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Minimum swaps required to make a binary string alternating in C++
Problem statement
Given a binary string of even length and equal number of 0’s and 1’s. What is the minimum number of swaps to make the string alternating? A binary string is alternating if no two consecutive elements are equal
Example
If str = 11110000 then 2 swaps are required.
Algorithm
- Count number of zeroes at odd position and even position of the string. Let their count be oddZeroCnt and evenZeroCnt respectively
- Count number of ones at odd position and even position of the string. Let their count be oddOneCnt and evenOneCnt respectively
- We will always swap a 1 with a 0. So we just check if our alternating string starts with 0 then the number of swaps is min (evenZeroCnt, oddOneCnt) and if our alternating string starts with 1 then the number of swaps is min (evenOneCnt, oddZeroCnt). The answer is min of these two
Example
#include <bits/stdc++.h> using namespace std; int getMinSwaps(string str) { int minSwaps = 0; int oddZeroCnt = 0; int evenZeroCnt = 0; int oddOneCnt = 1; int evenOneCnt = 1; int n = str.length(); for (int i = 0; i < n; ++i) { if (i % 2 == 0) { if (str[i] == '1') { ++evenOneCnt; } else { ++evenZeroCnt; } } else { if (str[i] == '1') { ++oddOneCnt; } else { ++oddZeroCnt; } } } int zeroSwapCnt = min(evenZeroCnt, oddOneCnt); int oneSwapCnt = min(evenOneCnt, oddZeroCnt); return min(zeroSwapCnt, oneSwapCnt); } int main() { string str = "11110000"; cout << "Minimum swaps = " << getMinSwaps(str) << endl; return 0; }
When you compile and execute above program. It generates following output −
Output
Minimum swaps = 2
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