{ "data": { "question": { "questionId": "918", "questionFrontendId": "882", "categoryTitle": "Algorithms", "boundTopicId": 1953, "title": "Reachable Nodes In Subdivided Graph", "titleSlug": "reachable-nodes-in-subdivided-graph", "content": "

You are given an undirected graph (the "original graph") with n nodes labeled from 0 to n - 1. You decide to subdivide each edge in the graph into a chain of nodes, with the number of new nodes varying between each edge.

\n\n

The graph is given as a 2D array of edges where edges[i] = [ui, vi, cnti] indicates that there is an edge between nodes ui and vi in the original graph, and cnti is the total number of new nodes that you will subdivide the edge into. Note that cnti == 0 means you will not subdivide the edge.

\n\n

To subdivide the edge [ui, vi], replace it with (cnti + 1) new edges and cnti new nodes. The new nodes are x1, x2, ..., xcnti, and the new edges are [ui, x1], [x1, x2], [x2, x3], ..., [xcnti-1, xcnti], [xcnti, vi].

\n\n

In this new graph, you want to know how many nodes are reachable from the node 0, where a node is reachable if the distance is maxMoves or less.

\n\n

Given the original graph and maxMoves, return the number of nodes that are reachable from node 0 in the new graph.

\n\n

 

\n

Example 1:

\n\"\"\n
\nInput: edges = [[0,1,10],[0,2,1],[1,2,2]], maxMoves = 6, n = 3\nOutput: 13\nExplanation: The edge subdivisions are shown in the image above.\nThe nodes that are reachable are highlighted in yellow.\n
\n\n

Example 2:

\n\n
\nInput: edges = [[0,1,4],[1,2,6],[0,2,8],[1,3,1]], maxMoves = 10, n = 4\nOutput: 23\n
\n\n

Example 3:

\n\n
\nInput: edges = [[1,2,4],[1,4,5],[1,3,1],[2,3,4],[3,4,5]], maxMoves = 17, n = 5\nOutput: 1\nExplanation: Node 0 is disconnected from the rest of the graph, so only node 0 is reachable.\n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "细分图中的可到达结点", "translatedContent": "

给你一个无向图（原始图），图中有 n 个节点，编号从 0 到 n - 1 。你决定将图中的每条边 细分 为一条节点链，每条边之间的新节点数各不相同。

\n\n

图用由边组成的二维数组 edges 表示，其中 edges[i] = [ui, vi, cnti] 表示原始图中节点 ui 和 vi 之间存在一条边，cnti 是将边 细分 后的新节点总数。注意，cnti == 0 表示边不可细分。

\n\n

要 细分 边 [ui, vi] ，需要将其替换为 (cnti + 1) 条新边，和 cnti 个新节点。新节点为 x1, x2, ..., xcnti ，新边为 [ui, x1], [x1, x2], [x2, x3], ..., [xcnti+1, xcnti], [xcnti, vi] 。

\n\n

现在得到一个 新的细分图 ，请你计算从节点 0 出发，可以到达多少个节点？如果节点间距离是 maxMoves 或更少，则视为 可以到达 。

\n\n

给你原始图和 maxMoves ，返回 新的细分图中从节点 0 出发 可到达的节点数 。

\n\n

 

\n\n

示例 1：

\n\"\"\n
\n输入：edges = [[0,1,10],[0,2,1],[1,2,2]], maxMoves = 6, n = 3\n输出：13\n解释：边的细分情况如上图所示。\n可以到达的节点已经用黄色标注出来。\n
\n\n

示例 2：

\n\n
\n输入：edges = [[0,1,4],[1,2,6],[0,2,8],[1,3,1]], maxMoves = 10, n = 4\n输出：23\n
\n\n

示例 3：

\n\n
\n输入：edges = [[1,2,4],[1,4,5],[1,3,1],[2,3,4],[3,4,5]], maxMoves = 17, n = 5\n输出：1\n解释：节点 0 与图的其余部分没有连通，所以只有节点 0 可以到达。\n
\n\n

 

\n\n

提示：

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