LeetCode 3017: Count the Number of Houses at a Certain Distance II Solution

Master LeetCode problem 3017 (Count the Number of Houses at a Certain Distance II), a hard challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.

3017. Count the Number of Houses at a Certain Distance II

Hard

Graph Prefix Sum

Problem Explanation

Explanation:

To solve this problem, we can iterate over each pair of houses and calculate the minimum distance between them. The minimum distance between two houses can be calculated by finding the minimum number of streets that need to be traveled to reach one house from the other.

We can calculate the minimum distance for each pair of houses using the formula:

If the houses are on the same side of the special street connecting x and y, the minimum distance is the absolute difference in their house numbers.
If the houses are on different sides of the special street connecting x and y, the minimum distance is the sum of the distances from each house to x and y.

We iterate over all pairs of houses and count the pairs based on the minimum distance. Finally, we return the count for each distance k in a 1-indexed array.

Time Complexity:

The time complexity of this approach is O(n^2) where n is the number of houses.

Space Complexity:

The space complexity of this approach is O(n) for storing the result array.

Solution Code

class Solution {
    public int[] countPairs(int n, int x, int y) {
        int[] result = new int[n];
        
        for (int i = 1; i <= n; i++) {
            for (int j = i + 1; j <= n; j++) {
                int dist = Math.min(Math.abs(j - i), Math.abs(x - i) + Math.abs(y - j) + 1);
                result[dist - 1]++;
            }
        }
        
        return result;
    }
}

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