# Length of smallest substring to be replaced to make frequency of each character as N/3

Given a string **str** of length **N** (divisible by 3) consisting of atmost three distinct characters, the task is to find the length of the smallest substring whose characters can be replaced so that each character occurs exactly **N/3** times.

**Examples:**

Input:str = “ABB”Output:1Explanation:One optimal way is to replace the substring “B” with any character, suppose “C”.

Hence, the resulting is “ABC” having frequency of each character as N/3.

Input:str = “ABCBBB”Output:2

**Approach:** The given problem can be solved using the sliding window technique. Since the frequency of each character should be **N/3**, hence the number of excess occurrences of the characters can be calculated. The idea is to find the length of the smallest substring such that it contains all the excess characters which can then be replaced. Below are the steps to follow:

- Create a map,
**extraChars**which stores the characters in**str**that appear more than**N/3**times along with their respective excess count. - Use sliding window to find the shortest substring that has all characters in
**extraChar**with the given frequency. It can be done similarly as discussed in the problem of finding the smallest substring which contains all characters of another string.

Below is the implementation of above approach:

## C++

`#include <bits/stdc++.h>` `using` `namespace` `std;` `int` `balanceString(string str){` ` ` `int` `N = str.length();` ` ` `// If length of str is 0` ` ` `if` `(N == 0) {` ` ` `return` `0;` ` ` `}` ` ` `// Stores the frequency of` ` ` `// each char in str` ` ` `map<` `char` `, ` `int` `> strFreq;` ` ` `for` `(` `char` `c : str)` ` ` `strFreq++;` ` ` `// Stores the characters having` ` ` `// excess occurences with count` ` ` `map<` `char` `, ` `int` `> extraChars;` ` ` `for` `(` `auto` `c : strFreq) {` ` ` `// If there are more than N/3` ` ` `// characters in the string str` ` ` `if` `(c.second > N / 3)` ` ` `extraChars = (c.second - N / 3);` ` ` `}` ` ` `// If no characters occurs more` ` ` `// than N/3 time in the string` ` ` `if` `(extraChars.size() == 0) {` ` ` `return` `0;` ` ` `}` ` ` `// Represents start of the window,` ` ` `// end of the window and the` ` ` `// required answer respectivelly` ` ` `int` `i = 0, j = 0;` ` ` `int` `minWindowLength = N + 1;` ` ` `// Stores the number of unique` ` ` `// characters to in substring` ` ` `int` `count = extraChars.size();` ` ` `while` `(j < N) {` ` ` `// Store current character` ` ` `char` `c = str[j];` ` ` `// Check if c is an excess char` ` ` `if` `(extraChars.find(c) != extraChars.end()) {` ` ` `// Reduce Count` ` ` `extraChars--;` ` ` `// If window has the` ` ` `// required count` ` ` `if` `(extraChars == 0)` ` ` `count--;` ` ` `}` ` ` `// If current window has all char` ` ` `if` `(count == 0) {` ` ` `// Reduce Window size` ` ` `while` `(i < N && count == 0) {` ` ` `// Update the minimum` ` ` `// length of window` ` ` `minWindowLength = min(minWindowLength, j - i + 1);` ` ` `// If character at index` ` ` `// i is an excess char` ` ` `if` `(extraChars.find(str[i]) != extraChars.end()) {` ` ` `// Update frequency` ` ` `extraChars[str[i]]++;` ` ` `// Update Count` ` ` `if` `(extraChars[str[i]] == 1)` ` ` `count++;` ` ` `}` ` ` `i++;` ` ` `}` ` ` `}` ` ` `j++;` ` ` `}` ` ` `return` `minWindowLength;` `}` `// Driver Code` `int` `main() {` ` ` `string str = ` `"ABCBBB"` `;` ` ` `cout << balanceString(str); ` ` ` `return` `0;` `}` `// This code is contributed by hrithikgarg03188` |

