mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
synced 2025-01-10 18:48:13 +08:00
189 lines
32 KiB
JSON
189 lines
32 KiB
JSON
{
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"data": {
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"question": {
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"questionId": "2678",
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"questionFrontendId": "2642",
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"categoryTitle": "Algorithms",
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"boundTopicId": 2225776,
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"title": "Design Graph With Shortest Path Calculator",
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"titleSlug": "design-graph-with-shortest-path-calculator",
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"content": "<p>There is a <strong>directed weighted</strong> graph that consists of <code>n</code> nodes numbered from <code>0</code> to <code>n - 1</code>. The edges of the graph are initially represented by the given array <code>edges</code> where <code>edges[i] = [from<sub>i</sub>, to<sub>i</sub>, edgeCost<sub>i</sub>]</code> meaning that there is an edge from <code>from<sub>i</sub></code> to <code>to<sub>i</sub></code> with the cost <code>edgeCost<sub>i</sub></code>.</p>\n\n<p>Implement the <code>Graph</code> class:</p>\n\n<ul>\n\t<li><code>Graph(int n, int[][] edges)</code> initializes the object with <code>n</code> nodes and the given edges.</li>\n\t<li><code>addEdge(int[] edge)</code> adds an edge to the list of edges where <code>edge = [from, to, edgeCost]</code>. It is guaranteed that there is no edge between the two nodes before adding this one.</li>\n\t<li><code>int shortestPath(int node1, int node2)</code> returns the <strong>minimum</strong> cost of a path from <code>node1</code> to <code>node2</code>. If no path exists, return <code>-1</code>. The cost of a path is the sum of the costs of the edges in the path.</li>\n</ul>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/01/11/graph3drawio-2.png\" style=\"width: 621px; height: 191px;\" />\n<pre>\n<strong>Input</strong>\n["Graph", "shortestPath", "shortestPath", "addEdge", "shortestPath"]\n[[4, [[0, 2, 5], [0, 1, 2], [1, 2, 1], [3, 0, 3]]], [3, 2], [0, 3], [[1, 3, 4]], [0, 3]]\n<strong>Output</strong>\n[null, 6, -1, null, 6]\n\n<strong>Explanation</strong>\nGraph g = new Graph(4, [[0, 2, 5], [0, 1, 2], [1, 2, 1], [3, 0, 3]]);\ng.shortestPath(3, 2); // return 6. The shortest path from 3 to 2 in the first diagram above is 3 -> 0 -> 1 -> 2 with a total cost of 3 + 2 + 1 = 6.\ng.shortestPath(0, 3); // return -1. There is no path from 0 to 3.\ng.addEdge([1, 3, 4]); // We add an edge from node 1 to node 3, and we get the second diagram above.\ng.shortestPath(0, 3); // return 6. The shortest path from 0 to 3 now is 0 -> 1 -> 3 with a total cost of 2 + 4 = 6.\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= n <= 100</code></li>\n\t<li><code>0 <= edges.length <= n * (n - 1)</code></li>\n\t<li><code>edges[i].length == edge.length == 3</code></li>\n\t<li><code>0 <= from<sub>i</sub>, to<sub>i</sub>, from, to, node1, node2 <= n - 1</code></li>\n\t<li><code>1 <= edgeCost<sub>i</sub>, edgeCost <= 10<sup>6</sup></code></li>\n\t<li>There are no repeated edges and no self-loops in the graph at any point.</li>\n\t<li>At most <code>100</code> calls will be made for <code>addEdge</code>.</li>\n\t<li>At most <code>100</code> calls will be made for <code>shortestPath</code>.</li>\n</ul>\n",
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"translatedTitle": "设计可以求最短路径的图类",
