Number of subsets with a given OR value
source link: https://www.geeksforgeeks.org/number-of-subsets-with-a-given-or-value/
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Given an array arr[] of length N, the task is to find the number of subsets with a given OR value M.
Examples:
Input: arr[] = {2, 3, 2} M = 3
Output: 4
All possible subsets and there OR values are:
{2} = 2
{3} = 3
{2} = 2
{2, 3} = 2 | 3 = 3
{3, 2} = 3 | 2 = 3
{2, 2} = 2 | 2 = 2
{2, 3, 2} = 2 | 3 | 2 = 3Input: arr[] = {1, 3, 2, 2}, M = 5
Output: 0
Approach: A simple approach is to solve the problem by generating all the possible subsets and then by counting the number of subsets with the given OR value. However, for smaller values of array elements, it can be solved using dynamic programming.
Let’s look at the recurrence relation first.
dp[i][curr_or] = dp[i + 1][curr_or] + dp[i + 1][curr_or | arr[i]]
The above recurrence relation can be defined as the number of subsets of sub-array arr[i…N-1] such that ORing them with curr_or will yield the required OR value.
The recurrence relation is justified as there are only paths. Either, take the current element and OR it with curr_or or ignore it and move forward.
Below is the implementation of the above approach:
- Python3
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// C++ implementation of the approach#include <bits/stdc++.h>using namespace std;#define maxN 20#define maxM 64// To store states of DPint dp[maxN][maxM];bool v[maxN][maxM];// Function to return the required countint findCnt(int* arr, int i, int curr, int n, int m){// Base caseif (i == n) {return (curr == m);}// If the state has been solved before// return the value of the stateif (v[i][curr])return dp[i][curr];// Setting the state as solvedv[i][curr] = 1;// Recurrence relationdp[i][curr]= findCnt(arr, i + 1, curr, n, m)+ findCnt(arr, i + 1, (curr | arr[i]), n, m);return dp[i][curr];}// Driver codeint main(){int arr[] = { 2, 3, 2 };int n = sizeof(arr) / sizeof(int);int m = 3;cout << findCnt(arr, 0, 0, n, m);return 0;}4
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