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<p>There is a tree (i.e. a connected, undirected graph with no cycles) consisting of <code>n</code> nodes numbered from <code>0</code> to <code>n - 1</code> and exactly <code>n - 1</code> edges.</p>
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<p>You are given a <strong>0-indexed</strong> integer array <code>vals</code> of length <code>n</code> where <code>vals[i]</code> denotes the value of the <code>i<sup>th</sup></code> node. You are also given a 2D integer array <code>edges</code> where <code>edges[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> denotes that there exists an <strong>undirected</strong> edge connecting nodes <code>a<sub>i</sub></code> and <code>b<sub>i</sub></code>.</p>
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<p>A <strong>good path</strong> is a simple path that satisfies the following conditions:</p>
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<ol>
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<li>The starting node and the ending node have the <strong>same</strong> value.</li>
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<li>All nodes between the starting node and the ending node have values <strong>less than or equal to</strong> the starting node (i.e. the starting node's value should be the maximum value along the path).</li>
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</ol>
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<p>Return <em>the number of distinct good paths</em>.</p>
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<p>Note that a path and its reverse are counted as the <strong>same</strong> path. For example, <code>0 -> 1</code> is considered to be the same as <code>1 -> 0</code>. A single node is also considered as a valid path.</p>
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<p> </p>
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<p><strong>Example 1:</strong></p>
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<img alt="" src="https://assets.leetcode.com/uploads/2022/08/04/f9caaac15b383af9115c5586779dec5.png" style="width: 400px; height: 333px;" />
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<pre>
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<strong>Input:</strong> vals = [1,3,2,1,3], edges = [[0,1],[0,2],[2,3],[2,4]]
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<strong>Output:</strong> 6
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<strong>Explanation:</strong> There are 5 good paths consisting of a single node.
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There is 1 additional good path: 1 -> 0 -> 2 -> 4.
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(The reverse path 4 -> 2 -> 0 -> 1 is treated as the same as 1 -> 0 -> 2 -> 4.)
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Note that 0 -> 2 -> 3 is not a good path because vals[2] > vals[0].
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</pre>
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<p><strong>Example 2:</strong></p>
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<img alt="" src="https://assets.leetcode.com/uploads/2022/08/04/149d3065ec165a71a1b9aec890776ff.png" style="width: 273px; height: 350px;" />
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<pre>
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<strong>Input:</strong> vals = [1,1,2,2,3], edges = [[0,1],[1,2],[2,3],[2,4]]
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<strong>Output:</strong> 7
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<strong>Explanation:</strong> There are 5 good paths consisting of a single node.
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There are 2 additional good paths: 0 -> 1 and 2 -> 3.
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</pre>
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<p><strong>Example 3:</strong></p>
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<img alt="" src="https://assets.leetcode.com/uploads/2022/08/04/31705e22af3d9c0a557459bc7d1b62d.png" style="width: 100px; height: 88px;" />
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<pre>
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<strong>Input:</strong> vals = [1], edges = []
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<strong>Output:</strong> 1
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<strong>Explanation:</strong> The tree consists of only one node, so there is one good path.
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</pre>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>n == vals.length</code></li>
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<li><code>1 <= n <= 3 * 10<sup>4</sup></code></li>
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<li><code>0 <= vals[i] <= 10<sup>5</sup></code></li>
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<li><code>edges.length == n - 1</code></li>
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<li><code>edges[i].length == 2</code></li>
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<li><code>0 <= a<sub>i</sub>, b<sub>i</sub> < n</code></li>
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<li><code>a<sub>i</sub> != b<sub>i</sub></code></li>
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<li><code>edges</code> represents a valid tree.</li>
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</ul>
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<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code> of size <code>n</code> and a positive integer <code>k</code>.</p>
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<p>We call an index <code>i</code> in the range <code>k <= i < n - k</code> <strong>good</strong> if the following conditions are satisfied:</p>
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<ul>
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<li>The <code>k</code> elements that are just <strong>before</strong> the index <code>i</code> are in <strong>non-increasing</strong> order.</li>
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<li>The <code>k</code> elements that are just <strong>after</strong> the index <code>i</code> are in <strong>non-decreasing</strong> order.</li>
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</ul>
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<p>Return <em>an array of all good indices sorted in <strong>increasing</strong> order</em>.</p>
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<p> </p>
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<p><strong>Example 1:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [2,1,1,1,3,4,1], k = 2
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<strong>Output:</strong> [2,3]
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<strong>Explanation:</strong> There are two good indices in the array:
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- Index 2. The subarray [2,1] is in non-increasing order, and the subarray [1,3] is in non-decreasing order.
