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<p>There is a circle of red and blue tiles. You are given an array of integers <code>colors</code>. The color of tile <code>i</code> is represented by <code>colors[i]</code>:</p>
<ul>
<li><code>colors[i] == 0</code> means that tile <code>i</code> is <strong>red</strong>.</li>
<li><code>colors[i] == 1</code> means that tile <code>i</code> is <strong>blue</strong>.</li>
</ul>
<p>Every 3 contiguous tiles in the circle with <strong>alternating</strong> colors (the middle tile has a different color from its <strong>left</strong> and <strong>right</strong> tiles) is called an <strong>alternating</strong> group.</p>
<p>Return the number of <strong>alternating</strong> groups.</p>
<p><strong>Note</strong> that since <code>colors</code> represents a <strong>circle</strong>, the <strong>first</strong> and the <strong>last</strong> tiles are considered to be next to each other.</p>
<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">colors = [1,1,1]</span></p>
<p><strong>Output:</strong> <span class="example-io">0</span></p>
<p><strong>Explanation:</strong></p>
<p><img alt="" src="https://assets.leetcode.com/uploads/2024/05/16/image_2024-05-16_23-53-171.png" style="width: 150px; height: 150px; padding: 10px; background: #fff; border-radius: .5rem;" /></p>
</div>
<p><strong class="example">Example 2:</strong></p>
<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">colors = [0,1,0,0,1]</span></p>
<p><strong>Output:</strong> 3</p>
<p><strong>Explanation:</strong></p>
<p><img alt="" src="https://assets.leetcode.com/uploads/2024/05/16/image_2024-05-16_23-47-491.png" style="width: 150px; height: 150px; padding: 10px; background: #fff; border-radius: .5rem;" /></p>
<p>Alternating groups:</p>
<p><strong class="example"><img alt="" src="https://assets.leetcode.com/uploads/2024/05/16/image_2024-05-16_23-50-441.png" style="width: 150px; height: 150px; padding: 10px; background: #fff; border-radius: .5rem;" /></strong><img alt="" src="https://assets.leetcode.com/uploads/2024/05/16/image_2024-05-16_23-48-211.png" style="width: 150px; height: 150px; padding: 10px; background: #fff; border-radius: .5rem;" /><strong class="example"><img alt="" src="https://assets.leetcode.com/uploads/2024/05/16/image_2024-05-16_23-49-351.png" style="width: 150px; height: 150px; padding: 10px; background: #fff; border-radius: .5rem;" /></strong></p>
</div>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>
<ul>
<li><code>3 &lt;= colors.length &lt;= 100</code></li>
<li><code>0 &lt;= colors[i] &lt;= 1</code></li>
</ul>

