCat (63μs)
      • Illuminate\Cache\Events\KeyWritten (298μs)
      • Illuminate\Cache\Events\CacheHit (230μs)
      • Illuminate\Cache\Events\CacheHit (162μs)
      • Illuminate\Cache\Events\CacheHit (121μs)
      • Illuminate\Cache\Events\CacheHit (136μs)
      • Illuminate\Cache\Events\CacheHit (113μs)
      • Illuminate\Cache\Events\CacheHit (129μs)
      • Illuminate\Cache\Events\CacheHit (114μs)
      • Illuminate\Cache\Events\CacheMissed (189μs)
      • Illuminate\Database\Events\StatementPrepared (594μs)
      • Illuminate\Database\Events\QueryExecuted (884μs)
      • eloquent.retrieved: App\Models\SubjectCat (59μs)
      • Illuminate\Cache\Events\KeyWritten (270μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • Illuminate\Cache\Events\CacheHit (110μs)
      • Illuminate\Cache\Events\CacheHit (120μs)
      • Illuminate\Cache\Events\CacheHit (101μs)
      • Illuminate\Cache\Events\CacheHit (141μs)
      • Illuminate\Cache\Events\CacheHit (139μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (126μs)
      • Illuminate\Cache\Events\CacheHit (135μs)
      • Illuminate\Cache\Events\CacheHit (102μs)
      • Illuminate\Cache\Events\CacheHit (125μs)
      • Illuminate\Cache\Events\CacheHit (109μs)
      • Illuminate\Cache\Events\CacheHit (121μs)
      • Illuminate\Cache\Events\CacheHit (98μs)
      • Illuminate\Cache\Events\CacheHit (114μs)
      • Illuminate\Cache\Events\CacheHit (97μs)
      • Illuminate\Cache\Events\CacheHit (114μs)
      • Illuminate\Cache\Events\CacheHit (96μs)
      • Illuminate\Cache\Events\CacheHit (111μs)
      • Illuminate\Cache\Events\CacheHit (98μs)
      • Illuminate\Cache\Events\CacheHit (128μs)
      • Illuminate\Cache\Events\CacheHit (107μs)
      • Illuminate\Cache\Events\CacheHit (121μs)
      • Illuminate\Cache\Events\CacheHit (100μs)
      • Illuminate\Cache\Events\CacheHit (126μs)
      • Illuminate\Cache\Events\CacheHit (109μs)
      • Illuminate\Cache\Events\CacheHit (123μs)
      • Illuminate\Cache\Events\CacheHit (103μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (123μs)
      • Illuminate\Cache\Events\CacheMissed (194μs)
      • Illuminate\Database\Events\StatementPrepared (710μs)
      • Illuminate\Database\Events\QueryExecuted (919μs)
      • eloquent.retrieved: App\Models\SubjectCat (67μs)
      • Illuminate\Cache\Events\KeyWritten (346μs)
      • Illuminate\Cache\Events\CacheHit (234μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (154μs)
      • Illuminate\Cache\Events\CacheHit (220μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (241μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (355μs)
      • Illuminate\Cache\Events\CacheHit (210μs)
      • Illuminate\Cache\Events\CacheHit (211μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (208μs)
      • Illuminate\Cache\Events\CacheHit (196μs)
      • Illuminate\Cache\Events\CacheHit (201μs)
      • Illuminate\Cache\Events\CacheHit (218μs)
      • Illuminate\Cache\Events\CacheHit (205μs)
      • Illuminate\Cache\Events\CacheHit (208μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (208μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (182μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (259μs)
      • Illuminate\Cache\Events\CacheHit (170μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (195μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (195μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (332μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheMissed (303μs)
      • Illuminate\Database\Events\StatementPrepared (834μs)
      • Illuminate\Database\Events\QueryExecuted (1.04ms)
      • eloquent.retrieved: App\Models\SubjectCat (74μs)
      • Illuminate\Cache\Events\KeyWritten (340μs)
      • Illuminate\Cache\Events\CacheHit (226μs)
      • Illuminate\Cache\Events\CacheHit (208μs)
      • Illuminate\Cache\Events\CacheHit (642μs)
      • Illuminate\Cache\Events\CacheHit (193μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (156μs)
      • Illuminate\Cache\Events\CacheMissed (271μs)
      • Illuminate\Database\Events\StatementPrepared (657μs)
      • Illuminate\Database\Events\QueryExecuted (953μs)
      • eloquent.retrieved: App\Models\SubjectCat (63μs)
      • Illuminate\Cache\Events\KeyWritten (288μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • Illuminate\Cache\Events\CacheHit (124μs)
      • Illuminate\Cache\Events\CacheHit (228μs)
      • Illuminate\Cache\Events\CacheHit (146μs)
      • Illuminate\Cache\Events\CacheHit (135μs)
