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Solve Transitive Closure of a Graph using JavaScript Language

Solve Transitive Closure of a Graph using JavaScript to enhance your skills with javascript coding practice , master coding concepts, and prepare for interviews with practical exercises and detailed solutions.

Transitive Closure of a Graph

Difficulty : Medium

Categories :

  • Graphs
  • Dynamic programming

Given a directed graph represented as an adjacency matrix with N vertices, find its transitive closure. The transitive closure is a reachability matrix where matrix[i][j] indicates whether vertex j is reachable from vertex i through a path.

Constraints:

  • 1 ≤ N ≤ 100
  • Graph is represented as NxN adjacency matrix
  • Matrix values are either 0 or 1

Examples:

Input:
N = 4
graph = [
  [1,1,0,1],
  [0,1,1,0],
  [0,0,1,1],
  [0,0,0,1]
]
Output: [
  [1,1,1,1],
  [0,1,1,1],
  [0,0,1,1],
  [0,0,0,1]
]
Explanation: Output[i][j] = 1 if vertex j is reachable from vertex i
Input:
N = 3
graph = [
  [1,0,0],
  [0,1,0],
  [0,0,1]
]
Output: [
  [1,0,0],
  [0,1,0],
  [0,0,1]
]
Explanation: Each vertex can only reach itself

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Graphs A collection of nodes (vertices) connected by edges, representing relationships, widely used in networking, routing, and social networks.

Dynamic Programming An optimization technique that solves problems by breaking them into overlapping subproblems and storing their results.

Backtracking A problem-solving method that explores all possibilities recursively, backtracking when a solution is not feasible.

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Searching Algorithms Methods for finding elements in a dataset, such as binary search, linear search, and graph traversal techniques.

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