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<p>There is a circle of red and blue tiles. You are given an array of integers <code>colors</code> and an integer <code>k</code>. The color of tile <code>i</code> is represented by <code>colors[i]</code>:</p>
<ul>
<li><code>colors[i] == 0</code> means that tile <code>i</code> is <strong>red</strong>.</li>
<li><code>colors[i] == 1</code> means that tile <code>i</code> is <strong>blue</strong>.</li>
</ul>
<p>An <strong>alternating</strong> group is every <code>k</code> contiguous tiles in the circle with <strong>alternating</strong> colors (each tile in the group except the first and last one has a different color from its <strong>left</strong> and <strong>right</strong> tiles).</p>
<p>Return the number of <strong>alternating</strong> groups.</p>
<p><strong>Note</strong> that since <code>colors</code> represents a <strong>circle</strong>, the <strong>first</strong> and the <strong>last</strong> tiles are considered to be next to each other.</p>
<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">colors = [0,1,0,1,0], k = 3</span></p>
<p><strong>Output:</strong> <span class="example-io">3</span></p>
<p><strong>Explanation:</strong></p>
<p><strong><img alt="" data-darkreader-inline-bgcolor="" data-darkreader-inline-bgimage="" src="https://assets.leetcode.com/uploads/2024/06/19/screenshot-2024-05-28-183519.png" style="width: 150px; height: 150px; padding: 10px; background: rgb(255, 255, 255); border-radius: 0.5rem; --darkreader-inline-bgimage: initial; --darkreader-inline-bgcolor: #181a1b;" /></strong></p>
<p>Alternating groups:</p>
<p><img alt="" data-darkreader-inline-bgcolor="" data-darkreader-inline-bgimage="" src="https://assets.leetcode.com/uploads/2024/05/28/screenshot-2024-05-28-182448.png" style="width: 150px; height: 150px; padding: 10px; background: rgb(255, 255, 255); border-radius: 0.5rem; --darkreader-inline-bgimage: initial; --darkreader-inline-bgcolor: #181a1b;" /><img alt="" data-darkreader-inline-bgcolor="" data-darkreader-inline-bgimage="" src="https://assets.leetcode.com/uploads/2024/05/28/screenshot-2024-05-28-182844.png" style="width: 150px; height: 150px; padding: 10px; background: rgb(255, 255, 255); border-radius: 0.5rem; --darkreader-inline-bgimage: initial; --darkreader-inline-bgcolor: #181a1b;" /><img alt="" data-darkreader-inline-bgcolor="" data-darkreader-inline-bgimage="" src="https://assets.leetcode.com/uploads/2024/05/28/screenshot-2024-05-28-183057.png" style="width: 150px; height: 150px; padding: 10px; background: rgb(255, 255, 255); border-radius: 0.5rem; --darkreader-inline-bgimage: initial; --darkreader-inline-bgcolor: #181a1b;" /></p>
</div>
<p><strong class="example">Example 2:</strong></p>
<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">colors = [0,1,0,0,1,0,1], k = 6</span></p>
<p><strong>Output:</strong> <span class="example-io">2</span></p>
<p><strong>Explanation:</strong></p>
<p><strong><img alt="" data-darkreader-inline-bgcolor="" data-darkreader-inline-bgimage="" src="https://assets.leetcode.com/uploads/2024/06/19/screenshot-2024-05-28-183907.png" style="width: 150px; height: 150px; padding: 10px; background: rgb(255, 255, 255); border-radius: 0.5rem; --darkreader-inline-bgimage: initial; --darkreader-inline-bgcolor: #181a1b;" /></strong></p>
<p>Alternating groups:</p>
<p><img alt="" data-darkreader-inline-bgcolor="" data-darkreader-inline-bgimage="" src="https://assets.leetcode.com/uploads/2024/06/19/screenshot-2024-05-28-184128.png" style="width: 150px; height: 150px; padding: 10px; background: rgb(255, 255, 255); border-radius: 0.5rem; --darkreader-inline-bgimage: initial; --darkreader-inline-bgcolor: #181a1b;" /><img alt="" data-darkreader-inline-bgcolor="" data-darkreader-inline-bgimage="" src="https://assets.leetcode.com/uploads/2024/06/19/screenshot-2024-05-28-184240.png" style="width: 150px; height: 150px; padding: 10px; background: rgb(255, 255, 255); border-radius: 0.5rem; --darkreader-inline-bgimage: initial; --darkreader-inline-bgcolor: #181a1b;" /></p>
</div>
<p><strong class="example">Example 3:</strong></p>
<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">colors = [1,1,0,1], k = 4</span></p>
<p><strong>Output:</strong> <span class="example-io">0</span></p>
<p><strong>Explanation:</strong></p>
<p><img alt="" data-darkreader-inline-bgcolor="" data-darkreader-inline-bgimage="" src="https://assets.leetcode.com/uploads/2024/06/19/screenshot-2024-05-28-184516.png" style="width: 150px; height: 150px; padding: 10px; background: rgb(255, 255, 255); border-radius: 0.5rem; --darkreader-inline-bgimage: initial; --darkreader-inline-bgcolor: #181a1b;" /></p>
</div>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>
<ul>
<li><code>3 &lt;= colors.length &lt;= 10<sup>5</sup></code></li>
<li><code>0 &lt;= colors[i] &lt;= 1</code></li>
<li><code>3 &lt;= k &lt;= colors.length</code></li>
</ul>

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<p>You are given a string <code>target</code>, an array of strings <code>words</code>, and an integer array <code>costs</code>, both arrays of the same length.</p>
<p>Imagine an empty string <code>s</code>.</p>
<p>You can perform the following operation any number of times (including <strong>zero</strong>):</p>
<ul>
<li>Choose an index <code>i</code> in the range <code>[0, words.length - 1]</code>.</li>
<li>Append <code>words[i]</code> to <code>s</code>.</li>
<li>The cost of operation is <code>costs[i]</code>.</li>
</ul>
<p>Return the <strong>minimum</strong> cost to make <code>s</code> equal to <code>target</code>. If it&#39;s not possible, return <code>-1</code>.</p>
<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">target = &quot;abcdef&quot;, words = [&quot;abdef&quot;,&quot;abc&quot;,&quot;d&quot;,&quot;def&quot;,&quot;ef&quot;], costs = [100,1,1,10,5]</span></p>
<p><strong>Output:</strong> <span class="example-io">7</span></p>
<p><strong>Explanation:</strong></p>
<p>The minimum cost can be achieved by performing the following operations:</p>
<ul>
<li>Select index 1 and append <code>&quot;abc&quot;</code> to <code>s</code> at a cost of 1, resulting in <code>s = &quot;abc&quot;</code>.</li>
<li>Select index 2 and append <code>&quot;d&quot;</code> to <code>s</code> at a cost of 1, resulting in <code>s = &quot;abcd&quot;</code>.</li>
<li>Select index 4 and append <code>&quot;ef&quot;</code> to <code>s</code> at a cost of 5, resulting in <code>s = &quot;abcdef&quot;</code>.</li>
</ul>
</div>
<p><strong class="example">Example 2:</strong></p>
<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">target = &quot;aaaa&quot;, words = [&quot;z&quot;,&quot;zz&quot;,&quot;zzz&quot;], costs = [1,10,100]</span></p>
<p><strong>Output:</strong> <span class="example-io">-1</span></p>
<p><strong>Explanation:</strong></p>
<p>It is impossible to make <code>s</code> equal to <code>target</code>, so we return -1.</p>
</div>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>
<ul>
<li><code>1 &lt;= target.length &lt;= 5 * 10<sup>4</sup></code></li>
<li><code>1 &lt;= words.length == costs.length &lt;= 5 * 10<sup>4</sup></code></li>
<li><code>1 &lt;= words[i].length &lt;= target.length</code></li>
<li>The total sum of <code>words[i].length</code> is less than or equal to <code>5 * 10<sup>4</sup></code>.</li>
<li><code>target</code> and <code>words[i]</code> consist only of lowercase English letters.</li>
<li><code>1 &lt;= costs[i] &lt;= 10<sup>4</sup></code></li>
</ul>

