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Maximum difference of zeros and ones in binary string in C++
Given the task is to find a sub-string from a given binary string and then the maximum difference between the number of zeroes and the ones.
Let’s now understand what we have to do using an example −
Input
str = “100100110”
Output
2
Explanation
In the sub-array from the position 1 to 5 (“00100”), the difference between the zeros and ones = 4 – 1 = 3 which is the maximum that can be found.
Input
str = “00000”
Output
5
Approach used in the below program as follows
In main() function create a string str to store the binary string. Also initialize a variable int size to store the size of string and pass both of them into the Max() function.
In Max() function first check if all the elements are 1 by calling the One() function.
Create One() function of type bool and inside it create a variable int O = 0.
Loop from i = 0 till i< str.size() and if str[i] == 1 then add 1 to variable O.
Outside the loop, check if(O == size). If so, then return true.
Back in the Max() function if the One() function returned true then, return -1 as the answer.
Else proceed to find length. Initialize an array int a[100] = { 0 }.
Loop from i = 0 till i< size and put a[i] = (str[i] == '0' ? 1 : -1) and check every element of str this way.
Outside the loop, initialize another array int arr[100][3] and replace all its elements by -1 using memset(arr, -1, sizeof arr) and finally call Length(a, str, size, 0, 0, arr)
In Length() function, first check if (i >= size), if so, then it means the string is over and return 0.
Then check if (arr[i][s] != -1). If so, then it means the state has been already calculated and return arr[i][s].
Then check if(s == 0). If so, then return arr[i][s] = max(a[i] + Length(a, str, size, i + 1, 1, arr), Length(a, str, size, i + 1, 0, arr));
Else return arr[i][s] = max(a[i] + Length(a, str, size, i + 1, 1, arr), 0);
Example
#include <bits/stdc++.h>
using namespace std;
bool One(string str, int size){
int O = 0;
for (int i = 0; i < str.size(); i++)
O += (str[i] == '1');
return (O == size);
}
int Length(int a[], string str, int size,
int i, int s, int arr[][3]){
// If string is over.
if (i >= size)
return 0;
// If the already calculated.
if (arr[i][s] != -1)
return arr[i][s];
if (s == 0)
return arr[i][s] = max(a[i] +
Length(a, str, size, i + 1, 1, arr),
Length(a, str, size, i + 1, 0, arr));
else
return arr[i][s] = max(a[i] +
Length(a, str, size, i + 1, 1, arr), 0);
}
int Max(string str, int size){
// Checking if all elements are 1
if (One(str, size))
return -1;
// Finding length
int a[100] = { 0 };
for (int i = 0; i < size; i++)
a[i] = (str[i] == '0' ? 1 : -1);
int arr[100][3];
memset(arr, -1, sizeof arr);
return Length(a, str, size, 0, 0, arr);
}
// main function
int main(){
string str = "100100110";
int size = 9;
cout << Max(str, size);
return 0;
}Output
3
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