Package g3001_3100.s3015_count_the_number_of_houses_at_a_certain_distance_i

Class Solution

  • All Implemented Interfaces:
    
public final class Solution

    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 &lt;= k &lt;= n, you need to find the number of pairs of houses <code>(house<sub>1</sub>, house<sub>2</sub>)</code> such that the minimum number of streets that need to be traveled to reach <code>house<sub>2</sub></code> from <code>house<sub>1</sub></code> 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 &lt;= n &lt;= 100

    • 1 &lt;= x, y &lt;= n

    • Nested Class Summary

      Nested Classes 
      Modifier and Type Class Description

    • Field Summary

      Fields 
      Modifier and Type Field Description

    • Constructor Summary

      Constructors 
      Constructor Description
      Solution()

    • Enum Constant Summary

      Enum Constants 
      Enum Constant Description

    • Method Summary

      Modifier and Type Method Description
      final IntArray countOfPairs(Integer n, Integer x, Integer y)

      • Methods inherited from class java.lang.Object

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