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<p>Given a 2D character matrix <code>grid</code>, where <code>grid[i][j]</code> is either <code>&#39;X&#39;</code>, <code>&#39;Y&#39;</code>, or <code>&#39;.&#39;</code>, return the number of <span data-keyword="submatrix">submatrices</span> that contain:</p>
<ul>
<li><code>grid[0][0]</code></li>
<li>an <strong>equal</strong> frequency of <code>&#39;X&#39;</code> and <code>&#39;Y&#39;</code>.</li>
<li><strong>at least</strong> one <code>&#39;X&#39;</code>.</li>
</ul>
<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">grid = [[&quot;X&quot;,&quot;Y&quot;,&quot;.&quot;],[&quot;Y&quot;,&quot;.&quot;,&quot;.&quot;]]</span></p>
<p><strong>Output:</strong> <span class="example-io">3</span></p>
<p><strong>Explanation:</strong></p>
<p><strong><img alt="" src="https://assets.leetcode.com/uploads/2024/06/07/examplems.png" style="padding: 10px; background: rgb(255, 255, 255); border-radius: 0.5rem; width: 175px; height: 350px;" /></strong></p>
</div>
<p><strong class="example">Example 2:</strong></p>
<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">grid = [[&quot;X&quot;,&quot;X&quot;],[&quot;X&quot;,&quot;Y&quot;]]</span></p>
<p><strong>Output:</strong> <span class="example-io">0</span></p>
<p><strong>Explanation:</strong></p>
<p>No submatrix has an equal frequency of <code>&#39;X&#39;</code> and <code>&#39;Y&#39;</code>.</p>
</div>
<p><strong class="example">Example 3:</strong></p>
<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">grid = [[&quot;.&quot;,&quot;.&quot;],[&quot;.&quot;,&quot;.&quot;]]</span></p>
<p><strong>Output:</strong> <span class="example-io">0</span></p>
<p><strong>Explanation:</strong></p>
<p>No submatrix has at least one <code>&#39;X&#39;</code>.</p>
</div>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>
<ul>
<li><code>1 &lt;= grid.length, grid[i].length &lt;= 1000</code></li>
<li><code>grid[i][j]</code> is either <code>&#39;X&#39;</code>, <code>&#39;Y&#39;</code>, or <code>&#39;.&#39;</code>.</li>
</ul>

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<p>You are given an array of integers <code>nums</code> and the <code>head</code> of a linked list. Return the <code>head</code> of the modified linked list after <strong>removing</strong> all nodes from the linked list that have a value that exists in <code>nums</code>.</p>
<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">nums = [1,2,3], head = [1,2,3,4,5]</span></p>
<p><strong>Output:</strong> <span class="example-io">[4,5]</span></p>
<p><strong>Explanation:</strong></p>
<p><strong><img alt="" src="https://assets.leetcode.com/uploads/2024/06/11/linkedlistexample0.png" style="width: 400px; height: 66px;" /></strong></p>
<p>Remove the nodes with values 1, 2, and 3.</p>
</div>
<p><strong class="example">Example 2:</strong></p>
<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">nums = [1], head = [1,2,1,2,1,2]</span></p>
<p><strong>Output:</strong> <span class="example-io">[2,2,2]</span></p>
<p><strong>Explanation:</strong></p>
<p><img alt="" src="https://assets.leetcode.com/uploads/2024/06/11/linkedlistexample1.png" style="height: 62px; width: 450px;" /></p>
<p>Remove the nodes with value 1.</p>
</div>
<p><strong class="example">Example 3:</strong></p>
<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">nums = [5], head = [1,2,3,4]</span></p>
<p><strong>Output:</strong> <span class="example-io">[1,2,3,4]</span></p>
<p><strong>Explanation:</strong></p>
<p><strong><img alt="" src="https://assets.leetcode.com/uploads/2024/06/11/linkedlistexample2.png" style="width: 400px; height: 83px;" /></strong></p>
<p>No node has value 5.</p>
</div>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>
<ul>
<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
<li><code>1 &lt;= nums[i] &lt;= 10<sup>5</sup></code></li>
<li>All elements in <code>nums</code> are unique.</li>
<li>The number of nodes in the given list is in the range <code>[1, 10<sup>5</sup>]</code>.</li>
<li><code>1 &lt;= Node.val &lt;= 10<sup>5</sup></code></li>
<li>The input is generated such that there is at least one node in the linked list that has a value not present in <code>nums</code>.</li>
</ul>

