Given two nodes of a binary tree v1 and v2, the task is to check if two nodes are on the same path in a tree.
Example:
Input: v1 = 1, v2 = 5
1
/ | \
2 3 4
/ | \
5 6 7
Output: Yes
Explanation:
Both nodes 1 and 5
lie in the path 1 -> 2 -> 5.
Input: v1 = 2, v2 = 6
1
/ | \
2 3 4
/ | \
5 6 7
Output: NO
DFS Approach: Refer to Check if two nodes are on same path in a tree for the DFS approach.
LCA Approach: The idea is to use Lowest Common Ancestor. Find the LCA of the given vertices v1 and v2. If the LCA is equal to any of the given two vertices, print Yes. Otherwise, print No.
Below is the implementation of above approach:
C++
// C++ program to check if two nodes// are on same path in a tree without// using any extra space#include <bits/stdc++.h>using namespace std;// Function to filter// the return Valuesint filter(int x, int y, int z){ if (x != -1 && y != -1) { return z; } return x == -1 ? y : x;}// Utility function to check if nodes// are on same path or notint samePathUtil(int mtrx[][7], int vrtx, int v1, int v2, int i){ int ans = -1; // Condition to check // if any vertex // is equal to given two // vertex or not if (i == v1 || i == v2) return i; for (int j = 0; j < vrtx; j++) { // Check if the current // position has 1 if (mtrx[i][j] == 1) { // Recursive call ans = filter(ans, samePathUtil(mtrx, vrtx, v1, v2, j), i); } } // Return LCA return ans;}// Function to check if nodes// lies on same path or notbool isVertexAtSamePath(int mtrx[][7], int vrtx, int v1, int v2, int i){ int lca = samePathUtil(mtrx, vrtx, v1 - 1, v2 - 1, i); if (lca == v1 - 1 || lca == v2 - 1) return true; return false;}// Driver Programint main(){ int vrtx = 7, edge = 6; int mtrx[7][7] = { { 0, 1, 1, 1, 0, 0, 0 }, { 0, 0, 0, 0, 1, 0, 0 }, { 0, 0, 0, 0, 0, 1, 0 }, { 0, 0, 0, 0, 0, 0, 1 }, { 0, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0 } }; int v1 = 1, v2 = 5; if (isVertexAtSamePath(mtrx, vrtx, v1, v2, 0)) cout << "Yes"; else cout << "No"; return 0;} |
Java
// Java program to check if two nodes// are on same path in a tree without// using any extra spaceclass GFG{// Function to filter// the return Valuesstatic int filter(int x, int y, int z){ if (x != -1 && y != -1) { return z; } return x == -1 ? y : x;}// Utility function to check if nodes// are on same path or notstatic int samePathUtil(int mtrx[][], int vrtx, int v1, int v2, int i){ int ans = -1; // Condition to check // if any vertex // is equal to given two // vertex or not if (i == v1 || i == v2) return i; for(int j = 0; j < vrtx; j++) { // Check if the current // position has 1 if (mtrx[i][j] == 1) { // Recursive call ans = filter(ans, samePathUtil( mtrx, vrtx, v1, v2, j), i); } } // Return LCA return ans;}// Function to check if nodes// lies on same path or notstatic boolean isVertexAtSamePath(int mtrx[][], int vrtx, int v1, int v2, int i){ int lca = samePathUtil(mtrx, vrtx, v1 - 1, v2 - 1, i); if (lca == v1 - 1 || lca == v2 - 1) return true; return false;}// Driver codepublic static void main(String[] args){ int vrtx = 7; int mtrx[][] = { { 0, 1, 1, 1, 0, 0, 0 }, { 0, 0, 0, 0, 1, 0, 0 }, { 0, 0, 0, 0, 0, 1, 0 }, { 0, 0, 0, 0, 0, 0, 1 }, { 0, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0 } }; int v1 = 1, v2 = 5; if (isVertexAtSamePath(mtrx, vrtx, v1, v2, 0)) System.out.print("Yes"); else System.out.print("No");}}// This code is contributed by Rajput-Ji |
Python3
