LeetCode #1358 — MEDIUM

Number of Substrings Containing All Three Characters

Move from brute-force thinking to an efficient approach using hash map strategy.

The Problem

Problem Statement

Given a string s consisting only of characters a, b and c.

Return the number of substrings containing at least one occurrence of all these characters a, b and c.

Example 1:

Input: s = "abcabc"
Output: 10
Explanation: The substrings containing at least one occurrence of the characters a, b and c are "abc", "abca", "abcab", "abcabc", "bca", "bcab", "bcabc", "cab", "cabc" and "abc" (again).

Example 2:

Input: s = "aaacb"
Output: 3
Explanation: The substrings containing at least one occurrence of the characters a, b and c are "aaacb", "aacb" and "acb".

Example 3:

Input: s = "abc"
Output: 1

Constraints:

3 <= s.length <= 5 x 10^4
s only consists of a, b or c characters.

Step 01

Brute Force Baseline

Problem summary: Given a string s consisting only of characters a, b and c. Return the number of substrings containing at least one occurrence of all these characters a, b and c.

Baseline thinking

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

Pattern signal: Hash Map · Sliding Window

Example 1

"abcabc"

Example 2

"aaacb"

Example 3

"abc"

Core Insight

What unlocks the optimal approach

For each position we simply need to find the first occurrence of a/b/c on or after this position.
So we can pre-compute three link-list of indices of each a, b, and c.

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

Upper-end input sizes

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 #1358: Number of Substrings Containing All Three Characters
class Solution {
    public int numberOfSubstrings(String s) {
        int[] d = new int[] {-1, -1, -1};
        int ans = 0;
        for (int i = 0; i < s.length(); ++i) {
            char c = s.charAt(i);
            d[c - 'a'] = i;
            ans += Math.min(d[0], Math.min(d[1], d[2])) + 1;
        }
        return ans;
    }
}

// Accepted solution for LeetCode #1358: Number of Substrings Containing All Three Characters
func numberOfSubstrings(s string) (ans int) {
	d := [3]int{-1, -1, -1}
	for i, c := range s {
		d[c-'a'] = i
		ans += min(d[0], min(d[1], d[2])) + 1
	}
	return
}

# Accepted solution for LeetCode #1358: Number of Substrings Containing All Three Characters
class Solution:
    def numberOfSubstrings(self, s: str) -> int:
        d = {"a": -1, "b": -1, "c": -1}
        ans = 0
        for i, c in enumerate(s):
            d[c] = i
            ans += min(d["a"], d["b"], d["c"]) + 1
        return ans

// Accepted solution for LeetCode #1358: Number of Substrings Containing All Three Characters
struct Solution;

impl Solution {
    fn number_of_substrings(s: String) -> i32 {
        let mut count: [usize; 3] = [0; 3];
        let s: Vec<u8> = s.bytes().collect();
        let n = s.len();
        let mut j = 0;
        let mut res = 0;
        for i in 0..n {
            count[(s[i] - b'a') as usize] += 1;
            while count[0] > 0 && count[1] > 0 && count[2] > 0 {
                count[(s[j] - b'a') as usize] -= 1;
                j += 1;
            }
            res += j;
        }
        res as i32
    }
}

#[test]
fn test() {
    let s = "abcabc".to_string();
    let res = 10;
    assert_eq!(Solution::number_of_substrings(s), res);
    let s = "aaacb".to_string();
    let res = 3;
    assert_eq!(Solution::number_of_substrings(s), res);
    let s = "abc".to_string();
    let res = 1;
    assert_eq!(Solution::number_of_substrings(s), res);
}

// Accepted solution for LeetCode #1358: Number of Substrings Containing All Three Characters
// Auto-generated TypeScript example from java.
function exampleSolution(): void {
}
// Reference (java):
// // Accepted solution for LeetCode #1358: Number of Substrings Containing All Three Characters
// class Solution {
//     public int numberOfSubstrings(String s) {
//         int[] d = new int[] {-1, -1, -1};
//         int ans = 0;
//         for (int i = 0; i < s.length(); ++i) {
//             char c = s.charAt(i);
//             d[c - 'a'] = i;
//             ans += Math.min(d[0], Math.min(d[1], d[2])) + 1;
//         }
//         return ans;
//     }
// }

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(n)

Space

O(k)

Approach Breakdown

BRUTE FORCE

O(n × k) time

O(1) space

For each starting index, scan the next k elements to compute the window aggregate. There are n−k+1 starting positions, each requiring O(k) work, giving O(n × k) total. No extra space since we recompute from scratch each time.

SLIDING WINDOW

O(n) time

O(k) space

The window expands and contracts as we scan left to right. Each element enters the window at most once and leaves at most once, giving 2n total operations = O(n). Space depends on what we track inside the window (a hash map of at most k distinct elements, or O(1) for a fixed-size window).

Shortcut: Each element enters and exits the window once → O(n) amortized, regardless of window size.

Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Mutating counts without cleanup

Wrong move: Zero-count keys stay in map and break distinct/count constraints.

Usually fails on: Window/map size checks are consistently off by one.

Fix: Delete keys when count reaches zero.

Shrinking the window only once

Wrong move: Using `if` instead of `while` leaves the window invalid for multiple iterations.

Usually fails on: Over-limit windows stay invalid and produce wrong lengths/counts.

Fix: Shrink in a `while` loop until the invariant is valid again.