      • Illuminate\Cache\Events\CacheHit (139μs)
      • Illuminate\Cache\Events\CacheHit (143μs)
      • Illuminate\Cache\Events\CacheHit (103μs)
      • Illuminate\Cache\Events\CacheHit (124μs)
      • Illuminate\Cache\Events\CacheHit (106μs)
      • Illuminate\Cache\Events\CacheHit (579μs)
      • Illuminate\Cache\Events\CacheHit (115μs)
      • Illuminate\Cache\Events\CacheHit (120μs)
      • Illuminate\Cache\Events\CacheHit (100μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (99μs)
      • Illuminate\Cache\Events\CacheHit (111μs)
      • Illuminate\Cache\Events\CacheHit (95μs)
      • Illuminate\Cache\Events\CacheHit (108μs)
      • Illuminate\Cache\Events\CacheHit (141μs)
      • Illuminate\Cache\Events\CacheHit (126μs)
      • Illuminate\Cache\Events\CacheHit (98μs)
      • Illuminate\Cache\Events\CacheHit (111μs)
      • Illuminate\Cache\Events\CacheHit (96μs)
      • Illuminate\Cache\Events\CacheHit (113μs)
      • Illuminate\Cache\Events\CacheHit (102μs)
      • Illuminate\Cache\Events\CacheHit (137μs)
      • Illuminate\Cache\Events\CacheHit (110μs)
      • Illuminate\Cache\Events\CacheMissed (185μs)
      • Illuminate\Database\Events\StatementPrepared (717μs)
      • Illuminate\Database\Events\QueryExecuted (865μs)
      • eloquent.retrieved: App\Models\SubjectCat (66μs)
      • Illuminate\Cache\Events\KeyWritten (257μs)
      • Illuminate\Cache\Events\CacheHit (162μs)
      • Illuminate\Cache\Events\CacheHit (137μs)
      • Illuminate\Cache\Events\CacheHit (104μs)
      • Illuminate\Cache\Events\CacheHit (116μs)
      • Illuminate\Cache\Events\CacheHit (97μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (96μs)
      • Illuminate\Cache\Events\CacheHit (263μs)
      • Illuminate\Cache\Events\CacheHit (137μs)
      • Illuminate\Cache\Events\CacheHit (125μs)
      • Illuminate\Cache\Events\CacheHit (99μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (96μs)
      • Illuminate\Cache\Events\CacheHit (111μs)
      • Illuminate\Cache\Events\CacheHit (96μs)
      • Illuminate\Cache\Events\CacheHit (110μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (116μs)
      • Illuminate\Cache\Events\CacheHit (97μs)
      • Illuminate\Cache\Events\CacheHit (114μs)
      • Illuminate\Cache\Events\CacheHit (127μs)
      • Illuminate\Cache\Events\CacheHit (117μs)
      • Illuminate\Cache\Events\CacheHit (98μs)
      • Illuminate\Cache\Events\CacheHit (113μs)
      • Illuminate\Cache\Events\CacheHit (101μs)
      • Illuminate\Cache\Events\CacheHit (113μs)
      • Illuminate\Cache\Events\CacheHit (100μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (98μs)
      • Illuminate\Cache\Events\CacheHit (146μs)
      • Illuminate\Cache\Events\CacheHit (113μs)
      • Illuminate\Cache\Events\CacheHit (124μs)
      • Illuminate\Cache\Events\CacheHit (106μs)
      • Illuminate\Cache\Events\CacheHit (120μs)
      • Illuminate\Cache\Events\CacheHit (102μs)
      • Illuminate\Cache\Events\CacheHit (118μs)
      • Illuminate\Cache\Events\CacheHit (100μs)
      • Illuminate\Cache\Events\CacheHit (117μs)
      • Illuminate\Cache\Events\CacheHit (102μs)
      • Illuminate\Cache\Events\CacheHit (118μs)
      • Illuminate\Cache\Events\CacheHit (102μs)
      • Illuminate\Cache\Events\CacheHit (115μs)
      • Illuminate\Cache\Events\CacheHit (153μs)
      • Illuminate\Cache\Events\CacheHit (139μs)
      • Illuminate\Cache\Events\CacheHit (102μs)
      • Illuminate\Cache\Events\CacheHit (130μs)
      • Illuminate\Cache\Events\CacheHit (110μs)
      • Illuminate\Cache\Events\CacheHit (119μs)
      • Illuminate\Cache\Events\CacheHit (105μs)
      • Illuminate\Cache\Events\CacheHit (142μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (128μs)
      • Illuminate\Cache\Events\CacheHit (111μs)
      • Illuminate\Cache\Events\CacheHit (121μs)
      • Illuminate\Cache\Events\CacheHit (149μs)
      • Illuminate\Cache\Events\CacheHit (132μs)
      • Illuminate\Cache\Events\CacheHit (111μs)
      • Illuminate\Cache\Events\CacheHit (132μs)
      • Illuminate\Cache\Events\CacheHit (104μs)
      • Illuminate\Cache\Events\CacheHit (119μs)
      • Illuminate\Cache\Events\CacheHit (99μs)
      • Illuminate\Cache\Events\CacheHit (129μs)
      • Illuminate\Cache\Events\CacheHit (113μs)
      • Illuminate\Cache\Events\CacheMissed (212μs)
      • Illuminate\Database\Events\StatementPrepared (689μs)
      • Illuminate\Database\Events\QueryExecuted (1.02ms)
      • eloquent.retrieved: App\Models\SubjectCat (72μs)
