代码随想录算法训练营第六十五天| 图论10

Bellman_ford 队列优化算法（又名SPFA）

代码随想录

import collections

def main():
    n, m = map(int, input().strip().split())
    edges = [[] for _ in range(n + 1)]
    for _ in range(m):
        src, dest, weight = map(int, input().strip().split())
        edges[src].append([dest, weight])
    
    minDist = [float("inf")] * (n + 1)
    minDist[1] = 0
    que = collections.deque([1])
    visited = [False] * (n + 1)
    visited[1] = True
    
    while que:
        cur = que.popleft()
        visited[cur] = False
        for dest, weight in edges[cur]:
            if minDist[cur] != float("inf") and minDist[cur] + weight < minDist[dest]:
                minDist[dest] = minDist[cur] + weight
                if visited[dest] == False:
                    que.append(dest)
                    visited[dest] = True
    
    if minDist[-1] == float("inf"):
        return "unconnected"
    return minDist[-1]

if __name__ == "__main__":
    print(main())

bellman_ford之判断负权回路

代码随想录

import sys

def main():
    input = sys.stdin.read
    data = input().split()
    index = 0
    
    n = int(data[index])
    index += 1
    m = int(data[index])
    index += 1
    
    grid = []
    for i in range(m):
        p1 = int(data[index])
        index += 1
        p2 = int(data[index])
        index += 1
        val = int(data[index])
        index += 1
        # p1 指向 p2，权值为 val
        grid.append([p1, p2, val])

    start = 1  # 起点
    end = n    # 终点

    minDist = [float('inf')] * (n + 1)
    minDist[start] = 0
    flag = False

    for i in range(1, n + 1):  # 这里我们松弛n次，最后一次判断负权回路
        for side in grid:
            from_node = side[0]
            to = side[1]
            price = side[2]
            if i < n:
                if minDist[from_node] != float('inf') and minDist[to] > minDist[from_node] + price:
                    minDist[to] = minDist[from_node] + price
            else:  # 多加一次松弛判断负权回路
                if minDist[from_node] != float('inf') and minDist[to] > minDist[from_node] + price:
                    flag = True

    if flag:
        print("circle")
    elif minDist[end] == float('inf'):
        print("unconnected")
    else:
        print(minDist[end])

if __name__ == "__main__":
    main()

bellman_ford之单源有限最短路

代码随想录

def main():
    # 輸入
    n, m = map(int, input().split())
    edges = list()
    for _ in range(m):
        edges.append(list(map(int, input().split() )))
    
    start, end, k = map(int, input().split())
    min_dist = [float('inf') for _ in range(n + 1)]
    min_dist[start] = 0
    
    # 只能經過k個城市，所以從起始點到中間有(k + 1)個邊連接
    # 需要鬆弛(k + 1)次
    
    for _ in range(k + 1):
        update = False
        min_dist_copy = min_dist.copy()
        for src, desc, w in edges:
            if (min_dist_copy[src] != float('inf') and 
            min_dist_copy[src] + w < min_dist[desc]):
                min_dist[desc] = min_dist_copy[src] + w
                update = True
        if not update:
            break
    # 輸出
    if min_dist[end] == float('inf'):
        print('unreachable')
    else:
        print(min_dist[end])
            
            

if __name__ == "__main__":
    main()