Ex - Make Q

AtCoder
IDabc308_h
Time4000ms
Memory256MB
Difficulty
There is a simple undirected graph with $N$ vertices and $M$ edges. The edges are initially painted white. The vertices are numbered $1$ through $N$, and the edges are numbered $1$ through $M$. Edge $i$ connects vertex $A_i$ and vertex $B_i$, and the cost required to paint it black is $C_i$. "Making a Q" means painting four or more edges so that: * all but one of the edges painted black form a simple cycle, and * the edge painted black not forming the cycle connects a vertex on the cycle and another not on the cycle. Determine if one can make a Q. If one can, find the minimum total cost required to make a Q. ## Constraints * $4\leq N \leq 300$ * $4\leq M \leq \frac{N(N-1)}{2}$ * $1 \leq A_i < B_i \leq N$ * $(A_i,B_i) \neq (A_j,B_j)$, if $i \neq j$. * $1 \leq C_i \leq 10^5$ * All input values are integers. ## Input The 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]
Samples
Input #1
5 6
1 2 6
2 3 4
1 3 5
2 4 3
4 5 2
3 5 1
Output #1
15

By painting edges $2,3,4,5$, and $6$,

*   edges $2,4,5$, and $6$ forms a simple cycle, and
*   edge $3$ connects vertex $3$ (on the cycle) and vertex $1$ (not on the cycle),

so one can make a Q with a total cost of $4+5+3+2+1=15$. Making a Q in another way costs $15$ or greater, so the answer is $15$.
Input #2
4 4
1 2 1
2 3 1
3 4 1
1 4 1
Output #2
\-1
Input #3
6 15
2 6 48772
2 4 36426
1 6 94325
3 6 3497
2 3 60522
4 5 63982
4 6 4784
1 2 14575
5 6 68417
1 5 7775
3 4 33447
3 5 90629
1 4 47202
1 3 90081
2 5 79445
Output #3
78154
API Response (JSON)
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      "content": "There is a simple undirected graph with $N$ vertices and $M$ edges. The edges are initially painted white. The vertices are numbered $1$ through $N$, and the edges are numbered $1$ through $M$. Edge $",
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    "platform": "AtCoder",
    "limit": {
      "time_limit": 4000,
      "memory_limit": 262144
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    "difficulty": "None",
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    {
      "statement_type": "Markdown",
      "content": "There is a simple undirected graph with $N$ vertices and $M$ edges. The edges are initially painted white. The vertices are numbered $1$ through $N$, and the edges are numbered $1$ through $M$. Edge $...",
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