Maximize sum of Bitwise AND of same-indexed elements of a permutation of first N natural numbers and a given array
Given an array arr[] consisting of N positive integers, the task is to find the maximum sum of Bitwise AND of same-indexed elements of permutation of the first N natural numbers and the array arr[].
Examples:
Input: arr[] = {4, 2, 3, 6}
Output: 5
Explanation: Consider the permutation {1, 0, 3, 2}. Sum of Bitwise AND of the above permutation and the given array = 1 & 4 + 0 & 2 + 3 & 3 + 2 & 6 = 0 + 0 + 3 + 2 = 5, which is maximum among all permutations.Input: arr[] = {3, 4, 1, 0, 5}
Output: 8
Approach: The idea to solve the given problem is to generate all permutations of the first N natural numbers and calculate the sum of the Bitwise AND of the generated permutation with the array arr[]. After checking for each permutation, print the maximum value of the sum of Bitwise AND obtained.
Below is the implementation of the above approach:
C++
// C++ program for the above approach#include <bits/stdc++.h>using namespace std;// Function to calculate sum of// Bitwise AND of same indexed// elements of the arrays p[] and arr[]int calcScore(vector<int> p, int arr[], int N){ // Stores the resultant sum int ans = 0; // Traverse the array for (int i = 0; i < N; i++) { // Update sum of Bitwise AND ans += (p[i] & arr[i]); } // Return the value obtained return ans;}// Function to generate all permutations// and calculate the maximum sum of Bitwise// AND of same indexed elements present in// any permutation and an array arr[]int getMaxUtil(vector<int> p, int arr[], int ans, bool chosen[], int N){ // If the size of the array is N if (p.size() == N) { // Calculate cost of permutation ans = max(ans, calcScore(p, arr, N)); return ans; } // Generate all permutations for (int i = 0; i < N; i++) { if (chosen[i]) { continue; } // Update chosen[i] chosen[i] = true; // Update the permutation p[] p.push_back(i); // Generate remaining permutations ans = getMaxUtil(p, arr, ans, chosen, N); chosen[i] = false; p.pop_back(); } // Return the resultant sum return ans;}// Function to find the maximum sum of Bitwise// AND of same indexed elements in a permutation// of first N natural numbers and arr[]void getMax(int arr[], int N){ // Stores the resultant maximum sum int ans = 0; bool chosen[N]; for (int i = 0; i < N; i++) chosen[i] = false; // Stores the generated permutation P vector<int> p; // Function call to store result int res = getMaxUtil(p, arr, ans, chosen, N); // Print the result cout << res;}// Driven Programint main(){ int arr[] = { 4, 2, 3, 6 }; int N = sizeof(arr) / sizeof(arr[0]); // Function call getMax(arr, N); return 0;}// This code is contributed by Kingash. |
Java
// Java program for the above approachimport java.io.*;import java.lang.*;import java.util.*;class GFG { // Function to calculate sum of // Bitwise AND of same indexed // elements of the arrays p[] and arr[] static int calcScore(ArrayList<Integer> p, int arr[]) { // Stores the resultant sum int ans = 0; // Traverse the array for (int i = 0; i < arr.length; i++) { // Update sum of Bitwise AND ans += (p.get(i) & arr[i]); } // Return the value obtained return ans; } // Function to generate all permutations // and calculate the maximum sum of Bitwise // AND of same indexed elements present in // any permutation and an array arr[] static int getMaxUtil(ArrayList<Integer> p, int arr[], int ans, boolean chosen[], int N) { // If the size of the array is N if (p.size() == N) { // Calculate cost of permutation ans = Math.max(ans, calcScore(p, arr)); return ans; } // Generate all permutations for (int i = 0; i < N; i++) { if (chosen[i]) { continue; } // Update chosen[i] chosen[i] = true; // Update the permutation p[] p.add(i); // Generate remaining permutations ans = getMaxUtil(p, arr, ans, chosen, N); chosen[i] = false; p.remove(p.size() - 1); } // Return the resultant sum return ans; } // Function to find the maximum sum of Bitwise // AND of same indexed elements in a permutation // of first N natural numbers and arr[] static void getMax(int arr[], int N) { // Stores the resultant maximum sum int ans = 0; boolean chosen[] = new boolean[N]; // Stores the generated permutation P ArrayList<Integer> p = new ArrayList<>(); // Function call to store result int res = getMaxUtil(p, arr, ans, chosen, N); // Print the result System.out.println(res); } // Driver Code public static void main(String[] args) { int arr[] = { 4, 2, 3, 6 }; int N = arr.length; // Function Call getMax(arr, N); }}// This code is contributed by Kingash. |
Python3