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<p>There exist two <strong>undirected </strong>trees with <code>n</code> and <code>m</code> nodes, numbered from <code>0</code> to <code>n - 1</code> and from <code>0</code> to <code>m - 1</code>, respectively. You are given two 2D integer arrays <code>edges1</code> and <code>edges2</code> of lengths <code>n - 1</code> and <code>m - 1</code>, respectively, where <code>edges1[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> indicates that there is an edge between nodes <code>a<sub>i</sub></code> and <code>b<sub>i</sub></code> in the first tree and <code>edges2[i] = [u<sub>i</sub>, v<sub>i</sub>]</code> indicates that there is an edge between nodes <code>u<sub>i</sub></code> and <code>v<sub>i</sub></code> in the second tree.</p>
<p>You must connect one node from the first tree with another node from the second tree with an edge.</p>
<p>Return the <strong>minimum </strong>possible <strong>diameter </strong>of the resulting tree.</p>
<p>The <strong>diameter</strong> of a tree is the length of the <em>longest</em> path between any two nodes in the tree.</p>
<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong><img alt="" src="https://assets.leetcode.com/uploads/2024/04/22/example11-transformed.png" /></p>
<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">edges1 = [[0,1],[0,2],[0,3]], edges2 = [[0,1]]</span></p>
<p><strong>Output:</strong> <span class="example-io">3</span></p>
<p><strong>Explanation:</strong></p>
<p>We can obtain a tree of diameter 3 by connecting node 0 from the first tree with any node from the second tree.</p>
</div>
<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2024/04/22/example211.png" />
<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">edges1 = [[0,1],[0,2],[0,3],[2,4],[2,5],[3,6],[2,7]], edges2 = [[0,1],[0,2],[0,3],[2,4],[2,5],[3,6],[2,7]]</span></p>
<p><strong>Output:</strong> <span class="example-io">5</span></p>
<p><strong>Explanation:</strong></p>
<p>We can obtain a tree of diameter 5 by connecting node 0 from the first tree with node 0 from the second tree.</p>
</div>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>
<ul>
<li><code>1 &lt;= n, m &lt;= 10<sup>5</sup></code></li>
<li><code>edges1.length == n - 1</code></li>
<li><code>edges2.length == m - 1</code></li>
<li><code>edges1[i].length == edges2[i].length == 2</code></li>
<li><code>edges1[i] = [a<sub>i</sub>, b<sub>i</sub>]</code></li>
<li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt; n</code></li>
<li><code>edges2[i] = [u<sub>i</sub>, v<sub>i</sub>]</code></li>
<li><code>0 &lt;= u<sub>i</sub>, v<sub>i</sub> &lt; m</code></li>
<li>The input is generated such that <code>edges1</code> and <code>edges2</code> represent valid trees.</li>
</ul>

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<p>You are given a string <code>s</code> and an integer <code>k</code>. Encrypt the string using the following algorithm:</p>
<ul>
<li>For each character <code>c</code> in <code>s</code>, replace <code>c</code> with the <code>k<sup>th</sup></code> character after <code>c</code> in the string (in a cyclic manner).</li>
</ul>
<p>Return the <em>encrypted string</em>.</p>
<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">s = &quot;dart&quot;, k = 3</span></p>
<p><strong>Output:</strong> <span class="example-io">&quot;tdar&quot;</span></p>
<p><strong>Explanation:</strong></p>
<ul>
<li>For <code>i = 0</code>, the 3<sup>rd</sup> character after <code>&#39;d&#39;</code> is <code>&#39;t&#39;</code>.</li>
<li>For <code>i = 1</code>, the 3<sup>rd</sup> character after <code>&#39;a&#39;</code> is <code>&#39;d&#39;</code>.</li>
<li>For <code>i = 2</code>, the 3<sup>rd</sup> character after <code>&#39;r&#39;</code> is <code>&#39;a&#39;</code>.</li>
<li>For <code>i = 3</code>, the 3<sup>rd</sup> character after <code>&#39;t&#39;</code> is <code>&#39;r&#39;</code>.</li>
</ul>
</div>
<p><strong class="example">Example 2:</strong></p>
<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">s = &quot;aaa&quot;, k = 1</span></p>
<p><strong>Output:</strong> <span class="example-io">&quot;aaa&quot;</span></p>
<p><strong>Explanation:</strong></p>
<p>As all the characters are the same, the encrypted string will also be the same.</p>
</div>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>
<ul>
<li><code>1 &lt;= s.length &lt;= 100</code></li>
<li><code>1 &lt;= k &lt;= 10<sup>4</sup></code></li>
<li><code>s</code> consists only of lowercase English letters.</li>
</ul>

