Given a tree, and the weights of all the nodes and an integer x, the task is to find a node i such that weight[i] xor x is minimum.
Examples:
Input:
x = 15
Output: 3
Node 1: 5 xor 15 = 10
Node 2: 10 xor 15 = 5
Node 3: 11 xor 15 = 4
Node 4: 8 xor 15 = 7
Node 5: 6 xor 15 = 9
Approach: Perform dfs on the tree and keep track of the node whose weighted xor with x gives the minimum value.
Below is the implementation of above approach:
C++
// C++ implementation of the approach#include <bits/stdc++.h>using namespace std;int minimum = INT_MAX, x, ans;vector<int> graph[100];vector<int> weight(100);// Function to perform dfs to find// the minimum xored valuevoid dfs(int node, int parent){ // If current value is less than // the current minimum if (minimum > (weight[node] ^ x)) { minimum = weight[node] ^ x; ans = node; } for (int to : graph[node]) { if (to == parent) continue; dfs(to, node); }}// Driver codeint main(){ x = 15; // Weights of the node weight[1] = 5; weight[2] = 10; weight[3] = 11; weight[4] = 8; weight[5] = 6; // Edges of the tree graph[1].push_back(2); graph[2].push_back(3); graph[2].push_back(4); graph[1].push_back(5); dfs(1, 1); cout << ans; return 0;} |
Java
// Java implementation of the approachimport java.util.*;import java.lang.*;class GFG { static int minimum = Integer.MAX_VALUE, x, ans; @SuppressWarnings("unchecked") static Vector<Integer>[] graph = new Vector[100]; static int[] weight = new int[100]; // This block is executed even before main() function // This is necessary otherwise this program will // throw "NullPointerException" static { for (int i = 0; i < 100; i++) graph[i] = new Vector<>(); } // Function to perform dfs to find // the minimum xored value static void dfs(int node, int parent) { // If current value is less than // the current minimum if (minimum > (weight[node] ^ x)) { minimum = weight[node] ^ x; ans = node; } for (int to : graph[node]) { if (to == parent) continue; dfs(to, node); } } // Driver Code public static void main(String[] args) { x = 15; // Weights of the node weight[1] = 5; weight[2] = 10; weight[3] = 11; weight[4] = 8; weight[5] = 6; // Edges of the tree graph[1].add(2); graph[2].add(3); graph[2].add(4); graph[1].add(5); dfs(1, 1); System.out.println(ans); }}// This code is contributed by SHUBHAMSINGH10 |
C#
// C# implementation of the approach using System; using System.Collections.Generic; class GFG { static int minimum = int.MaxValue, x, ans; static List<List<int>> graph = new List<List<int>>(); static List<int> weight = new List<int>(); // Function to perform dfs to find // the minimum value static void dfs(int node, int parent) { // If current value is less than // the current minimum if (minimum > (weight[node] ^ x)) { minimum = weight[node] ^ x; ans = node; } for (int i = 0; i < graph[node].Count; i++) { if (graph[node][i] == parent) continue; dfs(graph[node][i], node); } } // Driver code public static void Main() { x = 15; // Weights of the node weight.Add(0); weight.Add(5); weight.Add(10); weight.Add(11);; weight.Add(8); weight.Add(6); for(int i = 0; i < 100; i++) graph.Add(new List<int>()); // Edges of the tree graph[1].Add(2); graph[2].Add(3); graph[2].Add(4); graph[1].Add(5); dfs(1, 1); Console.Write( ans); } } // This code is contributed by SHUBHAMSINGH10 |
Python3
# Python implementation of the approachfrom sys import maxsizeminimum, x, ans = maxsize, None, Nonegraph = [[] for i in range(100)]weight = [0] * 100# Function to perform dfs to find# the minimum xored valuedef dfs(node, parent): global x, ans, graph, weight, minimum # If current value is less than # the current minimum if minimum > weight[node] ^ x: minimum = weight[node] ^ x ans = node for to in graph[node]: if to == parent: continue dfs(to, node)# Driver Codeif __name__ == "__main__": x = 15 # Weights of the node weight[1] = 5 weight[2] = 10 weight[3] = 11 weight[4] = 8 weight[5] = 6 # Edges of the tree graph[1].append(2) graph[2].append(3) graph[2].append(4) graph[1].append(5) dfs(1, 1) print(ans)# This code is contributed by# sanjeev2552 |
Javascript
<script>// Javascript implementation of the approach let minimum = Number.MAX_VALUE, x, ans; let graph = new Array(100); let weight = new Array(100); for(let i = 0; i < 100; i++) { graph[i] = []; weight[i] = 0; } // Function to perform dfs to find // the minimum xored value function dfs(node, parent) { // If current value is less than // the current minimum if (minimum > (weight[node] ^ x)) { minimum = weight[node] ^ x; ans = node; } for (let to = 0; to < graph[node].length; to++) { if (graph[node][to] == parent) continue; dfs(graph[node][to], node); } } // Driver Code x = 15; // Weights of the node weight[1] = 5; weight[2] = 10; weight[3] = 11; weight[4] = 8; weight[5] = 6; // Edges of the tree graph[1].push(2); graph[2].push(3); graph[2].push(4); graph[1].push(5); dfs(1, 1); document.write(ans); // This code is contributed by unknown2108</script> |
Output:
3
Time Complexity: O(N) where N is the number of nodes in the graph.
Space Complexity: O(N)
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