2609. Find the Longest Balanced Substring of a Binary String

Description

You are given a binary string s consisting only of zeroes and ones.

A substring of s is considered balanced if all zeroes are before ones and the number of zeroes is equal to the number of ones inside the substring. Notice that the empty substring is considered a balanced substring.

Return the length of the longest balanced substring of s.

A substring is a contiguous sequence of characters within a string.

 

Example 1:

Input: s = "01000111"
Output: 6
Explanation: The longest balanced substring is "000111", which has length 6.

Example 2:

Input: s = "00111"
Output: 4
Explanation: The longest balanced substring is "0011", which has length 4. 

Example 3:

Input: s = "111"
Output: 0
Explanation: There is no balanced substring except the empty substring, so the answer is 0.

 

Constraints:

• 1 <= s.length <= 50
• '0' <= s[i] <= '1'

Solutions

Solution 1: Brute force

Since the range of $n$ is small, we can enumerate all substrings $s[i..j]$ to check if it is a balanced string. If so, update the answer.

The time complexity is $O(n^3)$, and the space complexity is $O(1)$. Where $n$ is the length of string $s$.

Python3JavaC++GoTypeScriptRust

class Solution:
    def findTheLongestBalancedSubstring(self, s: str) -> int:
        def check(i, j):
            cnt = 0
            for k in range(i, j + 1):
                if s[k] == '1':
                    cnt += 1
                elif cnt:
                    return False
            return cnt * 2 == (j - i + 1)

        n = len(s)
        ans = 0
        for i in range(n):
            for j in range(i + 1, n):
                if check(i, j):
                    ans = max(ans, j - i + 1)
        return ans

class Solution {
    public int findTheLongestBalancedSubstring(String s) {
        int n = s.length();
        int ans = 0;
        for (int i = 0; i < n; ++i) {
            for (int j = i + 1; j < n; ++j) {
                if (check(s, i, j)) {
                    ans = Math.max(ans, j - i + 1);
                }
            }
        }
        return ans;
    }

    private boolean check(String s, int i, int j) {
        int cnt = 0;
        for (int k = i; k <= j; ++k) {
            if (s.charAt(k) == '1') {
                ++cnt;
            } else if (cnt > 0) {
                return false;
            }
        }
        return cnt * 2 == j - i + 1;
    }
}

class Solution {
public:
    int findTheLongestBalancedSubstring(string s) {
        int n = s.size();
        int ans = 0;
        auto check = [&](int i, int j) -> bool {
            int cnt = 0;
            for (int k = i; k <= j; ++k) {
                if (s[k] == '1') {
                    ++cnt;
                } else if (cnt) {
                    return false;
                }
            }
            return cnt * 2 == j - i + 1;
        };
        for (int i = 0; i < n; ++i) {
            for (int j = i + 1; j < n; ++j) {
                if (check(i, j)) {
                    ans = max(ans, j - i + 1);
                }
            }
        }
        return ans;
    }
};

func findTheLongestBalancedSubstring(s string) (ans int) {
    n := len(s)
    check := func(i, j int) bool {
        cnt := 0
        for k := i; k <= j; k++ {
            if s[k] == '1' {
                cnt++
            } else if