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You are given an integer array <code>nums</code>.
<p>A <span data-keyword="subsequence-array">subsequence</span> <code>sub</code> of <code>nums</code> with length <code>x</code> is called <strong>valid</strong> if it satisfies:</p>
<ul>
<li><code>(sub[0] + sub[1]) % 2 == (sub[1] + sub[2]) % 2 == ... == (sub[x - 2] + sub[x - 1]) % 2.</code></li>
</ul>
<p>Return the length of the <strong>longest</strong> <strong>valid</strong> subsequence of <code>nums</code>.</p>
<p>A <strong>subsequence</strong> is an array that can be derived from another array by deleting some or no elements without changing the order of the remaining elements.</p>
<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">nums = [1,2,3,4]</span></p>
<p><strong>Output:</strong> <span class="example-io">4</span></p>
<p><strong>Explanation:</strong></p>
<p>The longest valid subsequence is <code>[1, 2, 3, 4]</code>.</p>
</div>
<p><strong class="example">Example 2:</strong></p>
<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">nums = [1,2,1,1,2,1,2]</span></p>
<p><strong>Output:</strong> 6</p>
<p><strong>Explanation:</strong></p>
<p>The longest valid subsequence is <code>[1, 2, 1, 2, 1, 2]</code>.</p>
</div>
<p><strong class="example">Example 3:</strong></p>
<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">nums = [1,3]</span></p>
<p><strong>Output:</strong> <span class="example-io">2</span></p>
<p><strong>Explanation:</strong></p>
<p>The longest valid subsequence is <code>[1, 3]</code>.</p>
</div>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>
<ul>
<li><code>2 &lt;= nums.length &lt;= 2 * 10<sup>5</sup></code></li>
<li><code>1 &lt;= nums[i] &lt;= 10<sup>7</sup></code></li>
</ul>

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You are given an integer array <code>nums</code> and a <strong>positive</strong> integer <code>k</code>.
<p>A <span data-keyword="subsequence-array">subsequence</span> <code>sub</code> of <code>nums</code> with length <code>x</code> is called <strong>valid</strong> if it satisfies:</p>
<ul>
<li><code>(sub[0] + sub[1]) % k == (sub[1] + sub[2]) % k == ... == (sub[x - 2] + sub[x - 1]) % k.</code></li>
</ul>
Return the length of the <strong>longest</strong> <strong>valid</strong> subsequence of <code>nums</code>.
<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">nums = [1,2,3,4,5], k = 2</span></p>
<p><strong>Output:</strong> <span class="example-io">5</span></p>
<p><strong>Explanation:</strong></p>
<p>The longest valid subsequence is <code>[1, 2, 3, 4, 5]</code>.</p>
</div>
<p><strong class="example">Example 2:</strong></p>
<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">nums = [1,4,2,3,1,4], k = 3</span></p>
<p><strong>Output:</strong> <span class="example-io">4</span></p>
<p><strong>Explanation:</strong></p>
<p>The longest valid subsequence is <code>[1, 4, 1, 4]</code>.</p>
</div>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>
<ul>
<li><code>2 &lt;= nums.length &lt;= 10<sup>3</sup></code></li>
<li><code>1 &lt;= nums[i] &lt;= 10<sup>7</sup></code></li>
<li><code>1 &lt;= k &lt;= 10<sup>3</sup></code></li>
</ul>

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<p>You are given a positive integer <code>n</code>.</p>
<p>A binary string <code>x</code> is <strong>valid</strong> if all <span data-keyword="substring-nonempty">substrings</span> of <code>x</code> of length 2 contain <strong>at least</strong> one <code>&quot;1&quot;</code>.</p>
<p>Return all <strong>valid</strong> strings with length <code>n</code><strong>, </strong>in <em>any</em> order.</p>
<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">n = 3</span></p>
<p><strong>Output:</strong> <span class="example-io">[&quot;010&quot;,&quot;011&quot;,&quot;101&quot;,&quot;110&quot;,&quot;111&quot;]</span></p>
<p><strong>Explanation:</strong></p>
<p>The valid strings of length 3 are: <code>&quot;010&quot;</code>, <code>&quot;011&quot;</code>, <code>&quot;101&quot;</code>, <code>&quot;110&quot;</code>, and <code>&quot;111&quot;</code>.</p>
</div>
<p><strong class="example">Example 2:</strong></p>
<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">n = 1</span></p>
<p><strong>Output:</strong> <span class="example-io">[&quot;0&quot;,&quot;1&quot;]</span></p>
<p><strong>Explanation:</strong></p>
<p>The valid strings of length 1 are: <code>&quot;0&quot;</code> and <code>&quot;1&quot;</code>.</p>
</div>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>
<ul>
<li><code>1 &lt;= n &lt;= 18</code></li>
</ul>

