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{
"data": {
"question": {
"questionId": "1000009",
"questionFrontendId": "面试题 04.12",
"categoryTitle": "LCCI",
"boundTopicId": 91459,
"title": "Paths with Sum LCCI",
"titleSlug": "paths-with-sum-lcci",
"content": "<p>You are given a binary tree in which each node contains an integer value (which might be positive or negative). Design an algorithm to count the number of paths that sum to a given value. The path does not need to start or end at the root or a leaf, but it must go downwards (traveling only from parent nodes to child nodes).</p>\r\n\r\n<p><strong>Example:</strong><br />\r\nGiven the following tree and &nbsp;<code>sum = 22,</code></p>\r\n\r\n<pre>\r\n 5\r\n / \\\r\n 4 8\r\n / / \\\r\n 11 13 4\r\n / \\ / \\\r\n 7 2 5 1\r\n</pre>\r\n\r\n<p>Output:</p>\r\n\r\n<pre>\r\n3\r\n<strong>Explanation: </strong>Paths that have sum 22 are: [5,4,11,2], [5,8,4,5], [4,11,7]</pre>\r\n\r\n<p>Note:</p>\r\n\r\n<ul>\r\n\t<li><code>node number &lt;= 10000</code></li>\r\n</ul>\r\n",
"translatedTitle": "求和路径",
"translatedContent": "<p>给定一棵二叉树,其中每个节点都含有一个整数数值(该值或正或负)。设计一个算法,打印节点数值总和等于某个给定值的所有路径的数量。注意,路径不一定非得从二叉树的根节点或叶节点开始或结束,但是其方向必须向下(只能从父节点指向子节点方向)。</p>\n\n<p><strong>示例:</strong><br>\n给定如下二叉树以及目标和&nbsp;<code>sum = 22</code></p>\n\n<pre> 5\n / \\\n 4 8\n / / \\\n 11 13 4\n / \\ / \\\n 7 2 5 1\n</pre>\n\n<p>返回:</p>\n\n<pre>3\n<strong>解释:</strong>和为 22&nbsp;的路径有:[5,4,11,2], [5,8,4,5], [4,11,7]</pre>\n\n<p>提示:</p>\n\n<ul>\n\t<li><code>节点总数 &lt;= 10000</code></li>\n</ul>\n",
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"hints": [
"尝试简化问题。如果路径必须从根开始会如何?",
"不要忘记路径可能会重叠。例如如果你正在寻找总和6那么路径1 -> 3 -> 2和1 -> 3 -> 2 -> 4 -> 6 -> 2都是有效的。",
"如果每条路径必须从根开始就从根开始遍历所有可能的路径。可以在遍历的同时追踪和每次找到一个路径满足我们的目标和就增加totalpaths的值。现在如何将它扩展到可以在任何地方开始呢记住只需要一个蛮力算法即可完成。你可以稍后再优化。",
"为了将其扩展到从任何地方开始的路径,我们可以对所有节点重复此过程。",
"如果你已经设计了以上描述的算法那么在平衡树中你会有一个O(NlogN)的算法。这是因为共N个节点在最坏情况下每个节点的深度是O(logN)。节点上方的每个节点都会访问一次。因此N个节点将被访问O(logN)的时间。有一种优化算法其运行时间为O(N)。",
"在当前的蛮力算法中重复了什么工作?",
"从根开始考虑每个路径有n个这样的路径作为一个数组。该蛮力算法具体运作如下拿着每个数组来寻找所有具有特定和的连续子序列。我们这样做是计算了所有子数组以及它们的和。把目光聚焦在这个小问题上可能会大有裨益。给定一个数组你如何寻找具有特定和的所有连续子序列同样想想蛮力算法中的重复工作。",
"我们正在寻找和为targetSum的子数组。注意可以在常数时间得到runningSumi的值这是从元素0到元素i的和。一个从i到j的子数组和为targetSum则 runningSumi-1 + targetSum必须等于runningSumj试着画一个数组或一条数字线。随着往下走可以追踪runningSum那么如何能快速查找i对应的使前面等式成立的值",
"尝试使用一个散列表从runningSum的值映射到使用runningSum元素的个数。",
"一旦你完成了这样的算法,找出了和为给定值的所有连续子数组,试着将它应用到一棵树上。请记住,在遍历和修改散列表时,你可能需要在遍历回来时将散列表的“损坏”逆转。"
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href=\\\"https:\\/\\/github.com\\/emirpasic\\/gods\\/tree\\/v1.18.1\\\" target=\\\"_blank\\\">https:\\/\\/godoc.org\\/github.com\\/emirpasic\\/gods@v1.18.1<\\/a> \\u7b2c\\u4e09\\u65b9\\u5e93\\u3002<\\/p>\"],\"python3\":[\"Python3\",\"<p>\\u7248\\u672c\\uff1a<code>Python 3.10<\\/code><\\/p>\\r\\n\\r\\n<p>\\u4e3a\\u4e86\\u65b9\\u4fbf\\u8d77\\u89c1\\uff0c\\u5927\\u90e8\\u5206\\u5e38\\u7528\\u5e93\\u5df2\\u7ecf\\u88ab\\u81ea\\u52a8 \\u5bfc\\u5165\\uff0c\\u5982<a href=\\\"https:\\/\\/docs.python.org\\/3\\/library\\/array.html\\\" target=\\\"_blank\\\">array<\\/a>, <a href=\\\"https:\\/\\/docs.python.org\\/3\\/library\\/bisect.html\\\" target=\\\"_blank\\\">bisect<\\/a>, <a href=\\\"https:\\/\\/docs.python.org\\/3\\/library\\/collections.html\\\" target=\\\"_blank\\\">collections<\\/a>\\u3002 \\u5982\\u679c\\u60a8\\u9700\\u8981\\u4f7f\\u7528\\u5176\\u4ed6\\u5e93\\u51fd\\u6570\\uff0c\\u8bf7\\u81ea\\u884c\\u5bfc\\u5165\\u3002<\\/p>\\r\\n\\r\\n<p>\\u5982\\u9700\\u4f7f\\u7528 Map\\/TreeMap 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