LeetCode #3398 — HARD

Smallest Substring With Identical Characters I

Break down a hard problem into reliable checkpoints, edge-case handling, and complexity trade-offs.

The Problem

Problem Statement

You are given a binary string s of length n and an integer numOps.

You are allowed to perform the following operation on s at most numOps times:

Select any index i (where 0 <= i < n) and flip s[i]. If s[i] == '1', change s[i] to '0' and vice versa.

You need to minimize the length of the longest substring of s such that all the characters in the substring are identical.

Return the minimum length after the operations.

Example 1:

Input: s = "000001", numOps = 1

Output: 2

Explanation:

By changing s[2] to '1', s becomes "001001". The longest substrings with identical characters are s[0..1] and s[3..4].

Example 2:

Input: s = "0000", numOps = 2

Output: 1

Explanation:

By changing s[0] and s[2] to '1', s becomes "1010".

Example 3:

Input: s = "0101", numOps = 0

Output: 1

Constraints:

1 <= n == s.length <= 1000
s consists only of '0' and '1'.
0 <= numOps <= n

Step 01

Brute Force Baseline

Problem summary: You are given a binary string s of length n and an integer numOps. You are allowed to perform the following operation on s at most numOps times: Select any index i (where 0 <= i < n) and flip s[i]. If s[i] == '1', change s[i] to '0' and vice versa. You need to minimize the length of the longest substring of s such that all the characters in the substring are identical. Return the minimum length after the operations.

Baseline thinking

Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.

Pattern signal: Array · Binary Search

Example 1

"000001"
1

Example 2

"0000"
2

Example 3

"0101"
0

Step 02

Core Insight

What unlocks the optimal approach

Can we use binary search here?
Use DP for predicate function

Interview move: turn each hint into an invariant you can check after every iteration/recursion step.

Step 03

Algorithm Walkthrough

Iteration Checklist

Define state (indices, window, stack, map, DP cell, or recursion frame).
Apply one transition step and update the invariant.
Record answer candidate when condition is met.
Continue until all input is consumed.

Use the first example testcase as your mental trace to verify each transition.

Step 04

Edge Cases

Minimum Input

Single element / shortest valid input

Validate boundary behavior before entering the main loop or recursion.

Duplicates & Repeats

Repeated values / repeated states

Decide whether duplicates should be merged, skipped, or counted explicitly.

Extreme Constraints

Largest constraint values

Re-check complexity target against constraints to avoid time-limit issues.

Invalid / Corner Shape

Empty collections, zeros, or disconnected structures

Handle special-case structure before the core algorithm path.

Step 05

Full Annotated Code

Source-backed implementations are provided below for direct study and interview prep.

// Accepted solution for LeetCode #3398: Smallest Substring With Identical Characters I
class Solution {
    private char[] s;
    private int numOps;

    public int minLength(String s, int numOps) {
        this.numOps = numOps;
        this.s = s.toCharArray();
        int l = 1, r = s.length();
        while (l < r) {
            int mid = (l + r) >> 1;
            if (check(mid)) {
                r = mid;
            } else {
                l = mid + 1;
            }
        }
        return l;
    }

    private boolean check(int m) {
        int cnt = 0;
        if (m == 1) {
            char[] t = {'0', '1'};
            for (int i = 0; i < s.length; ++i) {
                if (s[i] == t[i & 1]) {
                    ++cnt;
                }
            }
            cnt = Math.min(cnt, s.length - cnt);
        } else {
            int k = 0;
            for (int i = 0; i < s.length; ++i) {
                ++k;
                if (i == s.length - 1 || s[i] != s[i + 1]) {
                    cnt += k / (m + 1);
                    k = 0;
                }
            }
        }
        return cnt <= numOps;
    }
}

// Accepted solution for LeetCode #3398: Smallest Substring With Identical Characters I
func minLength(s string, numOps int) int {
	check := func(m int) bool {
		m++
		cnt := 0
		if m == 1 {
			t := "01"
			for i := range s {
				if s[i] == t[i&1] {
					cnt++
				}
			}
			cnt = min(cnt, len(s)-cnt)
		} else {
			k := 0
			for i := range s {
				k++
				if i == len(s)-1 || s[i] != s[i+1] {
					cnt += k / (m + 1)
					k = 0
				}
			}
		}
		return cnt <= numOps
	}
	return 1 + sort.Search(len(s), func(m int) bool { return check(m) })
}

