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            "questionId": "3402",
            "questionFrontendId": "3139",
            "categoryTitle": "Algorithms",
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            "title": "Minimum Cost to Equalize Array",
            "titleSlug": "minimum-cost-to-equalize-array",
            "content": "<p>You are given an integer array <code>nums</code> and two integers <code>cost1</code> and <code>cost2</code>. You are allowed to perform <strong>either</strong> of the following operations <strong>any</strong> number of times:</p>\n\n<ul>\n\t<li>Choose an index <code>i</code> from <code>nums</code> and <strong>increase</strong> <code>nums[i]</code> by <code>1</code> for a cost of <code>cost1</code>.</li>\n\t<li>Choose two <strong>different</strong> indices <code>i</code>, <code>j</code>, from <code>nums</code> and <strong>increase</strong> <code>nums[i]</code> and <code>nums[j]</code> by <code>1</code> for a cost of <code>cost2</code>.</li>\n</ul>\n\n<p>Return the <strong>minimum</strong> <strong>cost</strong> required to make all elements in the array <strong>equal</strong><em>. </em></p>\n\n<p>Since the answer may be very large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">nums = [4,1], cost1 = 5, cost2 = 2</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">15</span></p>\n\n<p><strong>Explanation: </strong></p>\n\n<p>The following operations can be performed to make the values equal:</p>\n\n<ul>\n\t<li>Increase <code>nums[1]</code> by 1 for a cost of 5. <code>nums</code> becomes <code>[4,2]</code>.</li>\n\t<li>Increase <code>nums[1]</code> by 1 for a cost of 5. <code>nums</code> becomes <code>[4,3]</code>.</li>\n\t<li>Increase <code>nums[1]</code> by 1 for a cost of 5. <code>nums</code> becomes <code>[4,4]</code>.</li>\n</ul>\n\n<p>The total cost is 15.</p>\n</div>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">nums = [2,3,3,3,5], cost1 = 2, cost2 = 1</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">6</span></p>\n\n<p><strong>Explanation: </strong></p>\n\n<p>The following operations can be performed to make the values equal:</p>\n\n<ul>\n\t<li>Increase <code>nums[0]</code> and <code>nums[1]</code> by 1 for a cost of 1. <code>nums</code> becomes <code>[3,4,3,3,5]</code>.</li>\n\t<li>Increase <code>nums[0]</code> and <code>nums[2]</code> by 1 for a cost of 1. <code>nums</code> becomes <code>[4,4,4,3,5]</code>.</li>\n\t<li>Increase <code>nums[0]</code> and <code>nums[3]</code> by 1 for a cost of 1. <code>nums</code> becomes <code>[5,4,4,4,5]</code>.</li>\n\t<li>Increase <code>nums[1]</code> and <code>nums[2]</code> by 1 for a cost of 1. <code>nums</code> becomes <code>[5,5,5,4,5]</code>.</li>\n\t<li>Increase <code>nums[3]</code> by 1 for a cost of 2. <code>nums</code> becomes <code>[5,5,5,5,5]</code>.</li>\n</ul>\n\n<p>The total cost is 6.</p>\n</div>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">nums = [3,5,3], cost1 = 1, cost2 = 3</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">4</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>The following operations can be performed to make the values equal:</p>\n\n<ul>\n\t<li>Increase <code>nums[0]</code> by 1 for a cost of 1. <code>nums</code> becomes <code>[4,5,3]</code>.</li>\n\t<li>Increase <code>nums[0]</code> by 1 for a cost of 1. <code>nums</code> becomes <code>[5,5,3]</code>.</li>\n\t<li>Increase <code>nums[2]</code> by 1 for a cost of 1. <code>nums</code> becomes <code>[5,5,4]</code>.</li>\n\t<li>Increase <code>nums[2]</code> by 1 for a cost of 1. <code>nums</code> becomes <code>[5,5,5]</code>.</li>\n</ul>\n\n<p>The total cost is 4.</p>\n</div>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 10<sup>6</sup></code></li>\n\t<li><code>1 &lt;= cost1 &lt;= 10<sup>6</sup></code></li>\n\t<li><code>1 &lt;= cost2 &lt;= 10<sup>6</sup></code></li>\n</ul>\n",
            "translatedTitle": "使数组中所有元素相等的最小开销",
