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Count subarrays with equal number of 1’s and 0’s in C++
We are given an array arr[] containing 0’s and 1’s only. The goal is to count all subarrays of arr[] such that occurrences of 0s and 1s is equal in all. If the array is [1,0,0] .Subarray will be [1,0] only.
Let us understand with examples.
Input − arr[] = { 0, 0, 1, 1, 1, 0 };
Output − Count of subarrays with an equal number of 1’s and 0’s are − 4
Explanation − Subaarays will be −
arr[0 to 3] = [0,0,1,1], arr[1 to 2] = [0,1], arr[4 to 5] =[1,0], Arr[0 to 5] =[0,0,1,1,1,0].
Input − arr[] = { 0, 1, 1, 1, 1 };
Output − Count of subarrays with equal number of 1’s and 0’s are − 1
Explanation − Subaarays will be − arr[0 to 1] = [0,1]
The approach used in the below program is as follows
We will traverse the array using two for loops to generate all subarrays possible. From i=0 to i<=size-1 and j=i to j<=size-1. Subarrays formed will be between arr[i] to arr[j]. Count frequency of 0 and 1 in each subarray. If equal then increment the count.
Take an array arr[] of numbers.
Function sub_zeroes_ones(int arr[], int size) takes the array and returns the count of subarrays with equal no. of 0’s and 1’s.
Take the initial count as 0.
We will traverse the array using two for loops from i=0 to i<=size-1 and j=0 to j<=size-1.
Take two variables total_0, total_1 as 0 for the number of 0’s and 1’s in subarray arr[i] to arr[j].
Compare arr[j] with 0 and 1. If arr[j] is 0 or 1 then increment respective count ( total_0 or total_1).
If total_0==total_1. Increment count. ( the subarray has the same number of 0’s and 1’s as elements).
At the end of both loops, return count as result.
Example
#include <bits/stdc++.h>
using namespace std;
int sub_zeroes_ones(int arr[], int size){
int count = 0;
for (int i = 0; i <= size - 1; i++){
int total_0 = 0;
int total_1 = 0;
for (int j = i; j <= size - 1; j++){
if (arr[j] == 0){
total_0++;
}
else if (arr[j] == 1){
total_1++;
}
if(total_0 == total_1){
count++;
}
}
}
return count;
}
int main(){
int arr[] = {0, 1, 1, 0, 0};
int size = sizeof(arr)/sizeof(arr[0]);
cout<<"Count of subarrays with equal number of 1’s and 0’s are: "<<sub_zeroes_ones(arr, size);
}Output
If we run the above code it will generate the following output −
Count of subarrays with equal number of 1’s and 0’s are: 4
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