# Accepted solution for LeetCode #3398: Smallest Substring With Identical Characters I
class Solution:
    def minLength(self, s: str, numOps: int) -> int:
        def check(m: int) -> bool:
            cnt = 0
            if m == 1:
                t = "01"
                cnt = sum(c == t[i & 1] for i, c in enumerate(s))
                cnt = min(cnt, n - cnt)
            else:
                k = 0
                for i, c in enumerate(s):
                    k += 1
                    if i == len(s) - 1 or c != s[i + 1]:
                        cnt += k // (m + 1)
                        k = 0
            return cnt <= numOps

        n = len(s)
        return bisect_left(range(n), True, lo=1, key=check)

// Accepted solution for LeetCode #3398: Smallest Substring With Identical Characters I
// Rust example auto-generated from java reference.
// Replace the signature and local types with the exact LeetCode harness for this problem.
impl Solution {
    pub fn rust_example() {
        // Port the logic from the reference block below.
    }
}

// Reference (java):
// // Accepted solution for LeetCode #3398: Smallest Substring With Identical Characters I
// class Solution {
//     private char[] s;
//     private int numOps;
// 
//     public int minLength(String s, int numOps) {
//         this.numOps = numOps;
//         this.s = s.toCharArray();
//         int l = 1, r = s.length();
//         while (l < r) {
//             int mid = (l + r) >> 1;
//             if (check(mid)) {
//                 r = mid;
//             } else {
//                 l = mid + 1;
//             }
//         }
//         return l;
//     }
// 
//     private boolean check(int m) {
//         int cnt = 0;
//         if (m == 1) {
//             char[] t = {'0', '1'};
//             for (int i = 0; i < s.length; ++i) {
//                 if (s[i] == t[i & 1]) {
//                     ++cnt;
//                 }
//             }
//             cnt = Math.min(cnt, s.length - cnt);
//         } else {
//             int k = 0;
//             for (int i = 0; i < s.length; ++i) {
//                 ++k;
//                 if (i == s.length - 1 || s[i] != s[i + 1]) {
//                     cnt += k / (m + 1);
//                     k = 0;
//                 }
//             }
//         }
//         return cnt <= numOps;
//     }
// }

// Accepted solution for LeetCode #3398: Smallest Substring With Identical Characters I
function minLength(s: string, numOps: number): number {
    const n = s.length;
    const check = (m: number): boolean => {
        let cnt = 0;
        if (m === 1) {
            const t = '01';
            for (let i = 0; i < n; ++i) {
                if (s[i] === t[i & 1]) {
                    ++cnt;
                }
            }
            cnt = Math.min(cnt, n - cnt);
        } else {
            let k = 0;
            for (let i = 0; i < n; ++i) {
                ++k;
                if (i === n - 1 || s[i] !== s[i + 1]) {
                    cnt += Math.floor(k / (m + 1));
                    k = 0;
                }
            }
        }
        return cnt <= numOps;
    };
    let [l, r] = [1, n];
    while (l < r) {
        const mid = (l + r) >> 1;
        if (check(mid)) {
            r = mid;
        } else {
            l = mid + 1;
        }
    }
    return l;
}

Step 06

Interactive Study Demo

Use this to step through a reusable interview workflow for this problem.

Custom checkpoints (one per line)

Press Step or Run All to begin.

Step 07

Complexity Analysis

Time

O(log n)

Space

O(1)

Approach Breakdown

LINEAR SCAN

O(n) time

O(1) space

Check every element from left to right until we find the target or exhaust the array. Each comparison is O(1), and we may visit all n elements, giving O(n). No extra space needed.

BINARY SEARCH

O(log n) time

O(1) space

Each comparison eliminates half the remaining search space. After k comparisons, the space is n/2ᵏ. We stop when the space is 1, so k = log₂ n. No extra memory needed — just two pointers (lo, hi).

Shortcut: Halving the input each step → O(log n). Works on any monotonic condition, not just sorted arrays.

Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Off-by-one on range boundaries

Wrong move: Loop endpoints miss first/last candidate.

Usually fails on: Fails on minimal arrays and exact-boundary answers.

Fix: Re-derive loops from inclusive/exclusive ranges before coding.

Boundary update without `+1` / `-1`

Wrong move: Setting `lo = mid` or `hi = mid` can stall and create an infinite loop.

Usually fails on: Two-element ranges never converge.

Fix: Use `lo = mid + 1` or `hi = mid - 1` where appropriate.