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"translatedContent": "<p>给你一个有 <code>n</code> 个节点的 <strong>有向带权</strong> 图，节点编号为 <code>0</code> 到 <code>n - 1</code> 。图中的初始边用数组 <code>edges</code> 表示，其中 <code>edges[i] = [from<sub>i</sub>, to<sub>i</sub>, edgeCost<sub>i</sub>]</code> 表示从 <code>from<sub>i</sub></code> 到 <code>to<sub>i</sub></code> 有一条代价为 <code>edgeCost<sub>i</sub></code> 的边。</p>\n\n<p>请你实现一个 <code>Graph</code> 类：</p>\n\n<ul>\n\t<li><code>Graph(int n, int[][] edges)</code> 初始化图有 <code>n</code> 个节点，并输入初始边。</li>\n\t<li><code>addEdge(int[] edge)</code> 向边集中添加一条边，其中<strong> </strong><code>edge = [from, to, edgeCost]</code> 。数据保证添加这条边之前对应的两个节点之间没有有向边。</li>\n\t<li><code>int shortestPath(int node1, int node2)</code> 返回从节点 <code>node1</code> 到 <code>node2</code> 的路径<strong> 最小</strong> 代价。如果路径不存在，返回 <code>-1</code> 。一条路径的代价是路径中所有边代价之和。</li>\n</ul>\n\n<p> </p>\n\n<p><strong>示例 1：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/01/11/graph3drawio-2.png\" style=\"width: 621px; height: 191px;\"></p>\n\n<pre><strong>输入：</strong>\n[\"Graph\", \"shortestPath\", \"shortestPath\", \"addEdge\", \"shortestPath\"]\n[[4, [[0, 2, 5], [0, 1, 2], [1, 2, 1], [3, 0, 3]]], [3, 2], [0, 3], [[1, 3, 4]], [0, 3]]\n<b>输出：</b>\n[null, 6, -1, null, 6]\n\n<strong>解释：</strong>\nGraph g = new Graph(4, [[0, 2, 5], [0, 1, 2], [1, 2, 1], [3, 0, 3]]);\ng.shortestPath(3, 2); // 返回 6 。从 3 到 2 的最短路径如第一幅图所示：3 -> 0 -> 1 -> 2 ，总代价为 3 + 2 + 1 = 6 。\ng.shortestPath(0, 3); // 返回 -1 。没有从 0 到 3 的路径。\ng.addEdge([1, 3, 4]); // 添加一条节点 1 到节点 3 的边，得到第二幅图。\ng.shortestPath(0, 3); // 返回 6 。从 0 到 3 的最短路径为 0 -> 1 -> 3 ，总代价为 2 + 4 = 6 。\n</pre>\n\n<p> </p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 <= n <= 100</code></li>\n\t<li><code>0 <= edges.length <= n * (n - 1)</code></li>\n\t<li><code>edges[i].length == edge.length == 3</code></li>\n\t<li><code>0 <= from<sub>i</sub>, to<sub>i</sub>, from, to, node1, node2 <= n - 1</code></li>\n\t<li><code>1 <= edgeCost<sub>i</sub>, edgeCost <= 10<sup>6</sup></code></li>\n\t<li>图中任何时候都不会有重边和自环。</li>\n\t<li>调用 <code>addEdge</code> 至多 <code>100</code> 次。</li>\n\t<li>调用 <code>shortestPath</code> 至多 <code>100</code> 次。</li>\n</ul>\n",
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"code": "class Graph {\npublic:\n Graph(int n, vector<vector<int>>& edges) {\n\n }\n \n void addEdge(vector<int> edge) {\n\n }\n \n int shortestPath(int node1, int node2) {\n\n }\n};\n\n/**\n * Your Graph object will be instantiated and called as such:\n * Graph* obj = new Graph(n, edges);\n * obj->addEdge(edge);\n * int param_2 = obj->shortestPath(node1,node2);\n */",
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"code": "class Graph {\n\n public Graph(int n, int[][] edges) {\n\n }\n \n public void addEdge(int[] edge) {\n\n }\n \n public int shortestPath(int node1, int node2) {\n\n }\n}\n\n/**\n * Your Graph object will be instantiated and called as such:\n * Graph obj = new Graph(n, edges);\n * obj.addEdge(edge);\n * int param_2 = obj.shortestPath(node1,node2);\n */",
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"code": "class Graph(object):\n\n def __init__(self, n, edges):\n \"\"\"\n :type n: int\n :type edges: List[List[int]]\n \"\"\"\n\n\n def addEdge(self, edge):\n \"\"\"\n :type edge: List[int]\n :rtype: None\n \"\"\"\n\n\n def shortestPath(self, node1, node2):\n \"\"\"\n :type node1: int\n :type node2: int\n :rtype: int\n \"\"\"\n\n\n\n# Your Graph object will be instantiated and called as such:\n# obj = Graph(n, edges)\n# obj.addEdge(edge)\n# param_2 = obj.shortestPath(node1,node2)",
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"code": "class Graph:\n\n def __init__(self, n: int, edges: List[List[int]]):\n\n\n def addEdge(self, edge: List[int]) -> None:\n\n\n def shortestPath(self, node1: int, node2: int) -> int:\n\n\n\n# Your Graph object will be instantiated and called as such:\n# obj = Graph(n, edges)\n# obj.addEdge(edge)\n# param_2 = obj.shortestPath(node1,node2)",
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"code": "\n\n\ntypedef struct {\n \n} Graph;\n\n\nGraph* graphCreate(int n, int** edges, int edgesSize, int* edgesColSize) {\n \n}\n\nvoid graphAddEdge(Graph* obj, int* edge, int edgeSize) {\n \n}\n\nint graphShortestPath(Graph* obj, int node1, int node2) {\n \n}\n\nvoid graphFree(Graph* obj) {\n \n}\n\n/**\n * Your Graph struct will be instantiated and called as such:\n * Graph* obj = graphCreate(n, edges, edgesSize, edgesColSize);\n * graphAddEdge(obj, edge, edgeSize);\n \n * int param_2 = graphShortestPath(obj, node1, node2);\n \n * graphFree(obj);\n*/",