      • Illuminate\Cache\Events\KeyWritten (306μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (164μs)
      • Illuminate\Cache\Events\CacheHit (116μs)
      • Illuminate\Cache\Events\CacheHit (150μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • Illuminate\Cache\Events\CacheHit (148μs)
      • Illuminate\Cache\Events\CacheHit (104μs)
      • Illuminate\Cache\Events\CacheHit (147μs)
      • Illuminate\Cache\Events\CacheHit (103μs)
      • Illuminate\Cache\Events\CacheHit (117μs)
      • Illuminate\Cache\Events\CacheHit (99μs)
      • Illuminate\Cache\Events\CacheHit (115μs)
      • Illuminate\Cache\Events\CacheHit (98μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (99μs)
      • Illuminate\Cache\Events\CacheHit (128μs)
      • Illuminate\Cache\Events\CacheHit (104μs)
      • Illuminate\Cache\Events\CacheHit (628μs)
      • Illuminate\Cache\Events\CacheHit (111μs)
      • Illuminate\Cache\Events\CacheHit (124μs)
      • Illuminate\Cache\Events\CacheHit (105μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (120μs)
      • Illuminate\Cache\Events\CacheHit (121μs)
      • Illuminate\Cache\Events\CacheHit (102μs)
      • Illuminate\Cache\Events\CacheHit (114μs)
      • Illuminate\Cache\Events\CacheHit (98μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (99μs)
      • Illuminate\Cache\Events\CacheHit (116μs)
      • Illuminate\Cache\Events\CacheHit (100μs)
      • Illuminate\Cache\Events\CacheHit (113μs)
      • Illuminate\Cache\Events\CacheHit (98μs)
      • Illuminate\Cache\Events\CacheHit (113μs)
      • Illuminate\Cache\Events\CacheHit (97μs)
      • Illuminate\Cache\Events\CacheHit (254μs)
      • Illuminate\Cache\Events\CacheHit (138μs)
      • Illuminate\Cache\Events\CacheHit (149μs)
      • Illuminate\Cache\Events\CacheHit (104μs)
      • Illuminate\Cache\Events\CacheHit (121μs)
      • Illuminate\Cache\Events\CacheHit (105μs)
      • Illuminate\Cache\Events\CacheHit (116μs)
      • Illuminate\Cache\Events\CacheHit (102μs)
      • Illuminate\Cache\Events\CacheHit (113μs)
      • Illuminate\Cache\Events\CacheHit (99μs)
      • Illuminate\Cache\Events\CacheHit (114μs)
      • Illuminate\Cache\Events\CacheHit (104μs)
      • Illuminate\Cache\Events\CacheHit (123μs)
      • Illuminate\Cache\Events\CacheHit (103μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (97μs)
      • Illuminate\Cache\Events\CacheHit (117μs)
      • Illuminate\Cache\Events\CacheHit (103μs)
      • Illuminate\Cache\Events\CacheHit (113μs)
      • Illuminate\Cache\Events\CacheHit (98μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (138μs)
      • Illuminate\Cache\Events\CacheHit (143μs)
      • Illuminate\Cache\Events\CacheHit (103μs)
      • Illuminate\Cache\Events\CacheHit (119μs)
      • Illuminate\Cache\Events\CacheHit (100μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (104μs)
      • Illuminate\Cache\Events\CacheHit (114μs)
      • Illuminate\Cache\Events\CacheHit (100μs)
      • Illuminate\Cache\Events\CacheHit (116μs)
      • Illuminate\Cache\Events\CacheHit (101μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (124μs)
      • Illuminate\Cache\Events\CacheHit (131μs)
      • Illuminate\Cache\Events\CacheHit (106μs)
      • Illuminate\Cache\Events\CacheHit (117μs)
      • Illuminate\Cache\Events\CacheHit (102μs)
      • Illuminate\Cache\Events\CacheHit (116μs)
      • Illuminate\Cache\Events\CacheHit (104μs)
      • Illuminate\Cache\Events\CacheHit (124μs)
      • Illuminate\Cache\Events\CacheHit (105μs)
      • Illuminate\Cache\Events\CacheHit (131μs)
      • Illuminate\Cache\Events\CacheHit (99μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (96μs)
      • Illuminate\Cache\Events\CacheHit (131μs)
      • Illuminate\Cache\Events\CacheHit (121μs)
      • Illuminate\Cache\Events\CacheHit (152μs)
      • Illuminate\Cache\Events\CacheHit (114μs)
      • Illuminate\Cache\Events\CacheHit (129μs)
      • Illuminate\Cache\Events\CacheHit (136μs)
      • Illuminate\Cache\Events\CacheMissed (239μs)
      • Illuminate\Database\Events\StatementPrepared (724μs)
      • Illuminate\Database\Events\QueryExecuted (993μs)
      • eloquent.retrieved: App\Models\SubjectCat (74μs)
      • Illuminate\Cache\Events\KeyWritten (276μs)
      • Illuminate\Cache\Events\CacheHit (173μs)
      • Illuminate\Cache\Events\CacheHit (160μs)
      • Illuminate\Cache\Events\CacheHit (113μs)
      • Illuminate\Cache\Events\CacheHit (132μs)
      • Illuminate\Cache\Events\CacheHit (122μs)
      • Illuminate\Cache\Events\CacheHit (124μs)