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<p>Given a string <code>s</code> containing only digits, return the <span data-keyword="lexicographically-smaller-string">lexicographically smallest string</span> that can be obtained after swapping <strong>adjacent</strong> digits in <code>s</code> with the same <strong>parity</strong> at most <strong>once</strong>.</p>
<p>Digits have the same parity if both are odd or both are even. For example, 5 and 9, as well as 2 and 4, have the same parity, while 6 and 9 do not.</p>
<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">s = &quot;45320&quot;</span></p>
<p><strong>Output:</strong> <span class="example-io">&quot;43520&quot;</span></p>
<p><strong>Explanation: </strong></p>
<p><code>s[1] == &#39;5&#39;</code> and <code>s[2] == &#39;3&#39;</code> both have the same parity, and swapping them results in the lexicographically smallest string.</p>
</div>
<p><strong class="example">Example 2:</strong></p>
<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">s = &quot;001&quot;</span></p>
<p><strong>Output:</strong> <span class="example-io">&quot;001&quot;</span></p>
<p><strong>Explanation:</strong></p>
<p>There is no need to perform a swap because <code>s</code> is already the lexicographically smallest.</p>
</div>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>
<ul>
<li><code>2 &lt;= s.length &lt;= 100</code></li>
<li><code>s</code> consists only of digits.</li>
</ul>

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<p>You are given two integers <code>red</code> and <code>blue</code> representing the count of red and blue colored balls. You have to arrange these balls to form a triangle such that the 1<sup>st</sup> row will have 1 ball, the 2<sup>nd</sup> row will have 2 balls, the 3<sup>rd</sup> row will have 3 balls, and so on.</p>
<p>All the balls in a particular row should be the <strong>same</strong> color, and adjacent rows should have <strong>different</strong> colors.</p>
<p>Return the <strong>maximum</strong><em> height of the triangle</em> that can be achieved.</p>
<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">red = 2, blue = 4</span></p>
<p><strong>Output:</strong> 3</p>
<p><strong>Explanation:</strong></p>
<p><img alt="" src="https://assets.leetcode.com/uploads/2024/06/16/brb.png" style="width: 300px; height: 240px; padding: 10px;" /></p>
<p>The only possible arrangement is shown above.</p>
</div>
<p><strong class="example">Example 2:</strong></p>
<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">red = 2, blue = 1</span></p>
<p><strong>Output:</strong> <span class="example-io">2</span></p>
<p><strong>Explanation:</strong></p>
<p><img alt="" src="https://assets.leetcode.com/uploads/2024/06/16/br.png" style="width: 150px; height: 135px; padding: 10px;" /><br />
The only possible arrangement is shown above.</p>
</div>
<p><strong class="example">Example 3:</strong></p>
<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">red = 1, blue = 1</span></p>
<p><strong>Output:</strong> <span class="example-io">1</span></p>
</div>
<p><strong class="example">Example 4:</strong></p>
<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">red = 10, blue = 1</span></p>
<p><strong>Output:</strong> <span class="example-io">2</span></p>
<p><strong>Explanation:</strong></p>
<p><img alt="" src="https://assets.leetcode.com/uploads/2024/06/16/br.png" style="width: 150px; height: 135px; padding: 10px;" /><br />
The only possible arrangement is shown above.</p>
</div>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>
<ul>
<li><code>1 &lt;= red, blue &lt;= 100</code></li>
</ul>

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<p>You are given an integer array <code>enemyEnergies</code> denoting the energy values of various enemies.</p>
<p>You are also given an integer <code>currentEnergy</code> denoting the amount of energy you have initially.</p>
<p>You start with 0 points, and all the enemies are unmarked initially.</p>
<p>You can perform <strong>either</strong> of the following operations <strong>zero </strong>or multiple times to gain points:</p>
<ul>
<li>Choose an <strong>unmarked</strong> enemy, <code>i</code>, such that <code>currentEnergy &gt;= enemyEnergies[i]</code>. By choosing this option:
<ul>
<li>You gain 1 point.</li>
<li>Your energy is reduced by the enemy&#39;s energy, i.e. <code>currentEnergy = currentEnergy - enemyEnergies[i]</code>.</li>
</ul>
</li>
<li>If you have <strong>at least</strong> 1 point, you can choose an <strong>unmarked</strong> enemy, <code>i</code>. By choosing this option:
<ul>
<li>Your energy increases by the enemy&#39;s energy, i.e. <code>currentEnergy = currentEnergy + enemyEnergies[i]</code>.</li>
<li>The <font face="monospace">e</font>nemy <code>i</code> is <strong>marked</strong>.</li>
</ul>
</li>
</ul>
<p>Return an integer denoting the <strong>maximum</strong> points you can get in the end by optimally performing operations.</p>
<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">enemyEnergies = [3,2,2], currentEnergy = 2</span></p>
<p><strong>Output:</strong> <span class="example-io">3</span></p>
<p><strong>Explanation:</strong></p>
<p>The following operations can be performed to get 3 points, which is the maximum:</p>
<ul>
<li>First operation on enemy 1: <code>points</code> increases by 1, and <code>currentEnergy</code> decreases by 2. So, <code>points = 1</code>, and <code>currentEnergy = 0</code>.</li>
<li>Second operation on enemy 0: <code>currentEnergy</code> increases by 3, and enemy 0 is marked. So, <code>points = 1</code>, <code>currentEnergy = 3</code>, and marked enemies = <code>[0]</code>.</li>
<li>First operation on enemy 2: <code>points</code> increases by 1, and <code>currentEnergy</code> decreases by 2. So, <code>points = 2</code>, <code>currentEnergy = 1</code>, and marked enemies = <code>[0]</code>.</li>
<li>Second operation on enemy 2: <code>currentEnergy</code> increases by 2, and enemy 2 is marked. So, <code>points = 2</code>, <code>currentEnergy = 3</code>, and marked enemies = <code>[0, 2]</code>.</li>
<li>First operation on enemy 1: <code>points</code> increases by 1, and <code>currentEnergy</code> decreases by 2. So, <code>points = 3</code>, <code>currentEnergy = 1</code>, and marked enemies = <code>[0, 2]</code>.</li>
</ul>
</div>
<p><strong class="example">Example 2:</strong></p>
<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">enemyEnergies = </span>[2]<span class="example-io">, currentEnergy = 10</span></p>
<p><strong>Output:</strong> <span class="example-io">5</span></p>
<p><strong>Explanation: </strong></p>
<p>Performing the first operation 5 times on enemy 0 results in the maximum number of points.</p>
</div>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>
<ul>
<li><code>1 &lt;= enemyEnergies.length &lt;= 10<sup>5</sup></code></li>
<li><code>1 &lt;= enemyEnergies[i] &lt;= 10<sup>9</sup></code></li>
<li><code>0 &lt;= currentEnergy &lt;= 10<sup>9</sup></code></li>
</ul>

