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3184. Count Pairs That Form a Complete Day I

Description

Given an integer array hours representing times in hours, return an integer denoting the number of pairs i, j where i < j and hours[i] + hours[j] forms a complete day.

A complete day is defined as a time duration that is an exact multiple of 24 hours.

For example, 1 day is 24 hours, 2 days is 48 hours, 3 days is 72 hours, and so on.

 

Example 1:

Input: hours = [12,12,30,24,24]

Output: 2

Explanation:

The pairs of indices that form a complete day are (0, 1) and (3, 4).

Example 2:

Input: hours = [72,48,24,3]

Output: 3

Explanation:

The pairs of indices that form a complete day are (0, 1), (0, 2), and (1, 2).

 

Constraints:

  • 1 <= hours.length <= 100
  • 1 <= hours[i] <= 109

Solutions

Solution 1: Counting

We can use a hash table or an array \(\textit{cnt}\) of length \(24\) to record the occurrence count of each hour modulo \(24\).

Iterate through the array \(\textit{hours}\). For each hour \(x\), we can find the number that, when added to \(x\), results in a multiple of \(24\), and after modulo \(24\), this number is \((24 - x \bmod 24) \bmod 24\). We then accumulate the occurrence count of this number from the hash table or array. After that, we increment the occurrence count of \(x\) modulo \(24\) by one.

After iterating through the array \(\textit{hours}\), we can obtain the number of index pairs that meet the problem requirements.

The time complexity is \(O(n)\), where \(n\) is the length of the array \(\textit{hours}\). The space complexity is \(O(C)\), where \(C=24\).

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class Solution:
    def countCompleteDayPairs(self, hours: List[int]) -> int:
        cnt = Counter()
        ans = 0
        for x in hours:
            ans += cnt[(24 - (x % 24)) % 24]
            cnt[x % 24] += 1
        return ans

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class Solution {
    public int countCompleteDayPairs(int[] hours) {
        int[] cnt = new int[24];
        int ans = 0;
        for (int x : hours) {
            ans += cnt[(24 - x % 24) % 24];
            ++cnt[x % 24];
        }
        return ans;
    }
}

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class Solution {
public:
    int countCompleteDayPairs(vector<int>& hours) {
        int cnt[24]{};
        int ans = 0;
        for (int x : hours) {
            ans += cnt[(24 - x % 24) % 24];
            ++cnt[x % 24];
        }
        return ans;
    }
};

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func countCompleteDayPairs(hours []int) (ans int) {
    cnt := [24]int{}
    for _, x := range hours {
        ans += cnt[(24-x%24)%24]
        cnt[x%24]++
    }
    return
}

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function countCompleteDayPairs(hours: number[]): number {
    const cnt: number[] = Array(24).fill(0);
    let ans: number = 0;
    for (const x of hours) {
        ans += cnt[(24 - (x % 24)) % 24];
        ++cnt[x % 24];
    }
    return ans;
}

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