      • Illuminate\Cache\Events\CacheHit (135μs)
      • Illuminate\Cache\Events\CacheHit (134μs)
      • Illuminate\Cache\Events\CacheHit (103μs)
      • Illuminate\Cache\Events\CacheHit (120μs)
      • Illuminate\Cache\Events\CacheHit (99μs)
      • Illuminate\Cache\Events\CacheHit (116μs)
      • Illuminate\Cache\Events\CacheHit (209μs)
      • Illuminate\Cache\Events\CacheHit (214μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (117μs)
      • Illuminate\Cache\Events\CacheHit (99μs)
      • creating: site.layouts.app (333μs)
      • composing: site.layouts.app (17μs)
      • creating: components.canonical (410μs)
      • composing: components.canonical (79μs)
      • creating: components.open-graph (192μs)
      • composing: components.open-graph (54μs)
      • creating: site.headers.header (226μs)
      • composing: site.headers.header (49μs)
      • Illuminate\Cache\Events\CacheHit (1.2ms)
      • creating: components.footer (68μs)
      • composing: components.footer (68μs)
      • Illuminate\Cache\Events\CacheHit (613μs)
      • Illuminate\Cache\Events\CacheMissed (451μs)
      • Illuminate\Database\Events\StatementPrepared (757μs)
      • Illuminate\Database\Events\QueryExecuted (1.02ms)
      • eloquent.retrieved: App\Models\SubjectCat (76μs)
      • Illuminate\Cache\Events\KeyWritten (384μs)
      • Illuminate\Cache\Events\CacheHit (352μs)
      • Illuminate\Cache\Events\CacheHit (224μs)
      • Illuminate\Cache\Events\CacheHit (213μs)
      • Illuminate\Cache\Events\CacheHit (150μs)
      • Illuminate\Cache\Events\CacheHit (128μs)
      • Illuminate\Cache\Events\CacheHit (425μs)
      • Illuminate\Cache\Events\CacheHit (336μs)
      • Illuminate\Cache\Events\CacheHit (204μs)
      • Illuminate\Cache\Events\CacheHit (195μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (205μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • creating: components.forms.contact-us (345μs)
      • composing: components.forms.contact-us (195μs)
      • creating: components.forms.get-started (215μs)
      • composing: components.forms.get-started (91μs)
      • creating: components.forms.free-tool-download (152μs)
      • composing: components.forms.free-tool-download (78μs)
      • creating: components.forms.claim-free-worksheet (147μs)
      • composing: components.forms.claim-free-worksheet (80μs)
      • creating: components.forms.tutor-subscription-waitlist (144μs)
      • composing: components.forms.tutor-subscription-waitlist (75μs)
      • creating: components.forms.tutor-subscription-join (145μs)
      • composing: components.forms.tutor-subscription-join (70μs)
      • creating: components.forms.tutor-support (125μs)
      • composing: components.forms.tutor-support (67μs)
      • 311 x Illuminate\Cache\Events\CacheHit (14.01%)
        57.43ms
        20 x Illuminate\Database\Events\StatementPrepared (6.36%)
        26.08ms
        20 x Illuminate\Database\Events\QueryExecuted (5.06%)
        20.76ms
        11 x Illuminate\Cache\Events\CacheMissed (1.74%)
        7.12ms
        1 x Illuminate\Foundation\Events\LocaleUpdated (1.05%)
        4.31ms
        11 x Illuminate\Cache\Events\KeyWritten (0.96%)
        3.93ms
        1 x Illuminate\Routing\Events\Routing (0.33%)
        1.36ms
        1 x Illuminate\Database\Events\ConnectionEstablished (0.24%)
        970μs
        12 x eloquent.retrieved: App\Models\SubjectCat (0.21%)
        848μs
        1 x Illuminate\Routing\Events\RouteMatched (0.13%)
        550μs
        1 x creating: components.canonical (0.1%)
        410μs
        1 x creating: components.forms.contact-us (0.08%)
        345μs
        1 x creating: site.layouts.app (0.08%)
        333μs
        1 x creating: homework.show (0.07%)
        300μs
        1 x eloquent.booting: App\Models\SubjectCat (0.07%)
        292μs
        1 x creating: components.breadcrumbs (0.07%)
        275μs
        7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.06%)
        236μs
        1 x creating: site.headers.header (0.06%)
        226μs
        1 x creating: components.forms.get-started (0.05%)
        215μs
        2 x eloquent.retrieved: App\Models\Subject (0.05%)
        205μs
        1 x composing: components.forms.contact-us (0.05%)
        195μs
        1 x creating: components.open-graph (0.05%)
        192μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.05%)
        187μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.04%)
        168μs
