> For the complete documentation index, see [llms.txt](https://1005281342.gitbook.io/code-porter/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://1005281342.gitbook.io/code-porter/suan-fa/zui-duan-lu/4spfa-suan-fa.md).

# SPFA

**SPFA算法适用于求解负权图最短路问题，时间复杂度为mlog(n)**

```python
# https://www.acwing.com/problem/content/description/853/
from collections import defaultdict, deque

n, m = [int(x) for x in input().split(" ")]

dd = defaultdict(set)

# dist 记录每个点离起点的距离
dist = [float('inf')] * (n + 1)

# st 该点最短路是否已确定
st = [False] * (n + 1)

for _ in range(m):
    a, b, c = [int(x) for x in input().split(" ")]
    dd[a].add((b, c))

# 起点为1号点
dist[1] = 0

# dq
dq = deque()
dq.append(1)
st[1] = True

while dq:
    node = dq.popleft()
    st[node] = False

    # 处理每条边
    for new_node, wight in dd[node]:
        if dist[new_node] > dist[node] + wight:
            dist[new_node] = dist[node] + wight
            if not st[new_node]:
                dq.append(new_node)
                st[new_node] = True

if dist[n] == float('inf'):
    print("impossible")
else:
    print(dist[n])
```

## [概率最大的路径](https://leetcode-cn.com/contest/weekly-contest-197/problems/path-with-maximum-probability/)

```python
from typing import List
from collections import defaultdict, deque


class Solution:
    def maxProbability(self, n: int, edges: List[List[int]], succProb: List[float], start: int, end: int) -> float:
        dd = defaultdict(set)
        for i, x in enumerate(edges):
            a, b = x
            dd[a].add((b, succProb[i]))
            dd[b].add((a, succProb[i]))

        dist = [0] * (n + 1)
        st = [False] * (n + 1)

        dist[start] = 1
        dq = deque()
        dq.append(start)
        st[start] = True

        while dq:
            node = dq.popleft()
            st[node] = False

            # 处理每条边
            for new_node, wight in dd[node]:
                if dist[new_node] < dist[node] * wight:
                    dist[new_node] = dist[node] * wight
                    if not st[new_node]:
                        dq.append(new_node)
                        st[new_node] = True
        return dist[end]
```