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"code": "public class Graph {\n\n public Graph(int n, int[][] edges) {\n\n }\n \n public void AddEdge(int[] edge) {\n\n }\n \n public int ShortestPath(int node1, int node2) {\n\n }\n}\n\n/**\n * Your Graph object will be instantiated and called as such:\n * Graph obj = new Graph(n, edges);\n * obj.AddEdge(edge);\n * int param_2 = obj.ShortestPath(node1,node2);\n */",
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"code": "/**\n * @param {number} n\n * @param {number[][]} edges\n */\nvar Graph = function(n, edges) {\n\n};\n\n/** \n * @param {number[]} edge\n * @return {void}\n */\nGraph.prototype.addEdge = function(edge) {\n\n};\n\n/** \n * @param {number} node1 \n * @param {number} node2\n * @return {number}\n */\nGraph.prototype.shortestPath = function(node1, node2) {\n\n};\n\n/**\n * Your Graph object will be instantiated and called as such:\n * var obj = new Graph(n, edges)\n * obj.addEdge(edge)\n * var param_2 = obj.shortestPath(node1,node2)\n */",
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"code": "class Graph {\n constructor(n: number, edges: number[][]) {\n \n }\n\n addEdge(edge: number[]): void {\n \n }\n\n shortestPath(node1: number, node2: number): number {\n \n }\n}\n\n/**\n * Your Graph object will be instantiated and called as such:\n * var obj = new Graph(n, edges)\n * obj.addEdge(edge)\n * var param_2 = obj.shortestPath(node1,node2)\n */",
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"code": "class Graph {\n /**\n * @param Integer $n\n * @param Integer[][] $edges\n */\n function __construct($n, $edges) {\n\n }\n\n /**\n * @param Integer[] $edge\n * @return NULL\n */\n function addEdge($edge) {\n\n }\n\n /**\n * @param Integer $node1\n * @param Integer $node2\n * @return Integer\n */\n function shortestPath($node1, $node2) {\n\n }\n}\n\n/**\n * Your Graph object will be instantiated and called as such:\n * $obj = Graph($n, $edges);\n * $obj->addEdge($edge);\n * $ret_2 = $obj->shortestPath($node1, $node2);\n */",
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"__typename": "CodeSnippetNode"
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"code": "\nclass Graph {\n\n init(_ n: Int, _ edges: [[Int]]) {\n\n }\n \n func addEdge(_ edge: [Int]) {\n\n }\n \n func shortestPath(_ node1: Int, _ node2: Int) -> Int {\n\n }\n}\n\n/**\n * Your Graph object will be instantiated and called as such:\n * let obj = Graph(n, edges)\n * obj.addEdge(edge)\n * let ret_2: Int = obj.shortestPath(node1, node2)\n */",
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"code": "class Graph(n: Int, edges: Array<IntArray>) {\n\n fun addEdge(edge: IntArray) {\n\n }\n\n fun shortestPath(node1: Int, node2: Int): Int {\n\n }\n\n}\n\n/**\n * Your Graph object will be instantiated and called as such:\n * var obj = Graph(n, edges)\n * obj.addEdge(edge)\n * var param_2 = obj.shortestPath(node1,node2)\n */",
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"code": "class Graph {\n\n Graph(int n, List<List<int>> edges) {\n \n }\n \n void addEdge(List<int> edge) {\n \n }\n \n int shortestPath(int node1, int node2) {\n \n }\n}\n\n/**\n * Your Graph object will be instantiated and called as such:\n * Graph obj = Graph(n, edges);\n * obj.addEdge(edge);\n * int param2 = obj.shortestPath(node1,node2);\n */",
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"__typename": "CodeSnippetNode"
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},
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"code": "type Graph struct {\n\n}\n\n\nfunc Constructor(n int, edges [][]int) Graph {\n\n}\n\n\nfunc (this *Graph) AddEdge(edge []int) {\n\n}\n\n\nfunc (this *Graph) ShortestPath(node1 int, node2 int) int {\n\n}\n\n\n/**\n * Your Graph object will be instantiated and called as such:\n * obj := Constructor(n, edges);\n * obj.AddEdge(edge);\n * param_2 := obj.ShortestPath(node1,node2);\n */",
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"__typename": "CodeSnippetNode"
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},
