leetcode-problemset/leetcode/originData/number-of-ways-to-earn-points.json

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            "title": "Number of Ways to Earn Points",
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            "content": "<p>There is a test that has <code>n</code> types of questions. You are given an integer <code>target</code> and a <strong>0-indexed</strong> 2D integer array <code>types</code> where <code>types[i] = [count<sub>i</sub>, marks<sub>i</sub>]</code> indicates that there are <code>count<sub>i</sub></code> questions of the <code>i<sup>th</sup></code> type, and each one of them is worth <code>marks<sub>i</sub></code> points.</p>\n\n<ul>\n</ul>\n\n<p>Return <em>the number of ways you can earn <strong>exactly</strong> </em><code>target</code><em> points in the exam</em>. Since the answer may be too large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>\n\n<p><strong>Note</strong> that questions of the same type are indistinguishable.</p>\n\n<ul>\n\t<li>For example, if there are <code>3</code> questions of the same type, then solving the <code>1<sup>st</sup></code> and <code>2<sup>nd</sup></code> questions is the same as solving the <code>1<sup>st</sup></code> and <code>3<sup>rd</sup></code> questions, or the <code>2<sup>nd</sup></code> and <code>3<sup>rd</sup></code> questions.</li>\n</ul>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> target = 6, types = [[6,1],[3,2],[2,3]]\n<strong>Output:</strong> 7\n<strong>Explanation:</strong> You can earn 6 points in one of the seven ways:\n- Solve 6 questions of the 0<sup>th</sup> type: 1 + 1 + 1 + 1 + 1 + 1 = 6\n- Solve 4 questions of the 0<sup>th</sup> type and 1 question of the 1<sup>st</sup> type: 1 + 1 + 1 + 1 + 2 = 6\n- Solve 2 questions of the 0<sup>th</sup> type and 2 questions of the 1<sup>st</sup> type: 1 + 1 + 2 + 2 = 6\n- Solve 3 questions of the 0<sup>th</sup> type and 1 question of the 2<sup>nd</sup> type: 1 + 1 + 1 + 3 = 6\n- Solve 1 question of the 0<sup>th</sup> type, 1 question of the 1<sup>st</sup> type and 1 question of the 2<sup>nd</sup> type: 1 + 2 + 3 = 6\n- Solve 3 questions of the 1<sup>st</sup> type: 2 + 2 + 2 = 6\n- Solve 2 questions of the 2<sup>nd</sup> type: 3 + 3 = 6\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> target = 5, types = [[50,1],[50,2],[50,5]]\n<strong>Output:</strong> 4\n<strong>Explanation:</strong> You can earn 5 points in one of the four ways:\n- Solve 5 questions of the 0<sup>th</sup> type: 1 + 1 + 1 + 1 + 1 = 5\n- Solve 3 questions of the 0<sup>th</sup> type and 1 question of the 1<sup>st</sup> type: 1 + 1 + 1 + 2 = 5\n- Solve 1 questions of the 0<sup>th</sup> type and 2 questions of the 1<sup>st</sup> type: 1 + 2 + 2 = 5\n- Solve 1 question of the 2<sup>nd</sup> type: 5\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> target = 18, types = [[6,1],[3,2],[2,3]]\n<strong>Output:</strong> 1\n<strong>Explanation:</strong> You can only earn 18 points by answering all questions.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= target &lt;= 1000</code></li>\n\t<li><code>n == types.length</code></li>\n\t<li><code>1 &lt;= n &lt;= 50</code></li>\n\t<li><code>types[i].length == 2</code></li>\n\t<li><code>1 &lt;= count<sub>i</sub>, marks<sub>i</sub> &lt;= 50</code></li>\n</ul>\n",
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                "Use Dynamic Programming",
                "Let ways[i][points] be the number of ways to score a given number of points after solving some questions of the first i types.",
                "ways[i][points] is equal to the sum of ways[i-1][points - solved * marks[i] over 0 <= solved <= count_i"
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