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2222. Number of Ways to Select Buildings

Description

You are given a 0-indexed binary string s which represents the types of buildings along a street where:

  • s[i] = '0' denotes that the ith building is an office and
  • s[i] = '1' denotes that the ith building is a restaurant.

As a city official, you would like to select 3 buildings for random inspection. However, to ensure variety, no two consecutive buildings out of the selected buildings can be of the same type.

  • For example, given s = "001101", we cannot select the 1st, 3rd, and 5th buildings as that would form "011" which is not allowed due to having two consecutive buildings of the same type.

Return the number of valid ways to select 3 buildings.

 

Example 1:

Input: s = "001101"
Output: 6
Explanation:
The following sets of indices selected are valid:
- [0,2,4] from "001101" forms "010"
- [0,3,4] from "001101" forms "010"
- [1,2,4] from "001101" forms "010"
- [1,3,4] from "001101" forms "010"
- [2,4,5] from "001101" forms "101"
- [3,4,5] from "001101" forms "101"
No other selection is valid. Thus, there are 6 total ways.

Example 2:

Input: s = "11100"
Output: 0
Explanation: It can be shown that there are no valid selections.

 

Constraints:

  • 3 <= s.length <= 105
  • s[i] is either '0' or '1'.

Solutions

Solution 1: Counting + Enumeration

According to the problem description, we need to choose $3$ buildings, and two adjacent buildings cannot be of the same type.

We can enumerate the middle building, assuming it is $x$, then the types of buildings on the left and right sides can only be $x \oplus 1$, where $\oplus$ denotes the XOR operation. Therefore, we can use two arrays $l$ and $r$ to record the number of building types on the left and right sides, respectively. Then, we enumerate the middle building and calculate the answer.

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

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class Solution:
    def numberOfWays(self, s: str) -> int:
        l = [0, 0]
        r = [s.count("0"), s.count("1")]
        ans = 0
        for x in map(int, s):
            r[x] -= 1
            ans += l[x ^ 1] * r[x ^ 1]
            l[x] += 1
        return ans

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class Solution {
    public long numberOfWays(String s) {
        int n = s.length();
        int[] l = new int[2];
        int[] r = new int[2];
        for (int i = 0; i < n; ++i) {
            r[s.charAt(i) - '0']++;
        }
        long ans = 0;
        for (int i = 0; i < n; ++i) {
            int x = s.charAt(i) - '0';
            r[x]--;
            ans += 1L * l[x ^ 1] * r[x ^ 1];
            l[x]++;
        }
        return ans;
    }
}

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class Solution {
public:
    long long numberOfWays(string s) {
        int n = s.size();
        int l[2]{};
        int r[2]{};
        r[0] = ranges::count(s, '0');
        r[1] = n - r[0];
        long long ans = 0;
        for (int i = 0; i < n; ++i) {
            int x = s[i] - '0';
            r[x]--;
            ans += 1LL * l[x ^ 1] * r[x ^ 1];
            l[x]++;
        }
        return ans;
    }
};

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func numberOfWays(s string) (ans int64) {
    n := len(s)
    l := [2]int{}
    r := [2]int{}
    r[0] = strings.Count(s, "0")
    r[1] = n - r[0]
    for _, c := range s {
        x := int(c - '0')
        r[x]--
        ans += int64(l[x^1] * r[x^1])
        l[x]++
    }
    return
}

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function numberOfWays(s: string): number {
    const n = s.length;
    const l: number[] = [0, 0];
    const r: number[] = [s.split('').filter(c => c === '0').length, 0];
    r[1] = n - r[0];
    let ans: number = 0;
    for (const c of s) {
        const x = c === '0' ? 0 : 1;
        r[x]--;
        ans += l[x ^ 1] * r[x ^ 1];
        l[x]++;
    }
    return ans;
}

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