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"code": "class Graph\n\n=begin\n :type n: Integer\n :type edges: Integer[][]\n=end\n def initialize(n, edges)\n\n end\n\n\n=begin\n :type edge: Integer[]\n :rtype: Void\n=end\n def add_edge(edge)\n\n end\n\n\n=begin\n :type node1: Integer\n :type node2: Integer\n :rtype: Integer\n=end\n def shortest_path(node1, node2)\n\n end\n\n\nend\n\n# Your Graph object will be instantiated and called as such:\n# obj = Graph.new(n, edges)\n# obj.add_edge(edge)\n# param_2 = obj.shortest_path(node1, node2)",
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"code": "class Graph(_n: Int, _edges: Array[Array[Int]]) {\n\n def addEdge(edge: Array[Int]) {\n\n }\n\n def shortestPath(node1: Int, node2: Int): Int = {\n\n }\n\n}\n\n/**\n * Your Graph object will be instantiated and called as such:\n * var obj = new Graph(n, edges)\n * obj.addEdge(edge)\n * var param_2 = obj.shortestPath(node1,node2)\n */",
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"__typename": "CodeSnippetNode"
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"code": "struct Graph {\n\n}\n\n\n/**\n * `&self` means the method takes an immutable reference.\n * If you need a mutable reference, change it to `&mut self` instead.\n */\nimpl Graph {\n\n fn new(n: i32, edges: Vec<Vec<i32>>) -> Self {\n\n }\n \n fn add_edge(&self, edge: Vec<i32>) {\n\n }\n \n fn shortest_path(&self, node1: i32, node2: i32) -> i32 {\n\n }\n}\n\n/**\n * Your Graph object will be instantiated and called as such:\n * let obj = Graph::new(n, edges);\n * obj.add_edge(edge);\n * let ret_2: i32 = obj.shortest_path(node1, node2);\n */",
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"code": "(define graph%\n (class object%\n (super-new)\n \n ; n : exact-integer?\n ; edges : (listof (listof exact-integer?))\n (init-field\n n\n edges)\n \n ; add-edge : (listof exact-integer?) -> void?\n (define/public (add-edge edge)\n )\n ; shortest-path : exact-integer? exact-integer? -> exact-integer?\n (define/public (shortest-path node1 node2)\n )))\n\n;; Your graph% object will be instantiated and called as such:\n;; (define obj (new graph% [n n] [edges edges]))\n;; (send obj add-edge edge)\n;; (define param_2 (send obj shortest-path node1 node2))",
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"code": "-spec graph_init_(N :: integer(), Edges :: [[integer()]]) -> any().\ngraph_init_(N, Edges) ->\n .\n\n-spec graph_add_edge(Edge :: [integer()]) -> any().\ngraph_add_edge(Edge) ->\n .\n\n-spec graph_shortest_path(Node1 :: integer(), Node2 :: integer()) -> integer().\ngraph_shortest_path(Node1, Node2) ->\n .\n\n\n%% Your functions will be called as such:\n%% graph_init_(N, Edges),\n%% graph_add_edge(Edge),\n%% Param_2 = graph_shortest_path(Node1, Node2),\n\n%% graph_init_ will be called before every test case, in which you can do some necessary initializations.",
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"code": "defmodule Graph do\n @spec init_(n :: integer, edges :: [[integer]]) :: any\n def init_(n, edges) do\n \n end\n\n @spec add_edge(edge :: [integer]) :: any\n def add_edge(edge) do\n \n end\n\n @spec shortest_path(node1 :: integer, node2 :: integer) :: integer\n def shortest_path(node1, node2) do\n \n end\nend\n\n# Your functions will be called as such:\n# Graph.init_(n, edges)\n# Graph.add_edge(edge)\n# param_2 = Graph.shortest_path(node1, node2)\n\n# Graph.init_ will be called before every test case, in which you can do some necessary initializations.",
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"hints": [
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"After adding each edge, update your graph with the new edge, and you can calculate the shortest path in your graph each time the shortestPath method is called.",
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"Use dijkstra’s algorithm to calculate the shortest paths."
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],
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"sampleTestCase": "[\"Graph\",\"shortestPath\",\"shortestPath\",\"addEdge\",\"shortestPath\"]\n[[4,[[0,2,5],[0,1,2],[1,2,1],[3,0,3]]],[3,2],[0,3],[[1,3,4]],[0,3]]",
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