Edge Deletion

AtCoder

IDabc243_e

Time2000ms

Memory256MB

Difficulty—

You are given a simple connected undirected graph with $N$ vertices and $M$ edges. Edge $i$ connects Vertex $A_i$ and Vertex $B_i$, and has a length of $C_i$. Let us delete some number of edges while satisfying the conditions below. Find the maximum number of edges that can be deleted. * The graph is still connected after the deletion. * For every pair of vertices $(s, t)$, the distance between $s$ and $t$ remains the same before and after the deletion. ## Constraints * $2 \leq N \leq 300$ * $N-1 \leq M \leq \frac{N(N-1)}{2}$ * $1 \leq A_i \lt B_i \leq N$ * $1 \leq C_i \leq 10^9$ * $(A_i, B_i) \neq (A_j, B_j)$ if $i \neq j$. * The given graph is connected. * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $M$ $A_1$ $B_1$ $C_1$ $A_2$ $B_2$ $C_2$ $\vdots$ $A_M$ $B_M$ $C_M$ [samples] ## Notes A simple connected undirected graph is a graph that is simple and connected and has undirected edges. A graph is simple when it has no self-loops and no multi-edges. A graph is connected when, for every pair of two vertices $s$ and $t$, $t$ is reachable from $s$ by traversing edges. The distance between Vertex $s$ and Vertex $t$ is the length of a shortest path between $s$ and $t$.

Samples

Input #1

Output #1

1

The distance between each pair of vertices before the deletion is as follows.

*   The distance between Vertex $1$ and Vertex $2$ is $2$.
*   The distance between Vertex $1$ and Vertex $3$ is $5$.
*   The distance between Vertex $2$ and Vertex $3$ is $3$.

Deleting Edge $3$ does not affect the distance between any pair of vertices. It is impossible to delete two or more edges while satisfying the condition, so the answer is $1$.

Input #2

Output #2

0

No edge can be deleted.

Input #3

Output #3

API Response (JSON)

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      "content": "You are given a simple connected undirected graph with $N$ vertices and $M$ edges.   Edge $i$ connects Vertex $A_i$ and Vertex $B_i$, and has a length of $C_i$. Let us delete some number of edges whil",
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    "platform": "AtCoder",
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      "statement_type": "Markdown",
      "content": "You are given a simple connected undirected graph with $N$ vertices and $M$ edges.  \nEdge $i$ connects Vertex $A_i$ and Vertex $B_i$, and has a length of $C_i$.\nLet us delete some number of edges whil...",
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      "language": "English"
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