        5 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.04%)
        154μs
        1 x creating: components.forms.free-tool-download (0.04%)
        152μs
        1 x creating: components.forms.claim-free-worksheet (0.04%)
        147μs
        1 x creating: components.forms.tutor-subscription-join (0.04%)
        145μs
        1 x creating: components.forms.tutor-subscription-waitlist (0.04%)
        144μs
        1 x composing: components.breadcrumbs (0.03%)
        125μs
        1 x creating: components.forms.tutor-support (0.03%)
        125μs
        1 x composing: homework.show (0.03%)
        120μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.03%)
        119μs
        1 x eloquent.booting: App\Models\Subject (0.03%)
        106μs
        1 x composing: components.forms.get-started (0.02%)
        91μs
        1 x composing: components.forms.claim-free-worksheet (0.02%)
        80μs
        1 x composing: components.canonical (0.02%)
        79μs
        1 x composing: components.forms.free-tool-download (0.02%)
        78μs
        1 x composing: components.forms.tutor-subscription-waitlist (0.02%)
        75μs
        1 x composing: components.forms.tutor-subscription-join (0.02%)
        70μs
        1 x creating: components.footer (0.02%)
        68μs
        1 x composing: components.footer (0.02%)
        68μs
        1 x composing: components.forms.tutor-support (0.02%)
        67μs
        1 x composing: components.open-graph (0.01%)
        54μs
        1 x composing: site.headers.header (0.01%)
        49μs
        1 x eloquent.booted: App\Models\Subject (0.01%)
        42μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.01%)
        42μs
        1 x eloquent.booted: App\Models\SubjectCat (0.01%)
        40μs
        1 x composing: site.layouts.app (0%)
        17μs
      14 templates were rendered
      • 1x homework.showshow.blade.phpblade
      • 1x components.breadcrumbsbreadcrumbs.blade.phpblade
      • 1x site.layouts.appapp.blade.phpblade
      • 1x components.canonicalcanonical.blade.phpblade
      • 1x components.open-graphopen-graph.blade.phpblade
      • 1x site.headers.headerheader.blade.phpblade
      • 1x components.footerfooter.blade.phpblade
      • 1x components.forms.contact-uscontact-us.blade.phpblade
      • 1x components.forms.get-startedget-started.blade.phpblade
      • 1x components.forms.free-tool-downloadfree-tool-download.blade.phpblade
      • 1x components.forms.claim-free-worksheetclaim-free-worksheet.blade.phpblade
      • 1x components.forms.tutor-subscription-waitlisttutor-subscription-waitlist.blade.phpblade
      • 1x components.forms.tutor-subscription-jointutor-subscription-join.blade.phpblade
      • 1x components.forms.tutor-supporttutor-support.blade.phpblade
      uri
      GET college-homework-library/{category}/{subject}/{id}
      middleware
      web, utm.parameters
      controller
      App\Http\Controllers\HomeworkLibraryController@show
      namespace
      where
      as
      homework.show
      file
      app/Http/Controllers/HomeworkLibraryController.php:79-176
      20 statements were executed, 5 of which were duplicates, 15 unique. Show only duplicated32.23ms
      • Connection Establishedtwenty4_siteHomeworkLibraryController.php#91
        Backtrace
        • 13. app/Http/Controllers/HomeworkLibraryController.php:91
        • 14. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 15. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 16. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary` where `status` = 'published' and `price` > 0 and `solutionslibrary`.`id` = '34592' limit 1
        9.97mstwenty4_siteHomeworkLibraryController.php#97
        Bindings
        • 0: published
        • 1: 0
        • 2: 34592
        Backtrace
        • 16. app/Http/Controllers/HomeworkLibraryController.php:97
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 18. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 19. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 20. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subjects` where `subjects`.`id` in (143)
        1.06mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` in (34592)
        860μstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subject_cats` where `subject_cats`.`id` = 3 limit 1
        1.32mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 3
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 26. app/Http/Controllers/HomeworkLibraryController.php:105
