{ "data": { "question": { "questionId": "2780", "questionFrontendId": "2673", "categoryTitle": "Algorithms", "boundTopicId": 2254957, "title": "Make Costs of Paths Equal in a Binary Tree", "titleSlug": "make-costs-of-paths-equal-in-a-binary-tree", "content": "

You are given an integer n representing the number of nodes in a perfect binary tree consisting of nodes numbered from 1 to n. The root of the tree is node 1 and each node i in the tree has two children where the left child is the node 2 * i and the right child is 2 * i + 1.

\n\n

Each node in the tree also has a cost represented by a given 0-indexed integer array cost of size n where cost[i] is the cost of node i + 1. You are allowed to increment the cost of any node by 1 any number of times.

\n\n

Return the minimum number of increments you need to make the cost of paths from the root to each leaf node equal.

\n\n

Note:

\n\n\n\n

 

\n

Example 1:

\n\"\"\n
\nInput: n = 7, cost = [1,5,2,2,3,3,1]\nOutput: 6\nExplanation: 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
\n\n

Example 2:

\n\"\"\n
\nInput: n = 3, cost = [5,3,3]\nOutput: 0\nExplanation: The two paths already have equal total costs, so no increments are needed.\n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "使二叉树所有路径值相等的最小代价", "translatedContent": "

给你一个整数 n 表示一棵 满二叉树 里面节点的数目，节点编号从 1 到 n 。根节点编号为 1 ，树中每个非叶子节点 i 都有两个孩子，分别是左孩子 2 * i 和右孩子 2 * i + 1 。

\n\n

树中每个节点都有一个值，用下标从 0 开始、长度为 n 的整数数组 cost 表示，其中 cost[i] 是第 i + 1 个节点的值。每次操作，你可以将树中 任意 节点的值 增加 1 。你可以执行操作 任意 次。

\n\n

你的目标是让根到每一个 叶子结点 的路径值相等。请你返回 最少 需要执行增加操作多少次。

\n\n

注意：

\n\n\n\n

 

\n\n

示例 1：

\n\n

\"\"

\n\n
\n输入：n = 7, cost = [1,5,2,2,3,3,1]\n输出：6\n解释：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
\n\n

示例 2：

\n\n

\"\"

\n\n
\n输入：n = 3, cost = [5,3,3]\n输出：0\n解释：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
\n\n

 

\n\n

提示：

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