g1401_1500.s1420_build_array_where_you_can_find_the_maximum_exactly_k_comparisons

Class Solution

java.lang.Object

g1401_1500.s1420_build_array_where_you_can_find_the_maximum_exactly_k_comparisons.Solution

public class Solution
extends Object

1420 - Build Array Where You Can Find The Maximum Exactly K Comparisons.

Hard

You are given three integers n, m and k. Consider the following algorithm to find the maximum element of an array of positive integers:

You should build the array arr which has the following properties:

• arr has exactly n integers.
• 1 <= arr[i] <= m where (0 <= i < n).
• After applying the mentioned algorithm to arr, the value search_cost is equal to k.

Return the number of ways to build the array arr under the mentioned conditions. As the answer may grow large, the answer must be computed modulo 109 + 7.

Example 1:

Input: n = 2, m = 3, k = 1

Output: 6

Explanation: The possible arrays are [1, 1], [2, 1], [2, 2], [3, 1], [3, 2] [3, 3]

Example 2:

Input: n = 5, m = 2, k = 3

Output: 0

Explanation: There are no possible arrays that satisify the mentioned conditions.

Example 3:

Input: n = 9, m = 1, k = 1

Output: 1

Explanation: The only possible array is [1, 1, 1, 1, 1, 1, 1, 1, 1]

Constraints:

• 1 <= n <= 50
• 1 <= m <= 100
• 0 <= k <= n

Constructor Summary

Constructors

Constructor and Description
Solution()

Method Summary

Modifier and Type	Method and Description
int	numOfArrays(int n, int m, int k)

Methods inherited from class java.lang.Object

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

Constructor Detail

Solution

public Solution()

Method Detail

numOfArrays

public int numOfArrays(int n,
                       int m,
                       int k)