Package g3001_3100.s3015_count_the_number_of_houses_at_a_certain_distance_i

Class Solution

java.lang.Object
g3001_3100.s3015_count_the_number_of_houses_at_a_certain_distance_i.Solution
public class Solution extends java.lang.Object
3015 - Count the Number of Houses at a Certain Distance I.

Medium

You are given three positive integers n, x, and y.

In a city, there exist houses numbered 1 to n connected by n streets. There is a street connecting the house numbered i with the house numbered i + 1 for all 1 <= i <= n - 1 . An additional street connects the house numbered x with the house numbered y.

For each k, such that 1 <= k <= n, you need to find the number of pairs of houses (house1, house2) such that the minimum number of streets that need to be traveled to reach house2 from house1 is k.

Return a 1-indexed array result of length n where result[k] represents the total number of pairs of houses such that the minimum streets required to reach one house from the other is k.

Note that x and y can be equal.

Example 1:

Input: n = 3, x = 1, y = 3

Output: [6,0,0]

Explanation: Let’s look at each pair of houses:

  • For the pair (1, 2), we can go from house 1 to house 2 directly.
  • For the pair (2, 1), we can go from house 2 to house 1 directly.
  • For the pair (1, 3), we can go from house 1 to house 3 directly.
  • For the pair (3, 1), we can go from house 3 to house 1 directly.
  • For the pair (2, 3), we can go from house 2 to house 3 directly.
  • For the pair (3, 2), we can go from house 3 to house 2 directly.

Example 2:

Input: n = 5, x = 2, y = 4

Output: [10,8,2,0,0]

Explanation: For each distance k the pairs are:

  • For k == 1, the pairs are (1, 2), (2, 1), (2, 3), (3, 2), (2, 4), (4, 2), (3, 4), (4, 3), (4, 5), and (5, 4).
  • For k == 2, the pairs are (1, 3), (3, 1), (1, 4), (4, 1), (2, 5), (5, 2), (3, 5), and (5, 3).
  • For k == 3, the pairs are (1, 5), and (5, 1).
  • For k == 4 and k == 5, there are no pairs.

Example 3:

Input: n = 4, x = 1, y = 1

Output: [6,4,2,0]

Explanation: For each distance k the pairs are:

  • For k == 1, the pairs are (1, 2), (2, 1), (2, 3), (3, 2), (3, 4), and (4, 3).
  • For k == 2, the pairs are (1, 3), (3, 1), (2, 4), and (4, 2).
  • For k == 3, the pairs are (1, 4), and (4, 1).
  • For k == 4, there are no pairs.

Constraints:

  • 2 <= n <= 100
  • 1 <= x, y <= n

  • Constructor Summary

    Constructors
    Constructor
    Description
    Solution()
     

  • Method Summary

    Modifier and Type
    Method
    Description
    int[]
    countOfPairs(int n, int x, int y)
     

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Constructor Details

    • Solution

      public Solution()

  • Method Details

    • countOfPairs

      public int[] countOfPairs(int n, int x, int y)