leetcode-problemset/leetcode-cn/originData/successful-pairs-of-spells-and-potions.json

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            "questionId": "2392",
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            "categoryTitle": "Algorithms",
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            "title": "Successful Pairs of Spells and Potions",
            "titleSlug": "successful-pairs-of-spells-and-potions",
            "content": "<p>You are given two positive integer arrays <code>spells</code> and <code>potions</code>, of length <code>n</code> and <code>m</code> respectively, where <code>spells[i]</code> represents the strength of the <code>i<sup>th</sup></code> spell and <code>potions[j]</code> represents the strength of the <code>j<sup>th</sup></code> potion.</p>\n\n<p>You are also given an integer <code>success</code>. A spell and potion pair is considered <strong>successful</strong> if the <strong>product</strong> of their strengths is <strong>at least</strong> <code>success</code>.</p>\n\n<p>Return <em>an integer array </em><code>pairs</code><em> of length </em><code>n</code><em> where </em><code>pairs[i]</code><em> is the number of <strong>potions</strong> that will form a successful pair with the </em><code>i<sup>th</sup></code><em> spell.</em></p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> spells = [5,1,3], potions = [1,2,3,4,5], success = 7\n<strong>Output:</strong> [4,0,3]\n<strong>Explanation:</strong>\n- 0<sup>th</sup> spell: 5 * [1,2,3,4,5] = [5,<u><strong>10</strong></u>,<u><strong>15</strong></u>,<u><strong>20</strong></u>,<u><strong>25</strong></u>]. 4 pairs are successful.\n- 1<sup>st</sup> spell: 1 * [1,2,3,4,5] = [1,2,3,4,5]. 0 pairs are successful.\n- 2<sup>nd</sup> spell: 3 * [1,2,3,4,5] = [3,6,<u><strong>9</strong></u>,<u><strong>12</strong></u>,<u><strong>15</strong></u>]. 3 pairs are successful.\nThus, [4,0,3] is returned.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> spells = [3,1,2], potions = [8,5,8], success = 16\n<strong>Output:</strong> [2,0,2]\n<strong>Explanation:</strong>\n- 0<sup>th</sup> spell: 3 * [8,5,8] = [<u><strong>24</strong></u>,15,<u><strong>24</strong></u>]. 2 pairs are successful.\n- 1<sup>st</sup> spell: 1 * [8,5,8] = [8,5,8]. 0 pairs are successful. \n- 2<sup>nd</sup> spell: 2 * [8,5,8] = [<strong><u>16</u></strong>,10,<u><strong>16</strong></u>]. 2 pairs are successful. \nThus, [2,0,2] is returned.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>n == spells.length</code></li>\n\t<li><code>m == potions.length</code></li>\n\t<li><code>1 &lt;= n, m &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= spells[i], potions[i] &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= success &lt;= 10<sup>10</sup></code></li>\n</ul>\n",
            "translatedTitle": "咒语和药水的成功对数",
            "translatedContent": "<p>给你两个正整数数组&nbsp;<code>spells</code> 和&nbsp;<code>potions</code>&nbsp;，长度分别为&nbsp;<code>n</code> 和&nbsp;<code>m</code>&nbsp;，其中&nbsp;<code>spells[i]</code>&nbsp;表示第&nbsp;<code>i</code>&nbsp;个咒语的能量强度，<code>potions[j]</code>&nbsp;表示第&nbsp;<code>j</code>&nbsp;瓶药水的能量强度。</p>\n\n<p>同时给你一个整数&nbsp;<code>success</code>&nbsp;。一个咒语和药水的能量强度 <strong>相乘</strong> 如果&nbsp;<strong>大于等于</strong>&nbsp;<code>success</code>&nbsp;，那么它们视为一对&nbsp;<strong>成功</strong>&nbsp;的组合。</p>\n\n<p>请你返回一个长度为 <code>n</code>&nbsp;的整数数组<em>&nbsp;</em><code>pairs</code>，其中<em>&nbsp;</em><code>pairs[i]</code>&nbsp;是能跟第 <code>i</code>&nbsp;个咒语成功组合的 <b>药水</b>&nbsp;数目。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre><b>输入：</b>spells = [5,1,3], potions = [1,2,3,4,5], success = 7\n<b>输出：</b>[4,0,3]\n<strong>解释：</strong>\n- 第 0 个咒语：5 * [1,2,3,4,5] = [5,<em><strong>10</strong></em>,<em><strong>15</strong></em>,<em><strong>20</strong></em>,<em><strong>25</strong></em>] 。总共 4 个成功组合。\n- 第 1 个咒语：1 * [1,2,3,4,5] = [1,2,3,4,5] 。总共 0 个成功组合。\n- 第 2 个咒语：3 * [1,2,3,4,5] = [3,6,<em><strong>9</strong></em>,<em><strong>12</strong></em>,<em><strong>15</strong></em>] 。总共 3 个成功组合。\n所以返回 [4,0,3] 。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre><b>输入：</b>spells = [3,1,2], potions = [8,5,8], success = 16\n<b>输出：</b>[2,0,2]\n<strong>解释：</strong>\n- 第 0 个咒语：3 * [8,5,8] = [<em><strong>24</strong></em>,15,<em><strong>24</strong></em>] 。总共 2 个成功组合。\n- 第 1 个咒语：1 * [8,5,8] = [8,5,8] 。总共 0 个成功组合。\n- 第 2 个咒语：2 * [8,5,8] = [<em><strong>16</strong></em>,10,<em><strong>16</strong></em>] 。总共 2 个成功组合。\n所以返回 [2,0,2] 。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>n == spells.length</code></li>\n\t<li><code>m == potions.length</code></li>\n\t<li><code>1 &lt;= n, m &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= spells[i], potions[i] &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= success &lt;= 10<sup>10</sup></code></li>\n</ul>\n",
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                "Notice that if a spell and potion pair is successful, then the spell and all stronger potions will be successful too.",
                "Thus, for each spell, we need to find the potion with the least strength that will form a successful pair.",
                "We can efficiently do this by sorting the potions based on strength and using binary search."
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