# Minimize String length by deleting Substring of same character when K flips are allowed

Given a binary string consisting of **‘0’** and **‘1’ **only and an integer **K**, the task is to minimize the string as far as possible by deleting a substring of the same character, when you can flip at most **K** characters.

**Examples:**

Input:S = “0110”, K = 2Output:0Explanation:We can make two ‘0’ s into ‘1’ or vice versa.

So we can delete all the four characters and

the remaining size of the string is 0

Input:S = “111”, K = 1Output:0

**Approach: **To solve the problem follow the below idea:

As we have to minimize the string by deleting characters so we have to delete the maximum length of substring consisting of equal letters. So, we can understand the minimum length will range from 1 to the size of the string(let’s say n).

Now if we apply binary search on this range of length and check for a shorter length until it is out of range, we can get the answer.

Follow the steps to solve the problem:

- At first, for the binary search, we will define
**our range from Low = 1 to High = n(size of string).**- Then after finding the mid we will keep passing the mid to check function to get one of the possible answers and
**keep incrementing the low to mid+1**as we want the**maximum length** - In the check function, first, we will create an
**array of sizes to 2 to count ‘0’ and ‘1’.** - Then,
**we will count ‘0’ and ‘1’**and store in that count array, and if the**minimum of the count**of both elements is less than K that means we can change those characters to the same character to**increase the goodness**of the string. - After that will
**slide the window by mid(limit) size**and**decrease the count of the first element**of the window as the window is not there anymore and**increase the count of the new element**as it is the new and last element of the window - Now, we will check again the minimum of the count of ‘0’ s and ‘1’s, if it is
**less than or equals to K**, then return true otherwise false - We will store every possible answer to the
**ans variable**and when**low ≥ high**the loop will terminate and we have our maximum possible**length**for deletion stored in**ans**variable.

- Then after finding the mid we will keep passing the mid to check function to get one of the possible answers and
- Now we will
**subtract**the**maximum length**from the size of the array to get the size of our minimized string

Below is the implementation for the above approach.

## C++

`// C++ code for the above approach:` `#include <bits/stdc++.h>` `using` `namespace` `std;` `bool` `check(string s, ` `int` `K, ` `int` `limit)` `{` ` ` ` ` `// Count array for counting` ` ` `// '0's and '1's` ` ` `int` `count[2] = { 0 };` ` ` ` ` `// Counting '0' and '1's in` ` ` `// window size` ` ` `for` `(` `int` `i = 0; i < limit; i++) {` ` ` `count[s[i] - ` `'0'` `]++;` ` ` `}` ` ` ` ` `// If the minimum of '0's count and` ` ` `// '1's count less than or equals to` ` ` `// k it is one of the possible` ` ` `// answer, returnn true` ` ` `if` `(K >= min(count[0], count[1]))` ` ` `return` `true` `;` ` ` ` ` `// Sliding the window` ` ` `for` `(` `int` `i = 0; i + limit < s.size(); i++) {` ` ` ` ` `// Decrementing the count of first` ` ` `// element as window is slided` ` ` `count[s[i] - ` `'0'` `]--;` ` ` ` ` `// Incrementing the count of new` ` ` `// element as this is the last` ` ` `// element of new window` ` ` `count[s[i + limit] - ` `'0'` `]++;` ` ` ` ` `// Checking the minimum count of` ` ` `// '0's and '1's because it is` ` ` `// the new window` ` ` `if` `(K >= min(count[0], count[1]))` ` ` `return` `true` `;` ` ` `}` ` ` ` ` `// If the above conditions are not` ` ` `// fullfilled return false` ` ` `return` `false` `;` `}` ` ` `void` `solve(string s, ` `int` `n, ` `int` `K)` `{` ` ` ` ` `// Defining range 1 to n` ` ` `int` `Low = 1, High = n;` ` ` ` ` `// Initializing ans to 0` ` ` `int` `ans = 0;` ` ` `while` `(Low <= High) {` ` ` ` ` `// Calculating mid` ` ` `int` `mid = Low + (High - Low) / 2;` ` ` ` ` `// Passing the mid to` ` ` `// check function` ` ` `if` `(check(s, K, mid)) {` ` ` ` ` `// We got one of the possible` ` ` `// answers so storing it in` ` ` `// ans variable` ` ` `ans = max(ans, mid);` ` ` ` ` `// Also incrementing the low` ` ` `// to check whether there is` ` ` `// any maximum length string` ` ` `// with maximum goodness` ` ` `// present or not` ` ` `Low = mid + 1;` ` ` `}` ` ` `else` `{` ` ` ` ` `// Decrementing the high` ` ` `High = mid - 1;` ` ` `}` ` ` `}` ` ` ` ` `// Printing the ans` ` ` `cout << ` `"Minimum length after deletion is: "` `;` ` ` `int` `res = n - ans;` ` ` `cout << res;` `}` ` ` `// Driver Code` `int` `main()` `{` ` ` ` ` `// Given input` ` ` `string s = ` `"0110"` `;` ` ` `int` `K = 2;` ` ` `int` `n = s.size();` ` ` ` ` `// Function call` ` ` `solve(s, n, K);` ` ` `return` `0;` `}` |

**Output**

Minimum length after deletion is: 0

**Time Complexity: **O(N * logN), as the size of the string, is N and we are applying binary search that has logN complexity. So complexity O(N*logN).**Auxiliary Space: **O(1)