# Python3 program to check if two nodes# are on same path in a tree without# using any extra space# Function to filter# the return Valuesdef filter(x, y, z): if (x != -1 and y != -1): return z return y if x == -1 else x# Utility function to check if nodes# are on same path or notdef samePathUtil(mtrx, vrtx, v1, v2, i): ans = -1 # Condition to check # if any vertex # is equal to given two # vertex or not if (i == v1 or i == v2): return i for j in range(0, vrtx): # Check if the current # position has 1 if (mtrx[i][j] == 1): # Recursive call ans = filter(ans, samePathUtil(mtrx, vrtx, v1, v2, j), i) # Return LCA return ans# Function to check if nodes# lies on same path or notdef isVertexAtSamePath(mtrx, vrtx, v1, v2, i): lca = samePathUtil(mtrx, vrtx, v1 - 1, v2 - 1, i) if (lca == v1 - 1 or lca == v2 - 1): return True return False# Driver codevrtx = 7edge = 6mtrx = [ [ 0, 1, 1, 1, 0, 0, 0 ] , [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0 ] ]v1 = 1v2 = 5if (isVertexAtSamePath(mtrx, vrtx, v1, v2, 0)): print("Yes")else: print("No")# This code is contributed by sanjoy_62 |
C#
// C# program to check if two nodes// are on same path in a tree without// using any extra spaceusing System;class GFG{// Function to filter// the return Valuesstatic int filter(int x, int y, int z){ if (x != -1 && y != -1) { return z; } return x == -1 ? y : x;}// Utility function to check if nodes// are on same path or notstatic int samePathUtil(int [,]mtrx, int vrtx, int v1, int v2, int i){ int ans = -1; // Condition to check // if any vertex // is equal to given two // vertex or not if (i == v1 || i == v2) return i; for(int j = 0; j < vrtx; j++) { // Check if the current // position has 1 if (mtrx[i,j] == 1) { // Recursive call ans = filter(ans, samePathUtil( mtrx, vrtx, v1, v2, j), i); } } // Return LCA return ans;}// Function to check if nodes// lies on same path or notstatic bool isVertexAtSamePath(int [,]mtrx, int vrtx, int v1, int v2, int i){ int lca = samePathUtil(mtrx, vrtx, v1 - 1, v2 - 1, i); if (lca == v1 - 1 || lca == v2 - 1) return true; return false;}// Driver codepublic static void Main(String[] args){ int vrtx = 7; int [,]mtrx = { { 0, 1, 1, 1, 0, 0, 0 }, { 0, 0, 0, 0, 1, 0, 0 }, { 0, 0, 0, 0, 0, 1, 0 }, { 0, 0, 0, 0, 0, 0, 1 }, { 0, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0, 0, 0 } }; int v1 = 1, v2 = 5; if (isVertexAtSamePath(mtrx, vrtx, v1, v2, 0)) Console.Write("Yes"); else Console.Write("No");}}// This code is contributed by sapnasingh4991 |
Javascript
<script> // Javascript program to check if two nodes // are on same path in a tree without // using any extra space // Function to filter // the return Values function filter(x, y, z) { if (x != -1 && y != -1) { return z; } return x == -1 ? y : x; } // Utility function to check if nodes // are on same path or not function samePathUtil(mtrx, vrtx, v1, v2, i) { let ans = -1; // Condition to check // if any vertex // is equal to given two // vertex or not if (i == v1 || i == v2) return i; for(let j = 0; j < vrtx; j++) { // Check if the current // position has 1 if (mtrx[i][j] == 1) { // Recursive call ans = filter(ans, samePathUtil( mtrx, vrtx, v1, v2, j), i); } } // Return LCA return ans; } // Function to check if nodes // lies on same path or not function isVertexAtSamePath(mtrx, vrtx, v1, v2, i) { let lca = samePathUtil(mtrx, vrtx, v1 - 1, v2 - 1, i); if (lca == v1 - 1 || lca == v2 - 1) return true; return false; } let vrtx = 7; let mtrx = [ [ 0, 1, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0 ] ]; let v1 = 1, v2 = 5; if (isVertexAtSamePath(mtrx, vrtx, v1, v2, 0)) document.write("Yes"); else document.write("No"); // This code is contributed by mukesh07. </script> |
Output:
Yes
Time Complexity: O(N2) where N is the number of vertices in the graph.
Auxiliary Space: O(1)
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