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"title": "Build Array Where You Can Find The Maximum Exactly K Comparisons",
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"content": "<p>You are given three integers <code>n</code>, <code>m</code> and <code>k</code>. Consider the following algorithm to find the maximum element of an array of positive integers:</p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/04/02/e.png\" style=\"width: 424px; height: 372px;\" />\n<p>You should build the array arr which has the following properties:</p>\n\n<ul>\n\t<li><code>arr</code> has exactly <code>n</code> integers.</li>\n\t<li><code>1 <= arr[i] <= m</code> where <code>(0 <= i < n)</code>.</li>\n\t<li>After applying the mentioned algorithm to <code>arr</code>, the value <code>search_cost</code> is equal to <code>k</code>.</li>\n</ul>\n\n<p>Return <em>the number of ways</em> to build the array <code>arr</code> under the mentioned conditions. As the answer may grow large, the answer <strong>must be</strong> computed modulo <code>10<sup>9</sup> + 7</code>.</p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 2, m = 3, k = 1\n<strong>Output:</strong> 6\n<strong>Explanation:</strong> The possible arrays are [1, 1], [2, 1], [2, 2], [3, 1], [3, 2] [3, 3]\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 5, m = 2, k = 3\n<strong>Output:</strong> 0\n<strong>Explanation:</strong> There are no possible arrays that satisfy the mentioned conditions.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 9, m = 1, k = 1\n<strong>Output:</strong> 1\n<strong>Explanation:</strong> The only possible array is [1, 1, 1, 1, 1, 1, 1, 1, 1]\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= n <= 50</code></li>\n\t<li><code>1 <= m <= 100</code></li>\n\t<li><code>0 <= k <= n</code></li>\n</ul>\n",
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"Use dynamic programming approach. Build dp table where dp[a][b][c] is the number of ways you can start building the array starting from index a where the search_cost = c and the maximum used integer was b.",
"Recursively, solve the small sub-problems first. Optimize your answer by stopping the search if you exceeded k changes."
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