LeetCode in Kotlin

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

Solution

class Solution {
    fun numOfArrays(n: Int, m: Int, k: Int): Int {
        var ways = Array(m + 1) { LongArray(k + 1) }
        var sums = Array(m + 1) { LongArray(k + 1) }
        for (max in 1..m) {
            ways[max][1] = 1
            sums[max][1] = ways[max][1] + sums[max - 1][1]
        }
        for (count in 2..n) {
            val ways2 = Array(m + 1) { LongArray(k + 1) }
            val sums2 = Array(m + 1) { LongArray(k + 1) }
            for (max in 1..m) {
                for (cost in 1..k) {
                    val noCost = max * ways[max][cost] % MOD
                    val newCost = sums[max - 1][cost - 1]
                    ways2[max][cost] = (noCost + newCost) % MOD
                    sums2[max][cost] = (sums2[max - 1][cost] + ways2[max][cost]) % MOD
                }
            }
            ways = ways2
            sums = sums2
        }
        return sums[m][k].toInt()
    }

    companion object {
        private const val MOD = 1000000007
    }
}

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