leetcode-problemset/leetcode-cn/originData/removing-minimum-number-of-magic-beans.json

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            "questionId": "2290",
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            "title": "Removing Minimum Number of Magic Beans",
            "titleSlug": "removing-minimum-number-of-magic-beans",
            "content": "<p>You are given an array of <strong>positive</strong> integers <code>beans</code>, where each integer represents the number of magic beans found in a particular magic bag.</p>\n\n<p><strong>Remove</strong> any number of beans (<strong>possibly none</strong>) from each bag such that the number of beans in each remaining <strong>non-empty</strong> bag (still containing <strong>at least one</strong> bean) is <strong>equal</strong>. Once a bean has been removed from a bag, you are <strong>not</strong> allowed to return it to any of the bags.</p>\n\n<p>Return <em>the <strong>minimum</strong> number of magic beans that you have to remove</em>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> beans = [4,1,6,5]\n<strong>Output:</strong> 4\n<strong>Explanation:</strong> \n- We remove 1 bean from the bag with only 1 bean.\n  This results in the remaining bags: [4,<strong><u>0</u></strong>,6,5]\n- Then we remove 2 beans from the bag with 6 beans.\n  This results in the remaining bags: [4,0,<strong><u>4</u></strong>,5]\n- Then we remove 1 bean from the bag with 5 beans.\n  This results in the remaining bags: [4,0,4,<strong><u>4</u></strong>]\nWe removed a total of 1 + 2 + 1 = 4 beans to make the remaining non-empty bags have an equal number of beans.\nThere are no other solutions that remove 4 beans or fewer.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> beans = [2,10,3,2]\n<strong>Output:</strong> 7\n<strong>Explanation:</strong>\n- We remove 2 beans from one of the bags with 2 beans.\n  This results in the remaining bags: [<u><strong>0</strong></u>,10,3,2]\n- Then we remove 2 beans from the other bag with 2 beans.\n  This results in the remaining bags: [0,10,3,<u><strong>0</strong></u>]\n- Then we remove 3 beans from the bag with 3 beans. \n  This results in the remaining bags: [0,10,<u><strong>0</strong></u>,0]\nWe removed a total of 2 + 2 + 3 = 7 beans to make the remaining non-empty bags have an equal number of beans.\nThere are no other solutions that removes 7 beans or fewer.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= beans.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= beans[i] &lt;= 10<sup>5</sup></code></li>\n</ul>\n",
            "translatedTitle": "拿出最少数目的魔法豆",
            "translatedContent": "<p>给定一个 <strong>正整数&nbsp;</strong>数组&nbsp;<code>beans</code>&nbsp;，其中每个整数表示一个袋子里装的魔法豆的数目。</p>\n\n<p>请你从每个袋子中&nbsp;<strong>拿出</strong>&nbsp;一些豆子（也可以<strong>&nbsp;不拿出</strong>），使得剩下的 <strong>非空</strong> 袋子中（即 <strong>至少还有一颗</strong>&nbsp;魔法豆的袋子）魔法豆的数目&nbsp;<strong>相等</strong>。一旦把魔法豆从袋子中取出，你不能再将它放到任何袋子中。</p>\n\n<p>请返回你需要拿出魔法豆的 <strong>最少数目</strong>。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre>\n<b>输入：</b>beans = [4,1,6,5]\n<b>输出：</b>4\n<b>解释：</b>\n- 我们从有 1 个魔法豆的袋子中拿出 1 颗魔法豆。\n  剩下袋子中魔法豆的数目为：[4,<u><strong>0</strong></u>,6,5]\n- 然后我们从有 6 个魔法豆的袋子中拿出 2 个魔法豆。\n  剩下袋子中魔法豆的数目为：[4,0,<u><strong>4</strong></u>,5]\n- 然后我们从有 5 个魔法豆的袋子中拿出 1 个魔法豆。\n  剩下袋子中魔法豆的数目为：[4,0,4,<u><strong>4</strong></u>]\n总共拿出了 1 + 2 + 1 = 4 个魔法豆，剩下非空袋子中魔法豆的数目相等。\n没有比取出 4 个魔法豆更少的方案。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<b>输入：</b>beans = [2,10,3,2]\n<b>输出：</b>7\n<strong>解释：</strong>\n- 我们从有 2 个魔法豆的其中一个袋子中拿出 2 个魔法豆。\n  剩下袋子中魔法豆的数目为：[<u><strong>0</strong></u>,10,3,2]\n- 然后我们从另一个有 2 个魔法豆的袋子中拿出 2 个魔法豆。\n  剩下袋子中魔法豆的数目为：[0,10,3,<u><strong>0</strong></u>]\n- 然后我们从有 3 个魔法豆的袋子中拿出 3 个魔法豆。\n  剩下袋子中魔法豆的数目为：[0,10,<u><strong>0</strong></u>,0]\n总共拿出了 2 + 2 + 3 = 7 个魔法豆，剩下非空袋子中魔法豆的数目相等。\n没有比取出 7 个魔法豆更少的方案。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= beans.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= beans[i] &lt;= 10<sup>5</sup></code></li>\n</ul>\n",
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                "Notice that if we choose to make x bags of beans empty, we should choose the x bags with the least amount of beans.",
                "Notice that if the minimum number of beans in a non-empty bag is m, then the best way to make all bags have an equal amount of beans is to reduce all the bags to have m beans.",
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