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            "questionId": "1912",
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            "title": "Number of Restricted Paths From First to Last Node",
            "titleSlug": "number-of-restricted-paths-from-first-to-last-node",
            "content": "<p>There is an undirected weighted connected graph. You are given a positive integer <code>n</code> which denotes that the graph has <code>n</code> nodes labeled from <code>1</code> to <code>n</code>, and an array <code>edges</code> where each <code>edges[i] = [u<sub>i</sub>, v<sub>i</sub>, weight<sub>i</sub>]</code> denotes that there is an edge between nodes <code>u<sub>i</sub></code> and <code>v<sub>i</sub></code> with weight equal to <code>weight<sub>i</sub></code>.</p>\n\n<p>A path from node <code>start</code> to node <code>end</code> is a sequence of nodes <code>[z<sub>0</sub>, z<sub>1</sub>,<sub> </sub>z<sub>2</sub>, ..., z<sub>k</sub>]</code> such that <code>z<sub>0 </sub>= start</code> and <code>z<sub>k</sub> = end</code> and there is an edge between <code>z<sub>i</sub></code> and <code>z<sub>i+1</sub></code> where <code>0 &lt;= i &lt;= k-1</code>.</p>\n\n<p>The distance of a path is the sum of the weights on the edges of the path. Let <code>distanceToLastNode(x)</code> denote the shortest distance of a path between node <code>n</code> and node <code>x</code>. A <strong>restricted path</strong> is a path that also satisfies that <code>distanceToLastNode(z<sub>i</sub>) &gt; distanceToLastNode(z<sub>i+1</sub>)</code> where <code>0 &lt;= i &lt;= k-1</code>.</p>\n\n<p>Return <em>the number of restricted paths from node</em> <code>1</code> <em>to node</em> <code>n</code>. Since that number may be too large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/02/17/restricted_paths_ex1.png\" style=\"width: 351px; height: 341px;\" />\n<pre>\n<strong>Input:</strong> n = 5, edges = [[1,2,3],[1,3,3],[2,3,1],[1,4,2],[5,2,2],[3,5,1],[5,4,10]]\n<strong>Output:</strong> 3\n<strong>Explanation:</strong> Each circle contains the node number in black and its <code>distanceToLastNode value in blue. </code>The three restricted paths are:\n1) 1 --&gt; 2 --&gt; 5\n2) 1 --&gt; 2 --&gt; 3 --&gt; 5\n3) 1 --&gt; 3 --&gt; 5\n</pre>\n\n<p><strong>Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/02/17/restricted_paths_ex22.png\" style=\"width: 356px; height: 401px;\" />\n<pre>\n<strong>Input:</strong> n = 7, edges = [[1,3,1],[4,1,2],[7,3,4],[2,5,3],[5,6,1],[6,7,2],[7,5,3],[2,6,4]]\n<strong>Output:</strong> 1\n<strong>Explanation:</strong> Each circle contains the node number in black and its <code>distanceToLastNode value in blue. </code>The only restricted path is 1 --&gt; 3 --&gt; 7.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n &lt;= 2 * 10<sup>4</sup></code></li>\n\t<li><code>n - 1 &lt;= edges.length &lt;= 4 * 10<sup>4</sup></code></li>\n\t<li><code>edges[i].length == 3</code></li>\n\t<li><code>1 &lt;= u<sub>i</sub>, v<sub>i</sub> &lt;= n</code></li>\n\t<li><code>u<sub>i </sub>!= v<sub>i</sub></code></li>\n\t<li><code>1 &lt;= weight<sub>i</sub> &lt;= 10<sup>5</sup></code></li>\n\t<li>There is at most one edge between any two nodes.</li>\n\t<li>There is at least one path between any two nodes.</li>\n</ul>\n",
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            "exampleTestcases": "5\n[[1,2,3],[1,3,3],[2,3,1],[1,4,2],[5,2,2],[3,5,1],[5,4,10]]\n7\n[[1,3,1],[4,1,2],[7,3,4],[2,5,3],[5,6,1],[6,7,2],[7,5,3],[2,6,4]]",
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                    "name": "Dynamic Programming",
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                    "name": "Graph",
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                    "name": "Topological Sort",
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                    "code": "class Solution(object):\n    def countRestrictedPaths(self, n, edges):\n        \"\"\"\n        :type n: int\n        :type edges: List[List[int]]\n        :rtype: int\n        \"\"\"\n        ",
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                    "code": "/**\n * @param {number} n\n * @param {number[][]} edges\n * @return {number}\n */\nvar countRestrictedPaths = function(n, edges) {\n    \n};",
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                    "code": "# @param {Integer} n\n# @param {Integer[][]} edges\n# @return {Integer}\ndef count_restricted_paths(n, edges)\n    \nend",
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                    "code": "object Solution {\n    def countRestrictedPaths(n: Int, edges: Array[Array[Int]]): Int = {\n        \n    }\n}",
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                    "code": "impl Solution {\n    pub fn count_restricted_paths(n: i32, edges: Vec<Vec<i32>>) -> i32 {\n        \n    }\n}",
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                    "code": "class Solution {\n\n    /**\n     * @param Integer $n\n     * @param Integer[][] $edges\n     * @return Integer\n     */\n    function countRestrictedPaths($n, $edges) {\n        \n    }\n}",
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            "hints": [
                "Run a Dijkstra from node numbered n to compute distance from the last node.",
                "Consider all edges [u, v] one by one and direct them such that distance of u to n > distance of v to n. If both u and v are at the same distance from n, discard this edge.",
                "Now this problem reduces to computing the number of paths from 1 to n in a DAG, a standard DP problem."
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