Find if there is a path between two vertices in a directed graph | Set 2 - GeeksforGeeks

30 Jun, 2021
Given a Directed Graph and two vertices in it, check whether there is a path from the first given vertex to second.
Example: 
Consider the following Graph:  
Input : (u, v) = (1, 3) Output: Yes Explanation: There is a path from 1 to 3, 1 -> 2 -> 3
Input : (u, v) = (3, 6) Output: No Explanation: There is no path from 3 to 6  
A BFS or DFS based solution of this problem is discussed here.Approach: Here we will discuss a Dynamic Programming based solution using Floyd Warshall Algorithm. 
Create a boolean 2D matrix mat where mat[i][j] will be true if there is a path from vertex i to j.
For every starting vertex i and ending vertex j iterate over all intermediate vertex k and do check if there is a path for i to j through k then mark mat[i][j] as true.
Finally, check if mat[u][v] is true then return true else return false.
Below is the implementation of the above approach: 
C++
Java
Python3
C#
Javascript
// C++ program to find if there is a// path between two vertices in a// directed graph using Dynamic Programming #include <bits/stdc++.h>using namespace std;#define X 6#define Z 2 // function to find if there is a// path between two vertices in a// directed graphbool existPath(int V, int edges[X][Z],               int u, int v){    // dp matrix    bool mat[V][V];    memset(mat, false, sizeof(mat));     // set dp[i][j]=true if there is    // edge between i to j    for (int i = 0; i < X; i++)        mat[edges[i][0]][edges[i][1]] = true;     // check for all intermediate vertex    for (int k = 0; k < V; k++) {        for (int i = 0; i < V; i++) {            for (int j = 0; j < V; j++) {                 mat[i][j] = mat[i][j]                            || mat[i][k]                                   && mat[k][j];            }        }    }     // if vertex is invalid    if (u >= V || v >= V) {        return false;    }     // if there is a path    if (mat[u][v])        return true;    return false;} // Driver functionint main(){    int V = 4;    int edges[X][Z]        = { { 0, 2 }, { 0, 1 },            { 1, 2 }, { 2, 3 },            { 2, 0 }, { 3, 3 } };    int u = 1, v = 3;     if (existPath(V, edges, u, v))        cout << "Yes\n";    else        cout << "No\n";    return 0;}
// Java program to find if there is a path// between two vertices in a directed graph// using Dynamic Programmingimport java.util.*; class GFG{     static final int X = 6;static final int Z = 2; // Function to find if there is a// path between two vertices in a// directed graphstatic boolean existPath(int V, int edges[][],                         int u, int v){         // mat matrix    boolean [][]mat = new boolean[V][V];     // set mat[i][j]=true if there is    // edge between i to j    for (int i = 0; i < X; i++)        mat[edges[i][0]][edges[i][1]] = true;     // Check for all intermediate vertex    for(int k = 0; k < V; k++)    {        for(int i = 0; i < V; i++)        {            for(int j = 0; j < V; j++)            {                mat[i][j] = mat[i][j] ||                            mat[i][k] &&                            mat[k][j];            }        }    }     // If vertex is invalid    if (u >= V || v >= V)    {        return false;    }     // If there is a path    if (mat[u][v])        return true;    return false;} // Driver codepublic static void main(String[] args){    int V = 4;    int edges[][] = { { 0, 2 }, { 0, 1 },                      { 1, 2 }, { 2, 3 },                      { 2, 0 }, { 3, 3 } };    int u = 1, v = 3;     if (existPath(V, edges, u, v))        System.out.print("Yes\n");    else        System.out.print("No\n");}} // This code is contributed by Princi Singh
# Python3 program to find if there# is a path between two vertices in a# directed graph using Dynamic ProgrammingX = 6Z = 2  # Function to find if there is a# path between two vertices in a# directed graphdef existPath(V, edges, u, v):         # dp matrix    mat = [[False for i in range(V)]                  for j in range(V)]      # Set dp[i][j]=true if there is    # edge between i to j    for i in range(X):        mat[edges[i][0]][edges[i][1]] = True      # Check for all intermediate vertex    for k in range(V):        for i in range(V):            for j in range(V):                mat[i][j] = (mat[i][j] or                             mat[i][k] and                             mat[k][j])      # If vertex is invalid    if (u >= V or v >= V):        return False      # If there is a path    if (mat[u][v]):        return True             return False # Driver codeV = 4edges = [ [ 0, 2 ], [ 0, 1 ],          [ 1, 2 ], [ 2, 3 ],          [ 2, 0 ], [ 3, 3 ] ]         u, v = 1, 3 if (existPath(V, edges, u, v)):    print("Yes")else:    print("No") # This code is contributed by divyeshrabadiya07
// C# program to find if there is a path// between two vertices in a directed graph// using Dynamic Programmingusing System;class GFG{     static readonly int X = 6;static readonly int Z = 2; // Function to find if there is a// path between two vertices in a// directed graphstatic bool existPath(int V, int [,]edges,                      int u, int v){         // mat matrix    bool [,]mat = new bool[V, V];     // set mat[i,j]=true if there is    // edge between i to j    for (int i = 0; i < X; i++)        mat[edges[i, 0], edges[i, 1]] = true;     // Check for all intermediate vertex    for(int k = 0; k < V; k++)    {        for(int i = 0; i < V; i++)        {            for(int j = 0; j < V; j++)            {                mat[i, j] = mat[i, j] ||                            mat[i, k] &&                            mat[k, j];            }        }    }     // If vertex is invalid    if (u >= V || v >= V)    {        return false;    }     // If there is a path    if (mat[u, v])        return true;    return false;} // Driver codepublic static void Main(String[] args){    int V = 4;    int [,]edges = { { 0, 2 }, { 0, 1 },                     { 1, 2 }, { 2, 3 },                     { 2, 0 }, { 3, 3 } };    int u = 1, v = 3;     if (existPath(V, edges, u, v))        Console.Write("Yes\n");    else        Console.Write("No\n");}} // This code is contributed by sapnasingh4991
<script> // Javascript program to find if there is a path// between two vertices in a directed graph// using Dynamic Programming     var X = 6;var Z = 2; // Function to find if there is a// path between two vertices in a// directed graphfunction existPath(V, edges, u, v){         // mat matrix    var mat = Array.from(Array(V), ()=>Array(V));     // set mat[i,j]=true if there is    // edge between i to j    for (var i = 0; i < X; i++)        mat[edges[i][0]][edges[i][1]] = true;     // Check for all intermediate vertex    for(var k = 0; k < V; k++)    {        for(var i = 0; i < V; i++)        {            for(var j = 0; j < V; j++)            {                mat[i][j] = mat[i][j] ||                            mat[i][k] &&                            mat[k][j];            }        }    }     // If vertex is invalid    if (u >= V || v >= V)    {        return false;    }     // If there is a path    if (mat[u][v])        return true;    return false;} // Driver codevar V = 4;var edges = [ [ 0, 2 ], [ 0, 1 ],                 [ 1, 2 ], [ 2, 3 ],                 [ 2, 0 ], [ 3, 3 ] ];var u = 1, v = 3;if (existPath(V, edges, u, v))    document.write("Yes<br>");else    document.write("No<br>"); </script>
Yes
 
Time Complexity : O ( V 3) Auxiliary Space : O ( V 2) 
 
princi singh
sapnasingh4991
divyeshrabadiya07
noob2000
Algorithms
Data Structures
Dynamic Programming
Graph
Matrix
Data Structures
Dynamic Programming
Matrix
Graph
Algorithms
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