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<p>There is an <code>m x n</code> cake that needs to be cut into <code>1 x 1</code> pieces.</p>
<p>You are given integers <code>m</code>, <code>n</code>, and two arrays:</p>
<ul>
<li><code>horizontalCut</code> of size <code>m - 1</code>, where <code>horizontalCut[i]</code> represents the cost to cut along the horizontal line <code>i</code>.</li>
<li><code>verticalCut</code> of size <code>n - 1</code>, where <code>verticalCut[j]</code> represents the cost to cut along the vertical line <code>j</code>.</li>
</ul>
<p>In one operation, you can choose any piece of cake that is not yet a <code>1 x 1</code> square and perform one of the following cuts:</p>
<ol>
<li>Cut along a horizontal line <code>i</code> at a cost of <code>horizontalCut[i]</code>.</li>
<li>Cut along a vertical line <code>j</code> at a cost of <code>verticalCut[j]</code>.</li>
</ol>
<p>After the cut, the piece of cake is divided into two distinct pieces.</p>
<p>The cost of a cut depends only on the initial cost of the line and does not change.</p>
<p>Return the <strong>minimum</strong> total cost to cut the entire cake into <code>1 x 1</code> pieces.</p>
<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">m = 3, n = 2, horizontalCut = [1,3], verticalCut = [5]</span></p>
<p><strong>Output:</strong> <span class="example-io">13</span></p>
<p><strong>Explanation:</strong></p>
<p><img alt="" src="https://assets.leetcode.com/uploads/2024/06/04/ezgifcom-animated-gif-maker-1.gif" style="width: 280px; height: 320px;" /></p>
<ul>
<li>Perform a cut on the vertical line 0 with cost 5, current total cost is 5.</li>
<li>Perform a cut on the horizontal line 0 on <code>3 x 1</code> subgrid with cost 1.</li>
<li>Perform a cut on the horizontal line 0 on <code>3 x 1</code> subgrid with cost 1.</li>
<li>Perform a cut on the horizontal line 1 on <code>2 x 1</code> subgrid with cost 3.</li>
<li>Perform a cut on the horizontal line 1 on <code>2 x 1</code> subgrid with cost 3.</li>
</ul>
<p>The total cost is <code>5 + 1 + 1 + 3 + 3 = 13</code>.</p>
</div>
<p><strong class="example">Example 2:</strong></p>
<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">m = 2, n = 2, horizontalCut = [7], verticalCut = [4]</span></p>
<p><strong>Output:</strong> <span class="example-io">15</span></p>
<p><strong>Explanation:</strong></p>
<ul>
<li>Perform a cut on the horizontal line 0 with cost 7.</li>
<li>Perform a cut on the vertical line 0 on <code>1 x 2</code> subgrid with cost 4.</li>
<li>Perform a cut on the vertical line 0 on <code>1 x 2</code> subgrid with cost 4.</li>
</ul>
<p>The total cost is <code>7 + 4 + 4 = 15</code>.</p>
</div>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>
<ul>
<li><code>1 &lt;= m, n &lt;= 20</code></li>
<li><code>horizontalCut.length == m - 1</code></li>
<li><code>verticalCut.length == n - 1</code></li>
<li><code>1 &lt;= horizontalCut[i], verticalCut[i] &lt;= 10<sup>3</sup></code></li>
</ul>