        • 27. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 28. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 29. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
      • select * from `solutionslibrary` where `id` <> 34592 and `subject` = 143 and `status` = 'published' and `price` > 0 order by RAND() limit 6
        3.07mstwenty4_siteHomeworkLibraryRepository.php#30
        Bindings
        • 0: 34592
        • 1: 143
        • 2: published
        • 3: 0
        Backtrace
        • 14. app/Repositories/HomeworkLibraryRepository.php:30
        • 15. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 16. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 18. app/Repositories/HomeworkLibraryRepository.php:39
        • 19. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `subjects` where `subjects`.`id` in (143)
        1.47mstwenty4_siteHomeworkLibraryRepository.php#30
        Backtrace
        • 19. app/Repositories/HomeworkLibraryRepository.php:30
        • 20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 21. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 23. app/Repositories/HomeworkLibraryRepository.php:39
        • 24. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 34592 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        870μstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 34592
        • 1: question
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:58
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 34592 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc
        960μstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 34592
        • 1: teaser
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:69
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 34592 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'solution' order by `order` asc, `id` asc
        820μstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 34592
        • 1: solution
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:80
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `subject_cats` where `subject_cats`.`id` = 3 limit 1
        960μstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 3
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 32. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 33. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 34. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
        • 35. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        1.01mstwenty4_siteSubject.php#100
        Bindings
        • 0: 1
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 3 limit 1
        1.14mstwenty4_siteSubject.php#100
        Bindings
        • 0: 3
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 4 limit 1
        900μstwenty4_siteSubject.php#100
        Bindings
        • 0: 4
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 10 limit 1
        1.12mstwenty4_siteSubject.php#100
        Bindings
        • 0: 10
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 33 limit 1
        1.26mstwenty4_siteSubject.php#100
        Bindings
        • 0: 33
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 11 limit 1
        1.07mstwenty4_siteSubject.php#100
        Bindings
        • 0: 11
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 5 limit 1
        1.07mstwenty4_siteSubject.php#100
        Bindings
        • 0: 5
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 34 limit 1
        1.04mstwenty4_siteSubject.php#100
        Bindings
        • 0: 34
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 31 limit 1
        1.09mstwenty4_siteSubject.php#100
        Bindings
        • 0: 31
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 36 limit 1
        1.17mstwenty4_siteSubject.php#100
        Bindings
        • 0: 36
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 28. view::components.footer:170
      App\Models\SubjectCat
      12SubjectCat.php
      App\Models\HomeworkLibrary\HomeworkLibrary
      7HomeworkLibrary.php
      App\Models\HomeworkLibrary\HomeworkLibraryFile
      5HomeworkLibraryFile.php
      App\Models\Subject
      2Subject.php
          _token
          VzDXZJtdBiNKbxcQXUYkht2QEZC5NFwzI2ik3Zwz
          utm_source
          direct
          redirectUrl
          /college-homework-library/Computer-Science/Theoretical-Computer-Science/34592
          _previous
          array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Computer-Scienc...