# Python3 program for the above approach# Function to calculate sum of# Bitwise AND of same indexed# elements of the arrays p[] and arr[]def calcScore(p, arr): # Stores the resultant sum ans = 0 # Traverse the array for i in range(len(arr)): # Update sum of Bitwise AND ans += (p[i] & arr[i]) # Return the value obtained return ans# Function to generate all permutations# and calculate the maximum sum of Bitwise# AND of same indexed elements present in# any permutation and an array arr[]def getMaxUtil(p, arr, ans, chosen, N): # If the size of the array is N if len(p) == N: # Calculate cost of permutation ans = max(ans, calcScore(p, arr)) return ans # Generate all permutations for i in range(N): if chosen[i]: continue # Update chosen[i] chosen[i] = True # Update the permutation p[] p.append(i) # Generate remaining permutations ans = getMaxUtil(p, arr, ans, chosen, N) chosen[i] = False p.pop() # Return the resultant sum return ans# Function to find the maximum sum of Bitwise# AND of same indexed elements in a permutation# of first N natural numbers and arr[]def getMax(arr, N): # Stores the resultant maximum sum ans = 0 chosen = [False for i in range(N)] # Stores the generated permutation P p = [] # Function call to store result res = getMaxUtil(p, arr, ans, chosen, N) # Print the result print(res)# Driver Codeif __name__ == '__main__': # Given array arr = [4, 2, 3, 6] N = len(arr) # Function Call getMax(arr, N) |
C#
// C# program for the above approachusing System;using System.Collections.Generic;class GFG{ // Function to calculate sum of// Bitwise AND of same indexed// elements of the arrays p[] and arr[]static int calcScore(List<int> p, int[] arr){ // Stores the resultant sum int ans = 0; // Traverse the array for(int i = 0; i < arr.Length; i++) { // Update sum of Bitwise AND ans += (p[i] & arr[i]); } // Return the value obtained return ans;}// Function to generate all permutations// and calculate the maximum sum of Bitwise// AND of same indexed elements present in// any permutation and an array arr[]static int getMaxUtil(List<int> p, int[] arr, int ans, bool[] chosen, int N){ // If the size of the array is N if (p.Count == N) { // Calculate cost of permutation ans = Math.Max(ans, calcScore(p, arr)); return ans; } // Generate all permutations for(int i = 0; i < N; i++) { if (chosen[i]) { continue; } // Update chosen[i] chosen[i] = true; // Update the permutation p[] p.Add(i); // Generate remaining permutations ans = getMaxUtil(p, arr, ans, chosen, N); chosen[i] = false; p.Remove(p.Count - 1); } // Return the resultant sum return ans;}// Function to find the maximum sum of Bitwise// AND of same indexed elements in a permutation// of first N natural numbers and arr[]static void getMax(int[] arr, int N){ // Stores the resultant maximum sum int ans = 0; bool[] chosen = new bool[N]; // Stores the generated permutation P List<int> p = new List<int>(); // Function call to store result int res = getMaxUtil(p, arr, ans, chosen, N); // Print the result Console.Write(res);}// Driver Codepublic static void Main(){ int[] arr = { 4, 2, 3, 6 }; int N = arr.Length; // Function Call getMax(arr, N);}}// This code is contributed by sanjoy_62 |
Javascript
<script>// Javascript program for the above approach// Function to calculate sum of// Bitwise AND of same indexed// elements of the arrays p[] and arr[]function calcScore(p, arr, N){ // Stores the resultant sum var ans = 0; // Traverse the array for (var i = 0; i < N; i++) { // Update sum of Bitwise AND ans += (p[i] & arr[i]); } // Return the value obtained return ans;}// Function to generate all permutations// and calculate the maximum sum of Bitwise// AND of same indexed elements present in// any permutation and an array arr[]function getMaxUtil(p, arr, ans, chosen, N){ // If the size of the array is N if (p.length == N) { // Calculate cost of permutation ans = Math.max(ans, calcScore(p, arr, N)); return ans; } // Generate all permutations for (var i = 0; i < N; i++) { if (chosen[i]) { continue; } // Update chosen[i] chosen[i] = true; // Update the permutation p[] p.push(i); // Generate remaining permutations ans = getMaxUtil(p, arr, ans, chosen, N); chosen[i] = false; p.pop(); } // Return the resultant sum return ans;}// Function to find the maximum sum of Bitwise// AND of same indexed elements in a permutation// of first N natural numbers and arr[]function getMax(arr, N){ // Stores the resultant maximum sum var ans = 0; var chosen = Array(N).fill(false); // Stores the generated permutation P var p = []; // Function call to store result var res = getMaxUtil(p, arr, ans, chosen, N); // Print the result document.write( res);}// Driven Programvar arr = [ 4, 2, 3, 6 ];var N = arr.length;// Function callgetMax(arr, N);</script> |
Output:
5
Time Complexity: O(N*N!)
Auxiliary Space: O(N)
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