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<p>There is an <code>m x n</code> cake that needs to be cut into <code>1 x 1</code> pieces.</p>
<p>You are given integers <code>m</code>, <code>n</code>, and two arrays:</p>
<ul>
<li><code>horizontalCut</code> of size <code>m - 1</code>, where <code>horizontalCut[i]</code> represents the cost to cut along the horizontal line <code>i</code>.</li>
<li><code>verticalCut</code> of size <code>n - 1</code>, where <code>verticalCut[j]</code> represents the cost to cut along the vertical line <code>j</code>.</li>
</ul>
<p>In one operation, you can choose any piece of cake that is not yet a <code>1 x 1</code> square and perform one of the following cuts:</p>
<ol>
<li>Cut along a horizontal line <code>i</code> at a cost of <code>horizontalCut[i]</code>.</li>
<li>Cut along a vertical line <code>j</code> at a cost of <code>verticalCut[j]</code>.</li>
</ol>
<p>After the cut, the piece of cake is divided into two distinct pieces.</p>
<p>The cost of a cut depends only on the initial cost of the line and does not change.</p>
<p>Return the <strong>minimum</strong> total cost to cut the entire cake into <code>1 x 1</code> pieces.</p>
<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">m = 3, n = 2, horizontalCut = [1,3], verticalCut = [5]</span></p>
<p><strong>Output:</strong> <span class="example-io">13</span></p>
<p><strong>Explanation:</strong></p>
<p><img alt="" src="https://assets.leetcode.com/uploads/2024/06/04/ezgifcom-animated-gif-maker-1.gif" style="width: 280px; height: 320px;" /></p>
<ul>
<li>Perform a cut on the vertical line 0 with cost 5, current total cost is 5.</li>
<li>Perform a cut on the horizontal line 0 on <code>3 x 1</code> subgrid with cost 1.</li>
<li>Perform a cut on the horizontal line 0 on <code>3 x 1</code> subgrid with cost 1.</li>
<li>Perform a cut on the horizontal line 1 on <code>2 x 1</code> subgrid with cost 3.</li>
<li>Perform a cut on the horizontal line 1 on <code>2 x 1</code> subgrid with cost 3.</li>
</ul>
<p>The total cost is <code>5 + 1 + 1 + 3 + 3 = 13</code>.</p>
</div>
<p><strong class="example">Example 2:</strong></p>
<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">m = 2, n = 2, horizontalCut = [7], verticalCut = [4]</span></p>
<p><strong>Output:</strong> <span class="example-io">15</span></p>
<p><strong>Explanation:</strong></p>
<ul>
<li>Perform a cut on the horizontal line 0 with cost 7.</li>
<li>Perform a cut on the vertical line 0 on <code>1 x 2</code> subgrid with cost 4.</li>
<li>Perform a cut on the vertical line 0 on <code>1 x 2</code> subgrid with cost 4.</li>
</ul>
<p>The total cost is <code>7 + 4 + 4 = 15</code>.</p>
</div>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>
<ul>
<li><code>1 &lt;= m, n &lt;= 10<sup>5</sup></code></li>
<li><code>horizontalCut.length == m - 1</code></li>
<li><code>verticalCut.length == n - 1</code></li>
<li><code>1 &lt;= horizontalCut[i], verticalCut[i] &lt;= 10<sup>3</sup></code></li>
</ul>

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<p>Given an array of integers <code>nums</code> and an integer <code>k</code>, return the number of <span data-keyword="subarray-nonempty">subarrays</span> of <code>nums</code> where the bitwise <code>AND</code> of the elements of the subarray equals <code>k</code>.</p>
<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">nums = [1,1,1], k = 1</span></p>
<p><strong>Output:</strong> <span class="example-io">6</span></p>
<p><strong>Explanation:</strong></p>
<p>All subarrays contain only 1&#39;s.</p>
</div>
<p><strong class="example">Example 2:</strong></p>
<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">nums = [1,1,2], k = 1</span></p>
<p><strong>Output:</strong> <span class="example-io">3</span></p>
<p><strong>Explanation:</strong></p>
<p>Subarrays having an <code>AND</code> value of 1 are: <code>[<u><strong>1</strong></u>,1,2]</code>, <code>[1,<u><strong>1</strong></u>,2]</code>, <code>[<u><strong>1,1</strong></u>,2]</code>.</p>
</div>
<p><strong class="example">Example 3:</strong></p>
<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">nums = [1,2,3], k = 2</span></p>
<p><strong>Output:</strong> <span class="example-io">2</span></p>
<p><strong>Explanation:</strong></p>
<p>Subarrays having an <code>AND</code> value of 2 are: <code>[1,<b><u>2</u></b>,3]</code>, <code>[1,<u><strong>2,3</strong></u>]</code>.</p>
</div>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>
<ul>
<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
<li><code>0 &lt;= nums[i], k &lt;= 10<sup>9</sup></code></li>
</ul>