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Numbers that are Bitwise AND of At Least One Non-Empty Sub-Array using C++
To solve a problem where we are given an array, and we need to find all possible integers which are bitwise AND of at least one not empty subarray, for example −
Input : nums[ ] = { 3, 5, 1, 2, 8 }
Output : { 2, 5, 0, 3, 8, 1 }
Explanation:
2 is the bitwise AND of subarray {2},
5 is the bitwise AND of subarray {5},
0 is the bitwise AND of subarray {1, 2}, {2, 8} and {1, 2, 8},
3 is the bitwise AND of subarray {3},
8 is the bitwise AND of subarray {8},
1 is the bitwise AND of subarray {1}, {3, 5} and {3, 5, 1}.
Input : nums[ ] = { 2, 6, 3, 8, 1 }
Output: { 1, 8, 3, 6, 2, 0 }Approach to Find the Solution
A Simple Approach that can be applied is,
Find all the possible non-empty subarrays.
While traversing through the array, calculate the bitwise AND of each element in the subarray.
To avoid duplicate values, store all the results in a set.
Example
#include <bits/stdc++.h>
using namespace std;
int main(){
int arr[] ={ 2, 6, 3, 8, 1 };
int n = sizeof(arr) / sizeof(arr[0]);
// Declaring set to store result of each AND operation.
unordered_set<int> result;
int val;
// nested loops to traverse through all the possible non empty subarrays.
for (int i = 0; i < n; ++i){
for (int j = i, val = INT_MAX; j < n; ++j){
val = val & arr[j];
// storing result of AND operation
result.insert(val);
}
}
cout << "All possible numbers are: ";
// printing all the values of set.
for (auto i = result.begin(); i != result.end();i++)
cout << *i << " ";
return 0;
}Output
All possible numbers are: 1 8 3 6 0 2
Explanation of the Above Code
Declaring set to store all the results of AND operation.
Initializing the ‘val’ variable with INT_MAX because we need to do AND operation with all the bits set to 1.
Inside loop to go through all possible subarrays from the ith index.
Calculating AND operation of each element with each other and with themselves and storing in the result set.
Printing all the values of the result set.
Conclusion
In this tutorial, We discussed a simple approach to solve this problem, i.e., calculating AND operation in every possible subarray. We also discussed the C++ program to solve this problem. Also, you can write this code in any other language like Java, C, Python, etc. We hope you find this tutorial helpful.
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