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- Index 3. The subarray [1,1] is in non-increasing order, and the subarray [3,4] is in non-decreasing order.
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Note that the index 4 is not good because [4,1] is not non-decreasing.</pre>
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<p><strong>Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [2,1,1,2], k = 2
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<strong>Output:</strong> []
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<strong>Explanation:</strong> There are no good indices in this array.
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</pre>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>n == nums.length</code></li>
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<li><code>3 <= n <= 10<sup>5</sup></code></li>
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<li><code>1 <= nums[i] <= 10<sup>6</sup></code></li>
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<li><code>1 <= k <= n / 2</code></li>
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</ul>
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<p>You are given an integer array <code>nums</code> of size <code>n</code>.</p>
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<p>Consider a <strong>non-empty</strong> subarray from <code>nums</code> that has the <strong>maximum</strong> possible <strong>bitwise AND</strong>.</p>
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<ul>
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<li>In other words, let <code>k</code> be the maximum value of the bitwise AND of <strong>any</strong> subarray of <code>nums</code>. Then, only subarrays with a bitwise AND equal to <code>k</code> should be considered.</li>
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</ul>
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<p>Return <em>the length of the <strong>longest</strong> such subarray</em>.</p>
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<p>The bitwise AND of an array is the bitwise AND of all the numbers in it.</p>
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<p>A <strong>subarray</strong> is a contiguous sequence of elements within an array.</p>
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<p> </p>
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<p><strong>Example 1:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [1,2,3,3,2,2]
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<strong>Output:</strong> 2
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<strong>Explanation:</strong>
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The maximum possible bitwise AND of a subarray is 3.
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The longest subarray with that value is [3,3], so we return 2.
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</pre>
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<p><strong>Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [1,2,3,4]
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<strong>Output:</strong> 1
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<strong>Explanation:</strong>
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The maximum possible bitwise AND of a subarray is 4.
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The longest subarray with that value is [4], so we return 1.
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</pre>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>1 <= nums.length <= 10<sup>5</sup></code></li>
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<li><code>1 <= nums[i] <= 10<sup>6</sup></code></li>
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</ul>
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<p>You are given an array of strings <code>names</code>, and an array <code>heights</code> that consists of <strong>distinct</strong> positive integers. Both arrays are of length <code>n</code>.</p>
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<p>For each index <code>i</code>, <code>names[i]</code> and <code>heights[i]</code> denote the name and height of the <code>i<sup>th</sup></code> person.</p>
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<p>Return <code>names</code><em> sorted in <strong>descending</strong> order by the people's heights</em>.</p>
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<p> </p>
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<p><strong>Example 1:</strong></p>
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<pre>
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<strong>Input:</strong> names = ["Mary","John","Emma"], heights = [180,165,170]
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<strong>Output:</strong> ["Mary","Emma","John"]
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<strong>Explanation:</strong> Mary is the tallest, followed by Emma and John.
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</pre>
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<p><strong>Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> names = ["Alice","Bob","Bob"], heights = [155,185,150]
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<strong>Output:</strong> ["Bob","Alice","Bob"]
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<strong>Explanation:</strong> The first Bob is the tallest, followed by Alice and the second Bob.
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</pre>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>n == names.length == heights.length</code></li>
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<li><code>1 <= n <= 10<sup>3</sup></code></li>
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<li><code>1 <= names[i].length <= 20</code></li>
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<li><code>1 <= heights[i] <= 10<sup>5</sup></code></li>
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<li><code>names[i]</code> consists of lower and upper case English letters.</li>
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<li>All the values of <code>heights</code> are distinct.</li>
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</ul>
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