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

Author: remy727

README.md

@@ -331,6 +331,7 @@
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+| 1420 | Build Array Where You Can Find The Maximum Exactly K Comparisons | [Ruby](./algorithms/ruby/1420-build-array-where-you-can-find-the-maximum-exactly-k-comparisons.rb) | Hard |
 | 1431 | Kids With the Greatest Number of Candies | [Ruby](./algorithms/ruby/1431-kids-with-the-greatest-number-of-candies.rb) | Easy |
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algorithms/ruby/1420-build-array-where-you-can-find-the-maximum-exactly-k-comparisons.rb

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+# frozen_string_literal: true
+
+# 1420. Build Array Where You Can Find The Maximum Exactly K Comparisons
+# Hard
+# https://leetcode.com/problems/build-array-where-you-can-find-the-maximum-exactly-k-comparisons
+
+=begin
+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
+=end
+
+# @param {Integer} n
+# @param {Integer} m
+# @param {Integer} k
+# @return {Integer}
+MOD = 1_000_000_007
+
+def num_of_arrays(n, m, k)
+  dp = Array.new(n + 1) { Array.new(m + 1) { Array.new(k + 1, 0) } }
+
+  1.upto(m) do |i|
+    dp[1][i][1] = 1
+  end
+
+  2.upto(n) do |len|
+    1.upto(m) do |max_val|
+      1.upto(k) do |cost|
+        sum = 0
+        1.upto(max_val - 1) do |i|
+          sum = (sum + dp[len - 1][i][cost - 1]) % MOD
+        end
+        dp[len][max_val][cost] = (dp[len - 1][max_val][cost] * max_val + sum) % MOD
+      end
+    end
+  end
+
+  ans = 0
+  1.upto(m) do |i|
+    ans = (ans + dp[n][i][k]) % MOD
+  end
+
+  ans
+end
+
+# **************** #
+#       TEST       #
+# **************** #
+
+require "test/unit"
+class Test_num_of_arrays < Test::Unit::TestCase
+  def test_
+    assert_equal 6, num_of_arrays(2, 3, 1)
+    assert_equal 0, num_of_arrays(5, 2, 3)
+    assert_equal 1, num_of_arrays(9, 1, 1)
+  end
+end