## Java

`// Java code to implement above approach` `import` `java.io.*;` `import` `java.util.*;` `class` `GFG {` ` ` `static` `int` `balanceString(String str)` ` ` `{` ` ` `int` `N = str.length();` ` ` `// If length of str is 0` ` ` `if` `(N == ` `0` `) {` ` ` `return` `0` `;` ` ` `}` ` ` `// Stores the frequency of` ` ` `// each char in str` ` ` `HashMap<Character, Integer> strFreq` ` ` `= ` `new` `HashMap<>();` ` ` `for` `(` `char` `c : str.toCharArray())` ` ` `strFreq.put(c,` ` ` `strFreq.getOrDefault(c, ` `0` `)` ` ` `+ ` `1` `);` ` ` `// Stores the characters having` ` ` `// excess occurences with count` ` ` `HashMap<Character, Integer> extraChars` ` ` `= ` `new` `HashMap<>();` ` ` `for` `(` `char` `c : strFreq.keySet()) {` ` ` `// If there are more than N/3` ` ` `// characters in the string str` ` ` `if` `(strFreq.get(c) > N / ` `3` `)` ` ` `extraChars.put(c,` ` ` `strFreq.get(c)` ` ` `- N / ` `3` `);` ` ` `}` ` ` `// If no characters occurs more` ` ` `// than N/3 time in the string` ` ` `if` `(extraChars.size() == ` `0` `) {` ` ` `return` `0` `;` ` ` `}` ` ` `// Represents start of the window,` ` ` `// end of the window and the` ` ` `// required answer respectivelly` ` ` `int` `i = ` `0` `, j = ` `0` `;` ` ` `int` `minWindowLength = N + ` `1` `;` ` ` `// Stores the number of unique` ` ` `// characters to in substring` ` ` `int` `count = extraChars.size();` ` ` `while` `(j < N) {` ` ` `// Store current character` ` ` `char` `c = str.charAt(j);` ` ` `// Check if c is an excess char` ` ` `if` `(extraChars.containsKey(c)) {` ` ` `// Reduce Count` ` ` `extraChars.put(c,` ` ` `extraChars.get(c)` ` ` `- ` `1` `);` ` ` `// If window has the` ` ` `// required count` ` ` `if` `(extraChars.get(c) == ` `0` `)` ` ` `count--;` ` ` `}` ` ` `// If current window has all char` ` ` `if` `(count == ` `0` `) {` ` ` `// Reduce Window size` ` ` `while` `(i < N && count == ` `0` `) {` ` ` `// Update the minimum` ` ` `// length of window` ` ` `minWindowLength` ` ` `= Math.min(minWindowLength,` ` ` `j - i + ` `1` `);` ` ` `// If character at index` ` ` `// i is an excess char` ` ` `if` `(extraChars.containsKey(` ` ` `str.charAt(i))) {` ` ` `// Update frequency` ` ` `extraChars.put(` ` ` `str.charAt(i),` ` ` `extraChars.get(` ` ` `str.charAt(i))` ` ` `+ ` `1` `);` ` ` `// Update Count` ` ` `if` `(extraChars.get(` ` ` `str.charAt(i))` ` ` `== ` `1` `)` ` ` `count++;` ` ` `}` ` ` `i++;` ` ` `}` ` ` `}` ` ` `j++;` ` ` `}` ` ` `return` `minWindowLength;` ` ` `}` ` ` `// Driver Code` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` `String str = ` `"ABCBBB"` `;` ` ` `System.out.println(balanceString(str));` ` ` `}` `}` |

## Javascript

`<script>` ` ` `// JavaScript code for the above approach` ` ` `function` `balanceString(str) {` ` ` `let N = str.length;` ` ` `// If length of str is 0` ` ` `if` `(N == 0) {` ` ` `return` `0;` ` ` `}` ` ` `// Stores the frequency of` ` ` `// each char in str` ` ` `let strFreq` ` ` `= ` `new` `Map();` ` ` `str = str.split(` `''` `)` ` ` `for` `(let c of str) {` ` ` `if` `(strFreq.has(c))` ` ` `strFreq.set(c,` ` ` `strFreq.get(c)` ` ` `+ 1);` ` ` `else` ` ` `strFreq.set(c, 1)` ` ` `}` ` ` `str = str.join(` `''` `)` ` ` `// Stores the characters having` ` ` `// excess occurences with count` ` ` `let extraChars` ` ` `= ` `new` `Map();` ` ` `for` `(let c of strFreq.keys()) {` ` ` `// If there are more than N/3` ` ` `// characters in the string str` ` ` `if` `(strFreq.get(c) > Math.floor(N / 3))` ` ` `extraChars.set(c,` ` ` `strFreq.get(c)` ` ` `- Math.floor(N / 3));` ` ` `}` ` ` `// If no characters occurs more` ` ` `// than N/3 time in the string` ` ` `if` `(extraChars.size == 0) {` ` ` `return` `0;` ` ` `}` ` ` `// Represents start of the window,` ` ` `// end of the window and the` ` ` `// required answer respectivelly` ` ` `let i = 0, j = 0;` ` ` `let minWindowLength = N + 1;` ` ` `// Stores the number of unique` ` ` `// characters to in substring` ` ` `let count = extraChars.size;` ` ` `while` `(j < N) {` ` ` `// Store current character` ` ` `let c = str.charAt(j);` ` ` `// Check if c is an excess char` ` ` `if` `(extraChars.has(c)) {` ` ` `// Reduce Count` ` ` `extraChars.set(c,` ` ` `extraChars.get(c)` ` ` `- 1);` ` ` `// If window has the` ` ` `// required count` ` ` `if` `(extraChars.get(c) == 0)` ` ` `count--;` ` ` `}` ` ` `// If current window has all char` ` ` `if` `(count == 0) {` ` ` `// Reduce Window size` ` ` `while` `(i < N && count == 0) {` ` ` `// Update the minimum` ` ` `// length of window` ` ` `minWindowLength` ` ` `= Math.min(minWindowLength,` ` ` `j - i + 1);` ` ` `// If character at index` ` ` `// i is an excess char` ` ` `if` `(extraChars.has(` ` ` `str.charAt(i))) {` ` ` `// Update frequency` ` ` `extraChars.set(` ` ` `str.charAt(i),` ` ` `extraChars.get(` ` ` `str.charAt(i))` ` ` `+ 1);` ` ` `// Update Count` ` ` `if` `(extraChars.get(` ` ` `str.charAt(i))` ` ` `== 1)` ` ` `count++;` ` ` `}` ` ` `i++;` ` ` `}` ` ` `}` ` ` `j++;` ` ` `}` ` ` `return` `minWindowLength;` ` ` `}` ` ` `// Driver Code` ` ` `let str = ` `"ABCBBB"` `;` ` ` `document.write(balanceString(str));` ` ` `// This code is contributed by Potta Lokesh` ` ` `</script>` |

**Output**

2

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