            "translatedContent": "<p>给你一个整数数组&nbsp;<code>nums</code>&nbsp;和两个整数&nbsp;<code>cost1</code> 和&nbsp;<code>cost2</code>&nbsp;。你可以执行以下&nbsp;<strong>任一</strong>&nbsp;操作&nbsp;<strong>任意</strong>&nbsp;次：</p>\n\n<ul>\n\t<li>从 <code>nums</code>&nbsp;中选择下标 <code>i</code>&nbsp;并且将 <code>nums[i]</code>&nbsp;<strong>增加</strong> <code>1</code>&nbsp;，开销为 <code>cost1</code>。</li>\n\t<li>选择 <code>nums</code>&nbsp;中两个 <strong>不同</strong>&nbsp;下标 <code>i</code>&nbsp;和 <code>j</code>&nbsp;，并且将 <code>nums[i]</code>&nbsp;和 <code>nums[j]</code>&nbsp;都&nbsp;<strong>增加</strong> <code>1</code>&nbsp;，开销为 <code>cost2</code>&nbsp;。</li>\n</ul>\n\n<p>你的目标是使数组中所有元素都 <strong>相等</strong>&nbsp;，请你返回需要的 <strong>最小开销</strong>&nbsp;之和。</p>\n\n<p>由于答案可能会很大，请你将它对&nbsp;<code>10<sup>9</sup> + 7</code>&nbsp;<strong>取余</strong>&nbsp;后返回。</p>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<div class=\"example-block\">\n<p><span class=\"example-io\"><b>输入：</b>nums = [4,1], cost1 = 5, cost2 = 2</span></p>\n\n<p><span class=\"example-io\"><b>输出：</b>15</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p>执行以下操作可以使数组中所有元素相等：</p>\n\n<ul>\n\t<li>将&nbsp;<code>nums[1]</code>&nbsp;增加 1 ，开销为 5 ，<code>nums</code> 变为&nbsp;<code>[4,2]</code>&nbsp;。</li>\n\t<li>将&nbsp;<code>nums[1]</code>&nbsp;增加 1 ，开销为 5 ，<code>nums</code> 变为&nbsp;<code>[4,3]</code>&nbsp;。</li>\n\t<li>将&nbsp;<code>nums[1]</code>&nbsp;增加 1 ，开销为 5 ，<code>nums</code> 变为&nbsp;<code>[4,4]</code>&nbsp;。</li>\n</ul>\n\n<p>总开销为 15 。</p>\n</div>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<div class=\"example-block\">\n<p><strong>输入：</strong><span class=\"example-io\">nums = [2,3,3,3,5], cost1 = 2, cost2 = 1</span></p>\n\n<p><span class=\"example-io\"><b>输出：</b>6</span></p>\n\n<p><b>解释：</b></p>\n\n<p>执行以下操作可以使数组中所有元素相等：</p>\n\n<ul>\n\t<li>将&nbsp;<code>nums[0]</code> 和&nbsp;<code>nums[1]</code>&nbsp;同时增加 1 ，开销为 1 ，<code>nums</code> 变为&nbsp;<code>[3,4,3,3,5]</code>&nbsp;。</li>\n\t<li>将&nbsp;<code>nums[0]</code> 和&nbsp;<code>nums[2]</code>&nbsp;同时增加 1 ，开销为 1 ，<code>nums</code> 变为&nbsp;<code>[4,4,4,3,5]</code>&nbsp;。</li>\n\t<li>将&nbsp;<code>nums[0]</code> 和&nbsp;<code>nums[3]</code>&nbsp;同时增加 1 ，开销为 1 ，<code>nums</code> 变为&nbsp;<code>[5,4,4,4,5]</code>&nbsp;。</li>\n\t<li>将&nbsp;<code>nums[1]</code> 和&nbsp;<code>nums[2]</code>&nbsp;同时增加 1 ，开销为 1 ，<code>nums</code> 变为&nbsp;<code>[5,5,5,4,5]</code>&nbsp;。</li>\n\t<li>将&nbsp;<code>nums[3]</code>&nbsp;增加 1 ，开销为 2 ，<code>nums</code> 变为&nbsp;<code>[5,5,5,5,5]</code>&nbsp;。</li>\n</ul>\n\n<p>总开销为 6 。</p>\n</div>\n\n<p><strong class=\"example\">示例 3：</strong></p>\n\n<div class=\"example-block\">\n<p><span class=\"example-io\"><b>输入：</b>nums = [3,5,3], cost1 = 1, cost2 = 3</span></p>\n\n<p><span class=\"example-io\"><b>输出：</b>4</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p>执行以下操作可以使数组中所有元素相等：</p>\n\n<ul>\n\t<li>将&nbsp;<code>nums[0]</code>&nbsp;增加 1 ，开销为 1 ，<code>nums</code> 变为&nbsp;<code>[4,5,3]</code>&nbsp;。</li>\n\t<li>将&nbsp;<code>nums[0]</code>&nbsp;增加 1 ，开销为 1 ，<code>nums</code> 变为&nbsp;<code>[5,5,3]</code>&nbsp;。</li>\n\t<li>将&nbsp;<code>nums[2]</code>&nbsp;增加 1 ，开销为 1 ，<code>nums</code> 变为&nbsp;<code>[5,5,4]</code>&nbsp;。</li>\n\t<li>将&nbsp;<code>nums[2]</code>&nbsp;增加 1 ，开销为 1 ，<code>nums</code> 变为&nbsp;<code>[5,5,5]</code>&nbsp;。</li>\n</ul>\n\n<p>总开销为 4 。</p>\n</div>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 10<sup>6</sup></code></li>\n\t<li><code>1 &lt;= cost1 &lt;= 10<sup>6</sup></code></li>\n\t<li><code>1 &lt;= cost2 &lt;= 10<sup>6</sup></code></li>\n</ul>\n",
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                "How can you determine the minimum cost if you know the maximum value in the array once all values are made equal?",
                "If <code>cost2 > cost1 * 2</code>, we should just use <code>cost1</code> to change all the values to the maximum one.",
                "Otherwise, it's optimal to choose the smallest two values and use <code>cost2</code> to increase both of them.",
                "Since the maximum value is known, calculate the required increases to equalize all values, instead of naively simulating the operations.",
                "There are not a lot of candidates for the maximum; we can try all of them and choose which uses the minimum number of operations."
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