leetcode-problemset/leetcode-cn/originData/make-costs-of-paths-equal-in-a-binary-tree.json

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            "questionId": "2780",
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            "categoryTitle": "Algorithms",
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            "title": "Make Costs of Paths Equal in a Binary Tree",
            "titleSlug": "make-costs-of-paths-equal-in-a-binary-tree",
            "content": "<p>You are given an integer <code>n</code> representing the number of nodes in a <strong>perfect binary tree</strong> consisting of nodes numbered from <code>1</code> to <code>n</code>. The root of the tree is node <code>1</code> and each node <code>i</code> in the tree has two children where the left child is the node <code>2 * i</code> and the right child is <code>2 * i + 1</code>.</p>\n\n<p>Each node in the tree also has a <strong>cost</strong> represented by a given <strong>0-indexed</strong> integer array <code>cost</code> of size <code>n</code> where <code>cost[i]</code> is the cost of node <code>i + 1</code>. You are allowed to <strong>increment</strong> the cost of <strong>any</strong> node by <code>1</code> <strong>any</strong> number of times.</p>\n\n<p>Return <em>the <strong>minimum</strong> number of increments you need to make the cost of paths from the root to each <strong>leaf</strong> node equal</em>.</p>\n\n<p><strong>Note</strong>:</p>\n\n<ul>\n\t<li>A <strong>perfect binary tree </strong>is a tree where each node, except the leaf nodes, has exactly 2 children.</li>\n\t<li>The <strong>cost of a path</strong> is the sum of costs of nodes in the path.</li>\n</ul>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/04/04/binaryytreeedrawio-4.png\" />\n<pre>\n<strong>Input:</strong> n = 7, cost = [1,5,2,2,3,3,1]\n<strong>Output:</strong> 6\n<strong>Explanation:</strong> We can do the following increments:\n- Increase the cost of node 4 one time.\n- Increase the cost of node 3 three times.\n- Increase the cost of node 7 two times.\nEach path from the root to a leaf will have a total cost of 9.\nThe total increments we did is 1 + 3 + 2 = 6.\nIt can be shown that this is the minimum answer we can achieve.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/04/04/binaryytreee2drawio.png\" style=\"width: 205px; height: 151px;\" />\n<pre>\n<strong>Input:</strong> n = 3, cost = [5,3,3]\n<strong>Output:</strong> 0\n<strong>Explanation:</strong> The two paths already have equal total costs, so no increments are needed.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>3 &lt;= n &lt;= 10<sup>5</sup></code></li>\n\t<li><code>n + 1</code> is a power of <code>2</code></li>\n\t<li><code>cost.length == n</code></li>\n\t<li><code>1 &lt;= cost[i] &lt;= 10<sup>4</sup></code></li>\n</ul>\n",
            "translatedTitle": "使二叉树所有路径值相等的最小代价",
            "translatedContent": "<p>给你一个整数&nbsp;<code>n</code>&nbsp;表示一棵 <b>满二叉树</b>&nbsp;里面节点的数目，节点编号从 <code>1</code>&nbsp;到 <code>n</code>&nbsp;。根节点编号为 <code>1</code>&nbsp;，树中每个非叶子节点&nbsp;<code>i</code>&nbsp;都有两个孩子，分别是左孩子&nbsp;<code>2 * i</code>&nbsp;和右孩子&nbsp;<code>2 * i + 1</code>&nbsp;。</p>\n\n<p>树中每个节点都有一个值，用下标从<b>&nbsp;0</b>&nbsp;开始、长度为 <code>n</code>&nbsp;的整数数组&nbsp;<code>cost</code>&nbsp;表示，其中&nbsp;<code>cost[i]</code>&nbsp;是第&nbsp;<code>i + 1</code>&nbsp;个节点的值。每次操作，你可以将树中&nbsp;<strong>任意</strong>&nbsp;节点的值&nbsp;<strong>增加</strong>&nbsp;<code>1</code>&nbsp;。你可以执行操作 <strong>任意</strong> 次。</p>\n\n<p>你的目标是让根到每一个 <strong>叶子结点</strong>&nbsp;的路径值相等。请你返回 <strong>最少</strong>&nbsp;需要执行增加操作多少次。</p>\n\n<p><b>注意：</b></p>\n\n<ul>\n\t<li><strong>满二叉树</strong>&nbsp;指的是一棵树，它满足树中除了叶子节点外每个节点都恰好有 2 个节点，且所有叶子节点距离根节点距离相同。</li>\n\t<li><strong>路径值</strong> 指的是路径上所有节点的值之和。</li>\n</ul>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/04/04/binaryytreeedrawio-4.png\" /></p>\n\n<pre>\n<b>输入：</b>n = 7, cost = [1,5,2,2,3,3,1]\n<b>输出：</b>6\n<b>解释：</b>我们执行以下的增加操作：\n- 将节点 4 的值增加一次。\n- 将节点 3 的值增加三次。\n- 将节点 7 的值增加两次。\n从根到叶子的每一条路径值都为 9 。\n总共增加次数为 1 + 3 + 2 = 6 。\n这是最小的答案。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/04/04/binaryytreee2drawio.png\" style=\"width: 205px; height: 151px;\" /></p>\n\n<pre>\n<b>输入：</b>n = 3, cost = [5,3,3]\n<b>输出：</b>0\n<b>解释：</b>两条路径已经有相等的路径值，所以不需要执行任何增加操作。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>3 &lt;= n &lt;= 10<sup>5</sup></code></li>\n\t<li><code>n + 1</code> 是&nbsp;<code>2</code>&nbsp;的幂</li>\n\t<li><code>cost.length == n</code></li>\n\t<li><code>1 &lt;= cost[i] &lt;= 10<sup>4</sup></code></li>\n</ul>\n",
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