# Minimum characters required to be removed to sort binary string in ascending order

Given a binary string str, the task is to remove the minimum number of characters from the given binary string such that the characters in the remaining string form a sorted order.

Examples:

Input: str = “1000101”
Output: 2
Explanation:
Removal of the first two occurrences of ‘1’ modifies the string to “00001”, which is a sorted order.
Therefore, the minimum count of characters to be removed is 2.

Input: str = “001111”
Output: 0
Explanation:
The string is already sorted.
Therefore, the minimum count of character to be removed is 0.

Approach: The idea is to count the number of 1s before the last occurrence of 0 and the number of 0s before the first occurrence of 1. The minimum of the two counts is the required number of characters to be removed. Below are the steps:

1. Traverse the string str and find the position of the first occurrence of 1 and the last occurrence of 0.
2. Print 0 if the str has only one type of character.
3. Now, count the number of 1 is present prior to the last occurrence of 0 and store in a variable, say cnt1.
4. Now, count the number of 0s present after the first occurrence of 1 in a variable, say cnt0.
5. Print the minimum of cnt0 and cnt1 as the minimum count of character required to be removed.

Below is the implementation of the above approach:

 `// C++ program for the above approach ` `#include ` `using` `namespace` `std;`   `// Function to find the minimum count ` `// of characters to be removed to make ` `// the string sorted in ascending order ` `int` `minDeletion(string str) ` `{ ` `    `  `    ``// Length of given string ` `    ``int` `n = str.length(); `   `    ``// Stores the first ` `    ``// occurrence of '1' ` `    ``int` `firstIdx1 = -1; `   `    ``// Stores the last ` `    ``// occurrence of '0' ` `    ``int` `lastIdx0 = -1; `   `    ``// Traverse the string to find ` `    ``// the first occurrence of '1' ` `    ``for``(``int` `i = 0; i < n; i++)` `    ``{ ` `        ``if` `(str[i] == ``'1'``)` `        ``{ ` `            ``firstIdx1 = i; ` `            ``break``; ` `        ``} ` `    ``} `   `    ``// Traverse the string to find ` `    ``// the last occurrence of '0' ` `    ``for``(``int` `i = n - 1; i >= 0; i--) ` `    ``{ ` `        ``if` `(str[i] == ``'0'``) ` `        ``{ ` `            ``lastIdx0 = i; ` `            ``break``; ` `        ``} ` `    ``} `   `    ``// Return 0 if the str have ` `    ``// only one type of character ` `    ``if` `(firstIdx1 == -1 || ` `         ``lastIdx0 == -1) ` `        ``return` `0; `   `    ``// Initialize count1 and count0 to ` `    ``// count '1's before lastIdx0 ` `    ``// and '0's after firstIdx1 ` `    ``int` `count1 = 0, count0 = 0; `   `    ``// Traverse the string to count0 ` `    ``for``(``int` `i = 0; i < lastIdx0; i++)` `    ``{ ` `        ``if` `(str[i] == ``'1'``)` `        ``{ ` `            ``count1++; ` `        ``} ` `    ``} `   `    ``// Traverse the string to count1 ` `    ``for``(``int` `i = firstIdx1 + 1; i < n; i++) ` `    ``{ ` `        ``if` `(str[i] == ``'1'``)` `        ``{ ` `            ``count0++; ` `        ``} ` `    ``} `   `    ``// Return the minimum of ` `    ``// count0 and count1 ` `    ``return` `min(count0, count1); ` `}` `    `  `// Driver code` `int` `main() ` `{` `    `  `    ``// Given string str ` `    ``string str = ``"1000101"``;` `    `  `    ``// Function call` `    ``cout << minDeletion(str);` `    `  `    ``return` `0;` `}`   `// This code is contributed by bikram2001jha`

 `// Java program for the above approach`   `import` `java.util.*;` `import` `java.lang.*;`   `class` `GFG {`   `    ``// Function to find the minimum count` `    ``// of characters to be removed to make` `    ``// the string sorted in ascending order` `    ``static` `int` `minDeletion(String str)` `    ``{`   `        ``// Length of given string` `        ``int` `n = str.length();`   `        ``// Stores the first` `        ``// occurrence of '1'` `        ``int` `firstIdx1 = -``1``;`   `        ``// Stores the last` `        ``// occurrence of '0'` `        ``int` `lastIdx0 = -``1``;`   `        ``// Traverse the string to find` `        ``// the first occurrence of '1'` `        ``for` `(``int` `i = ``0``; i < n; i++) {`   `            ``if` `(str.charAt(i) == ``'1'``) {`   `                ``firstIdx1 = i;` `                ``break``;` `            ``}` `        ``}`   `        ``// Traverse the string to find` `        ``// the last occurrence of '0'` `        ``for` `(``int` `i = n - ``1``; i >= ``0``; i--) {`   `            ``if` `(str.charAt(i) == ``'0'``) {`   `                ``lastIdx0 = i;` `                ``break``;` `            ``}` `        ``}`   `        ``// Return 0 if the str have` `        ``// only one type of character` `        ``if` `(firstIdx1 == -``1` `            ``|| lastIdx0 == -``1``)` `            ``return` `0``;`   `        ``// Initialize count1 and count0 to` `        ``// count '1's before lastIdx0` `        ``// and '0's after firstIdx1` `        ``int` `count1 = ``0``, count0 = ``0``;`   `        ``// Traverse the string to count0` `        ``for` `(``int` `i = ``0``; i < lastIdx0; i++) {`   `            ``if` `(str.charAt(i) == ``'1'``) {`   `                ``count1++;` `            ``}` `        ``}`   `        ``// Traverse the string to count1` `        ``for` `(``int` `i = firstIdx1 + ``1``; i < n; i++) {`   `            ``if` `(str.charAt(i) == ``'1'``) {`   `                ``count0++;` `            ``}` `        ``}`   `        ``// Return the minimum of` `        ``// count0 and count1` `        ``return` `Math.min(count0, count1);` `    ``}`   `    ``// Driver Code` `    ``public` `static` `void` `main(String[] args)` `    ``{` `        ``// Given string str` `        ``String str = ``"1000101"``;`   `        ``// Function Call` `        ``System.out.println(minDeletion(str));` `    ``}` `}`

