1358. Number of Substrings Containing All Three Characters

Description

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.

Solutions

Solution 1: Single Pass

We use an array $d$ of length $3$ to record the most recent occurrence of the three characters, initially all set to $-1$.

We traverse the string $s$. For the current position $i$, we first update $d[s[i]]=i$, then the number of valid strings is $\min(d[0], d[1], d[2]) + 1$, which is accumulated to the answer.

The time complexity is $O(n)$, where $n$ is the length of the string $s$. The space complexity is $O(1)$.

Python Code
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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

Java Code
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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;
    }
}

C++ Code
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class Solution {
public:
    int numberOfSubstrings(string s) {
        int d[3] = {-1, -1, -1};
        int ans = 0;
        for (int i = 0; i < s.size(); ++i) {
            d[s[i] - 'a'] = i;
            ans += min(d[0], min(d[1], d[2])) + 1;
        }
        return ans;
    }
};

Go Code
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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
}