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How to Solve Reachable Nodes In Subdivided Graph Problem
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LeetCode ProblemReachable Nodes In Subdivided Graph
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. 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. 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]. 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. Given the original graph and maxMoves, return the number of nodes that are reachable from node 0 in the new graph.
GraphHeap (Priority Queue)Shortest Path
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Problem Breakdown
Understanding the Reachable Nodes In Subdivided Graph Problem
Let's break down this LeetCode problem and understand what makes it challenging in interview settings.
Problem Statement
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. 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. 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]. 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. Given the original graph and maxMoves, return the number of nodes that are reachable from node 0 in the new graph.
HardProblem #882
LeetCodeReachable Nodes In Subdivided Graph
Related Topics
GraphHeap (Priority Queue)Shortest Path
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Examples
# Example 1
Input
edges = [[0,1,10],[0,2,1],[1,2,2]], maxMoves = 6, n = 3
Output
13
# Example 2
Input
edges = [[0,1,4],[1,2,6],[0,2,8],[1,3,1]], maxMoves = 10, n = 4
Output
23
# Example 3
Input
edges = [[1,2,4],[1,4,5],[1,3,1],[2,3,4],[3,4,5]], maxMoves = 17, n = 5
Output
1
Constraints
0 <= edges.length <= min(n * (n - 1) / 2, 104)
edges[i].length == 3
0 <= ui < vi < n
There are no multiple edges in the graph.
0 <= cnti <= 104
0 <= maxMoves <= 109
1 <= n <= 3000
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Solve Reachable Nodes In Subdivided Graph — You are given an undirected graph (the "original graph") with n nodes labeled fr...
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def solve(input):
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Phantom Code catches common mistakes like off-by-one errors, missing edge cases, incorrect base conditions, and suboptimal approaches. It provides clean, well-structured code that handles all edge cases.
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The AI provides structured guidance: first the approach (what algorithm/data structure to use and why), then the implementation with clean code, and finally complexity analysis. This helps you think clearly even under pressure.
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