 `# Python3 program for the above approach `   `# Function to find the minimum count ` `# of characters to be removed to make ` `# the string sorted in ascending order ` `def` `minDeletion(s):` `    `  `    ``# Length of given string ` `    ``n ``=` `len``(s)`   `    ``# Stores the first ` `    ``# occurrence of '1' ` `    ``firstIdx1 ``=` `-``1`   `    ``# Stores the last ` `    ``# occurrence of '0' ` `    ``lastIdx0 ``=` `-``1`   `    ``# Traverse the string to find ` `    ``# the first occurrence of '1' ` `    ``for` `i ``in` `range``(``0``, n):` `        ``if` `(``str``[i] ``=``=` `'1'``):` `            ``firstIdx1 ``=` `i` `            ``break`   `    ``# Traverse the string to find ` `    ``# the last occurrence of '0' ` `    ``for` `i ``in` `range``(n ``-` `1``, ``-``1``, ``-``1``):` `        ``if` `(``str``[i] ``=``=` `'0'``): ` `            ``lastIdx0 ``=` `i` `            ``break`   `    ``# Return 0 if the str have ` `    ``# only one type of character ` `    ``if` `(firstIdx1 ``=``=` `-``1` `or` `         ``lastIdx0 ``=``=` `-``1``):` `        ``return` `0`   `    ``# Initialize count1 and count0 to ` `    ``# count '1's before lastIdx0 ` `    ``# and '0's after firstIdx1 ` `    ``count1 ``=` `0` `    ``count0 ``=` `0`   `    ``# Traverse the string to count0 ` `    ``for` `i ``in` `range``(``0``, lastIdx0):` `        ``if` `(``str``[i] ``=``=` `'1'``): ` `            ``count1 ``+``=` `1`   `    ``# Traverse the string to count1 ` `    ``for` `i ``in` `range``(firstIdx1 ``+` `1``, n):` `        ``if` `(``str``[i] ``=``=` `'1'``):` `            ``count0 ``+``=` `1`   `    ``# Return the minimum of ` `    ``# count0 and count1 ` `    ``return` `min``(count0, count1)` `    `  `# Driver code`   `# Given string str ` `str` `=` `"1000101"` `    `  `# Function call ` `print``(minDeletion(``str``))`   `# This code is contributed by Stream_Cipher`

 `// C# program for the above approach ` `using` `System.Collections.Generic; ` `using` `System; `   `class` `GFG{ `   `// Function to find the minimum count ` `// of characters to be removed to make ` `// the string sorted in ascending order ` `static` `int` `minDeletion(``string` `str) ` `{ `   `    ``// Length of given string ` `    ``int` `n = str.Length; `   `    ``// Stores the first ` `    ``// occurrence of '1' ` `    ``int` `firstIdx1 = -1; `   `    ``// Stores the last ` `    ``// occurrence of '0' ` `    ``int` `lastIdx0 = -1; `   `    ``// Traverse the string to find ` `    ``// the first occurrence of '1' ` `    ``for``(``int` `i = 0; i < n; i++)` `    ``{ ` `        ``if` `(str[i] == ``'1'``)` `        ``{ ` `            ``firstIdx1 = i; ` `            ``break``; ` `        ``} ` `    ``} `   `    ``// Traverse the string to find ` `    ``// the last occurrence of '0' ` `    ``for``(``int` `i = n - 1; i >= 0; i--)` `    ``{ ` `        ``if` `(str[i] == ``'0'``)` `        ``{ ` `            ``lastIdx0 = i; ` `            ``break``; ` `        ``} ` `    ``} `   `    ``// Return 0 if the str have ` `    ``// only one type of character ` `    ``if` `(firstIdx1 == -1 || ` `         ``lastIdx0 == -1) ` `        ``return` `0; `   `    ``// Initialize count1 and count0 to ` `    ``// count '1's before lastIdx0 ` `    ``// and '0's after firstIdx1 ` `    ``int` `count1 = 0, count0 = 0; `   `    ``// Traverse the string to count0 ` `    ``for``(``int` `i = 0; i < lastIdx0; i++)` `    ``{ ` `        ``if` `(str[i] == ``'1'``)` `        ``{ ` `            ``count1++; ` `        ``} ` `    ``} `   `    ``// Traverse the string to count1 ` `    ``for``(``int` `i = firstIdx1 + 1; i < n; i++)` `    ``{ ` `        ``if` `(str[i] == ``'1'``) ` `        ``{ ` `            ``count0++; ` `        ``} ` `    ``} `   `    ``// Return the minimum of ` `    ``// count0 and count1 ` `    ``return` `Math.Min(count0, count1); ` `} `   `// Driver Code ` `public` `static` `void` `Main() ` `{ ` `    `  `    ``// Given string str ` `    ``string` `str = ``"1000101"``; `   `    ``// Function call ` `    ``Console.WriteLine(minDeletion(str)); ` `} ` `} `   `// This code is contributed by Stream_Cipher`

Output
`2`

Time Complexity: O(N)
Auxiliary Space: O(1)

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