leetcode-problemset/leetcode-cn/originData/largest-color-value-in-a-directed-graph.json

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        "question": {
            "questionId": "1986",
            "questionFrontendId": "1857",
            "categoryTitle": "Algorithms",
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            "title": "Largest Color Value in a Directed Graph",
            "titleSlug": "largest-color-value-in-a-directed-graph",
            "content": "<p>There is a <strong>directed graph</strong> of <code>n</code> colored nodes and <code>m</code> edges. The nodes are numbered from <code>0</code> to <code>n - 1</code>.</p>\n\n<p>You are given a string <code>colors</code> where <code>colors[i]</code> is a lowercase English letter representing the <strong>color</strong> of the <code>i<sup>th</sup></code> node in this graph (<strong>0-indexed</strong>). You are also given a 2D array <code>edges</code> where <code>edges[j] = [a<sub>j</sub>, b<sub>j</sub>]</code> indicates that there is a <strong>directed edge</strong> from node <code>a<sub>j</sub></code> to node <code>b<sub>j</sub></code>.</p>\n\n<p>A valid <strong>path</strong> in the graph is a sequence of nodes <code>x<sub>1</sub> -&gt; x<sub>2</sub> -&gt; x<sub>3</sub> -&gt; ... -&gt; x<sub>k</sub></code> such that there is a directed edge from <code>x<sub>i</sub></code> to <code>x<sub>i+1</sub></code> for every <code>1 &lt;= i &lt; k</code>. The <strong>color value</strong> of the path is the number of nodes that are colored the <strong>most frequently</strong> occurring color along that path.</p>\n\n<p>Return <em>the <strong>largest color value</strong> of any valid path in the given graph, or </em><code>-1</code><em> if the graph contains a cycle</em>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/04/21/leet1.png\" style=\"width: 400px; height: 182px;\" /></p>\n\n<pre>\n<strong>Input:</strong> colors = &quot;abaca&quot;, edges = [[0,1],[0,2],[2,3],[3,4]]\n<strong>Output:</strong> 3\n<strong>Explanation:</strong> The path 0 -&gt; 2 -&gt; 3 -&gt; 4 contains 3 nodes that are colored <code>&quot;a&quot; (red in the above image)</code>.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/04/21/leet2.png\" style=\"width: 85px; height: 85px;\" /></p>\n\n<pre>\n<strong>Input:</strong> colors = &quot;a&quot;, edges = [[0,0]]\n<strong>Output:</strong> -1\n<strong>Explanation:</strong> There is a cycle from 0 to 0.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>n == colors.length</code></li>\n\t<li><code>m == edges.length</code></li>\n\t<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>\n\t<li><code>0 &lt;= m &lt;= 10<sup>5</sup></code></li>\n\t<li><code>colors</code> consists of lowercase English letters.</li>\n\t<li><code>0 &lt;= a<sub>j</sub>, b<sub>j</sub>&nbsp;&lt; n</code></li>\n</ul>\n",
            "translatedTitle": "有向图中最大颜色值",
            "translatedContent": "<p>给你一个&nbsp;<strong>有向图</strong>&nbsp;，它含有&nbsp;<code>n</code>&nbsp;个节点和 <code>m</code>&nbsp;条边。节点编号从&nbsp;<code>0</code> 到&nbsp;<code>n - 1</code>&nbsp;。</p>\n\n<p>给你一个字符串&nbsp;<code>colors</code> ，其中&nbsp;<code>colors[i]</code>&nbsp;是小写英文字母，表示图中第 <code>i</code>&nbsp;个节点的 <b>颜色</b>&nbsp;（下标从 <strong>0</strong>&nbsp;开始）。同时给你一个二维数组&nbsp;<code>edges</code>&nbsp;，其中&nbsp;<code>edges[j] = [a<sub>j</sub>, b<sub>j</sub>]</code>&nbsp;表示从节点&nbsp;<code>a<sub>j</sub></code>&nbsp;到节点&nbsp;<code>b<sub>j</sub></code><sub>&nbsp;</sub>有一条&nbsp;<strong>有向边</strong>&nbsp;。</p>\n\n<p>图中一条有效 <strong>路径</strong>&nbsp;是一个点序列&nbsp;<code>x<sub>1</sub> -&gt; x<sub>2</sub> -&gt; x<sub>3</sub> -&gt; ... -&gt; x<sub>k</sub></code>&nbsp;，对于所有&nbsp;<code>1 &lt;= i &lt; k</code>&nbsp;，从&nbsp;<code>x<sub>i</sub></code> 到&nbsp;<code>x<sub>i+1</sub></code>&nbsp;在图中有一条有向边。路径的 <strong>颜色值</strong>&nbsp;是路径中 <strong>出现次数最多</strong> 颜色的节点数目。</p>\n\n<p>请你返回给定图中有效路径里面的&nbsp;<strong>最大颜色值</strong><strong>&nbsp;。</strong>如果图中含有环，请返回 <code>-1</code>&nbsp;。</p>\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/2021/04/21/leet1.png\" style=\"width: 400px; height: 182px;\" /></p>\n\n<pre>\n<b>输入：</b>colors = \"abaca\", edges = [[0,1],[0,2],[2,3],[3,4]]\n<b>输出：</b>3\n<b>解释：</b>路径 0 -&gt; 2 -&gt; 3 -&gt; 4 含有 3 个颜色为 \"a\" 的节点（上图中的红色节点）。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/04/21/leet2.png\" style=\"width: 85px; height: 85px;\" /></p>\n\n<pre>\n<b>输入：</b>colors = \"a\", edges = [[0,0]]\n<b>输出：</b>-1\n<b>解释：</b>从 0 到 0 有一个环。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>n == colors.length</code></li>\n\t<li><code>m == edges.length</code></li>\n\t<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>\n\t<li><code>0 &lt;= m &lt;= 10<sup>5</sup></code></li>\n\t<li><code>colors</code>&nbsp;只含有小写英文字母。</li>\n\t<li><code>0 &lt;= a<sub>j</sub>, b<sub>j</sub>&nbsp;&lt; n</code></li>\n</ul>\n",
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            "hints": [
                "Use topological sort.",
                "let dp[u][c] := the maximum count of vertices with color c of any path starting from vertex u. (by JerryJin2905)"
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