[Python] 弗洛伊德(Floyd)算法求圖的直徑並記錄路徑

程序輸出

（鄰接矩陣，矩陣元素M[i][j]表示頂點Vi與Vj間的距離）

（各個頂點間的最短路徑以及路徑長度，對於此例，頂點V4與V6或V8間的距離都是10，是距離最遠的兩個頂點對）

（此圖的直徑）

Python源代碼

# ----------------------------------------------
# Project： calculate diameter of graph
# Using floyd algorithm
# ----------------------------------------------


# define function: print shortest path
def getPath(i, j):
    if i != j:
        if path[i][j] == -1:
            print('-', j+1, end='')
        else:
            getPath(i, path[i][j])
            getPath(path[i][j], j)


def printPath(i, j):
    print(' Path:', i+1, end='')
    getPath(i, j)
    print()


print('---------------- Program start ----------------')
# read data
flag = input('please input type of graph(1:directed '
             'graph; 2:undirected graph): ')
vertex, edge = input('please input the number of '
                     'vertex and edge: ').strip().split()

# initialized
flag = int(flag)
vertex = int(vertex)
edge = int(edge)
inf = 99999999
dis = []  # matrix of the shortest distance
path = []  # record the shortest path
for i in range(vertex):
    dis += [[]]
    for j in range(vertex):
        if i == j:
            dis[i].append(0)
        else:
            dis[i].append(inf)
for i in range(vertex):
    path += [[]]
    for j in range(vertex):
        path[i].append(-1)


# read weight information
print('please input weight info(v1 v2 w[v1,v2]): ')
for i in range(edge):
    u, v, w = input().strip().split()
    u, v, w = int(u)-1, int(v)-1, int(w)
    if flag == 1:
        dis[u][v] = w
    elif flag == 2:
        dis[u][v] = w
        dis[v][u] = w
print('the weight matrix is:')
for i in range(vertex):
    for j in range(vertex):
        if dis[i][j] != inf:
            print('%5d' % dis[i][j], end='')
        else:
            print('%5s' % '∞', end='')
    print()


# floyd algorithm
for k in range(vertex):
    for i in range(vertex):
        for j in range(vertex):
            if dis[i][j] > dis[i][k] + dis[k][j]:
                dis[i][j] = dis[i][k] + dis[k][j]
                path[i][j] = k
print('===========================================')


# output the result
print('output the result:')
if flag == 1:
    for i in range(vertex):
        for j in range(vertex):
            if (i != j) and (dis[i][j] != inf):
                print('v%d ----> v%d  tol_weight:'
                      '%3d' % (i+1, j+1, dis[i][j]))
                printPath(i, j)
            if (i != j) and (dis[i][j] == inf):
                print('v%d ----> v%d  tol_weight:'
                      '  ∞' % (i+1, j+1))
                printPath(i, j)

if flag == 2:
    for i in range(vertex):
        for j in range(i+1, vertex):
            print('v%d <----> v%d  tol_weight:'
                  '%3d' % (i+1, j+1, dis[i][j]), '', end='')
            printPath(i, j)
print()
for i in range(vertex):
    for j in range(vertex):
        if dis[i][j] == inf:
            dis[i][j] = 0
# max(max(dis)): the max item of two dimension matrix
print('>> the diameter of graph: %d <<' % max(max(dis)))
print('-------------- Program end ----------------')

---

Reference

最短路徑_百度百科 最短路徑—Dijkstra算法和Floyd算法 最短路徑問題---Floyd算法詳解 - CSDN博客 Floyd算法(記錄路徑) - CSDN博客