          _flash
          array:2 [ "old" => [] "new" => [] ]
          PHPDEBUGBAR_STACK_DATA
          []
          path_info
          /college-homework-library/Computer-Science/Theoretical-Computer-Science/34592
          status_code
          200
          
          status_text
          OK
          format
          html
          content_type
          text/html; charset=UTF-8
          request_query
          []
          
          request_request
          []
          
          request_headers
          0 of 0
          array:21 [ "priority" => array:1 [ 0 => "u=0, i" ] "accept-encoding" => array:1 [ 0 => "gzip, deflate, br, zstd" ] "sec-fetch-dest" => array:1 [ 0 => "document" ] "sec-fetch-user" => array:1 [ 0 => "?1" ] "sec-fetch-mode" => array:1 [ 0 => "navigate" ] "sec-fetch-site" => array:1 [ 0 => "none" ] "accept" => array:1 [ 0 => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" ] "user-agent" => array:1 [ 0 => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" ] "upgrade-insecure-requests" => array:1 [ 0 => "1" ] "sec-ch-ua-platform" => array:1 [ 0 => ""Windows"" ] "sec-ch-ua-mobile" => array:1 [ 0 => "?0" ] "sec-ch-ua" => array:1 [ 0 => ""HeadlessChrome";v="129", "Not=A?Brand";v="8", "Chromium";v="129"" ] "cache-control" => array:1 [ 0 => "no-cache" ] "pragma" => array:1 [ 0 => "no-cache" ] "x-amzn-trace-id" => array:1 [ 0 => "Root=1-680ec1e9-1c014edc6e26e0f060a3ea53" ] "host" => array:1 [ 0 => "staging.dev.24houranswers.com" ] "x-forwarded-port" => array:1 [ 0 => "443" ] "x-forwarded-proto" => array:1 [ 0 => "https" ] "x-forwarded-for" => array:1 [ 0 => "18.219.202.234" ] "content-length" => array:1 [ 0 => "" ] "content-type" => array:1 [ 0 => "" ] ]
          request_cookies
          []
          
          response_headers
          0 of 0
          array:5 [ "content-type" => array:1 [ 0 => "text/html; charset=UTF-8" ] "cache-control" => array:1 [ 0 => "no-cache, private" ] "date" => array:1 [ 0 => "Sun, 27 Apr 2025 23:46:49 GMT" ] "set-cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6ImhNdFU0Z1E0WEFmTmxVbzJEL2xpeEE9PSIsInZhbHVlIjoiWFVIbFJzekFvZkJlVnB3OFFBMStBbld2R2QwbHphczliZWJTY1lKclgzODZMSDdoZ3Fkd0VTZk5lK1JwdmdmSTgvdDRRMjl4eGFJQXh4NDd3T1RVTTgra2YyWWVsUjlLZTdUSWxhSFdJSjcvMWo0QVlaZEV2T2t4WnRIWVNuZzQiLCJtYWMiOiJjY2NhMjdmNWNkOWQ1MDExODBkNjk0OGIxOGQ0NWI3NWRlMDlhOTFkYTgxZDdlNzUxZjdjYzNkNGYzYmEyYjI0IiwidGFnIjoiIn0%3D; expires=Mon, 28 Apr 2025 01:46:49 