[ICPC 2022 Jinan R] Shortest Path

Luogu

IDLGP9675

Time3000ms

Memory512MB

DifficultyP7

2022O2优化半平面交ICPC李超线段树济南

You are given an undirected weighted graph $G$ with vertices $1, 2, \ldots, n$. Please output the sum of the answers to the following $x$ questions: - The $i$-th question $(1\le i\le x$): What is the minimum length of path that starts at vertex $1$, ends at vertex $n$, and contains exactly $i$ edges? For each question, if such a path does not exist, the answer is considered to be $0$. A path may use one edge multiple times. Output the answer modulo $998244353$. ## Input The first line contains one integer $T~(1 \le T\le 2000)$, the number of test cases. For each test case, the first line contains three integers $n, m, x~(1\le n\le 2000, 0\le m\le 5000, 1\le x\le 10^9)$. Each of the next $m$ lines describes an edge of the graph. Edge $i$ is denoted by three integers $a_i, b_i, w_i$ $(1\le a_i, b_i\le n, 1\le w_i\le 10^9)$, the labels of vertices it connects and its weight. Note that self-loops and parallel edges may exist. It is guaranteed that the sum of $n$ over all test cases is no more than $2000$ and the sum of $m$ over all test cases is no more than $5000$. ## Output For each test case, output one integer modulo $998244353$ denoting the answer. [samples]

Samples

Input #1

4
3 2 10
1 2 5
2 3 4
3 0 1000000000
3 3 100
1 2 3
1 3 4
2 3 5
4 6 1000000000
1 2 244
1 2 325
1 4 927
3 3 248
2 4 834
3 4 285

Output #1

API Response (JSON)

{
  "problem": {
    "name": "[ICPC 2022 Jinan R] Shortest Path",
    "description": {
      "content": "You are given an undirected weighted graph $G$ with vertices $1, 2, \\ldots, n$. Please output the sum of the answers to the following $x$ questions: - The $i$-th question $(1\\le i\\le x$): What is the ",
      "description_type": "Markdown"
    },
    "platform": "Luogu",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 524288
    },
    "difficulty": {
      "LuoguStyle": "P7"
    },
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "LGP9675"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given an undirected weighted graph $G$ with vertices $1, 2, \\ldots, n$. Please output the sum of the answers to the following $x$ questions:\n- The $i$-th question $(1\\le i\\le x$): What is the ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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