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cpbook-code/ch4/sssp/bellman_ford.py
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def main(): | |
INF = int(1e9) | |
# Graph in Figure 4.18, has negative weight, but no negative cycle | |
# 5 5 0 | |
# 0 1 1 | |
# 0 2 10 | |
# 1 3 2 | |
# 2 3 -10 | |
# 3 4 3 | |
# Graph in Figure 4.19, negative cycle exists, Bellman Ford's can detect this | |
# 3 3 0 | |
# 0 1 1000 | |
# 1 2 15 | |
# 2 1 -42 | |
f = open("bellman_ford_in.txt", "r") | |
V, E, s = map(int, f.readline().split(" ")) | |
AL = [[] for u in range(V)] | |
for _ in range(E): | |
u, v, w = map(int, f.readline().split(" ")) | |
AL[u].append((v, w)) | |
# Bellman Ford's routine, basically = relax all E edges V-1 times | |
dist = [INF for u in range(V)] # INF = 1e9 here | |
dist[s] = 0 | |
for i in range(0, V-1): # total O(V*E) | |
modified = False # optimization | |
for u in range(0, V): # these two loops = O(E) | |
if (not dist[u] == INF): # important check | |
for v, w in AL[u]: | |
if (dist[u]+w >= dist[v]): continue # not improving, skip | |
dist[v] = dist[u]+w # relax operation | |
modified = True # optimization | |
if (not modified): break # optimization | |
hasNegativeCycle = False | |
for u in range(0, V): # one more pass to check | |
if (not dist[u] == INF): | |
for v, w in AL[u]: | |
if (dist[v] > dist[u] + w): # should be false | |
hasNegativeCycle = True # if true => -ve cycle | |
print("Negative Cycle Exist? {}".format("Yes" if hasNegativeCycle else "No")) | |
if (not hasNegativeCycle): | |
for u in range(0, V): | |
print("SSSP({}, {}) = {}".format(s, u, dist[u])) | |
main() |