GMT; Max-Age=7200; path=/; domain=.24houranswers.com; samesite=laxXSRF-TOKEN=eyJpdiI6ImhNdFU0Z1E0WEFmTmxVbzJEL2xpeEE9PSIsInZhbHVlIjoiWFVIbFJzekFvZkJlVnB3OFFBMStBbld2R2QwbHphczliZWJTY1lKclgzODZMSDdoZ3Fkd0VTZk5lK1JwdmdmSTgvdDRRM" 1 => "24houranswers_session=eyJpdiI6Iml1Nm1rU3pZWnZ2RXRrREVhcXlHWFE9PSIsInZhbHVlIjoiVUVYR2RrZmMreW94YmdUQ3RISnZHdkVoS0NUWCtReDRxMUd4YStkNmw3bmRPUlNrcXNrcktKT0M4Z3R0alhMZ3Rkbk9LSGtJSVhPMHY5c25wcld3U01zZkQrb0M1S0IzK2orQ2hPZW1rdG0vT0E0c3JFYWVQYmord2h4amtHZ2ciLCJtYWMiOiJjNTU1MmEzNGU0N2QxNGEyZDM2NDMzZjAzODU0YzYxOTZjZjQwOTA3OTViMDlmZWEyMjVlYjJmNmJjMGU3OTJiIiwidGFnIjoiIn0%3D; expires=Mon, 28 Apr 2025 01:46:49 GMT; Max-Age=7200; path=/; domain=.24houranswers.com; httponly; samesite=lax24houranswers_session=eyJpdiI6Iml1Nm1rU3pZWnZ2RXRrREVhcXlHWFE9PSIsInZhbHVlIjoiVUVYR2RrZmMreW94YmdUQ3RISnZHdkVoS0NUWCtReDRxMUd4YStkNmw3bmRPUlNrcXNrcktKT0M4Z3R0al" ] "Set-Cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6ImhNdFU0Z1E0WEFmTmxVbzJEL2xpeEE9PSIsInZhbHVlIjoiWFVIbFJzekFvZkJlVnB3OFFBMStBbld2R2QwbHphczliZWJTY1lKclgzODZMSDdoZ3Fkd0VTZk5lK1JwdmdmSTgvdDRRMjl4eGFJQXh4NDd3T1RVTTgra2YyWWVsUjlLZTdUSWxhSFdJSjcvMWo0QVlaZEV2T2t4WnRIWVNuZzQiLCJtYWMiOiJjY2NhMjdmNWNkOWQ1MDExODBkNjk0OGIxOGQ0NWI3NWRlMDlhOTFkYTgxZDdlNzUxZjdjYzNkNGYzYmEyYjI0IiwidGFnIjoiIn0%3D; expires=Mon, 28-Apr-2025 01:46:49 GMT; domain=.24houranswers.com; path=/XSRF-TOKEN=eyJpdiI6ImhNdFU0Z1E0WEFmTmxVbzJEL2xpeEE9PSIsInZhbHVlIjoiWFVIbFJzekFvZkJlVnB3OFFBMStBbld2R2QwbHphczliZWJTY1lKclgzODZMSDdoZ3Fkd0VTZk5lK1JwdmdmSTgvdDRRM" 1 => "24houranswers_session=eyJpdiI6Iml1Nm1rU3pZWnZ2RXRrREVhcXlHWFE9PSIsInZhbHVlIjoiVUVYR2RrZmMreW94YmdUQ3RISnZHdkVoS0NUWCtReDRxMUd4YStkNmw3bmRPUlNrcXNrcktKT0M4Z3R0alhMZ3Rkbk9LSGtJSVhPMHY5c25wcld3U01zZkQrb0M1S0IzK2orQ2hPZW1rdG0vT0E0c3JFYWVQYmord2h4amtHZ2ciLCJtYWMiOiJjNTU1MmEzNGU0N2QxNGEyZDM2NDMzZjAzODU0YzYxOTZjZjQwOTA3OTViMDlmZWEyMjVlYjJmNmJjMGU3OTJiIiwidGFnIjoiIn0%3D; expires=Mon, 28-Apr-2025 01:46:49 GMT; domain=.24houranswers.com; path=/; httponly24houranswers_session=eyJpdiI6Iml1Nm1rU3pZWnZ2RXRrREVhcXlHWFE9PSIsInZhbHVlIjoiVUVYR2RrZmMreW94YmdUQ3RISnZHdkVoS0NUWCtReDRxMUd4YStkNmw3bmRPUlNrcXNrcktKT0M4Z3R0al" ] ]
          session_attributes
          0 of 0
          array:6 [ "_token" => "VzDXZJtdBiNKbxcQXUYkht2QEZC5NFwzI2ik3Zwz" "utm_source" => "direct" "redirectUrl" => "/college-homework-library/Computer-Science/Theoretical-Computer-Science/34592" "_previous" => array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Computer-Science/Theoretical-Computer-Science/34592" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]