Problem:
 Score : 400 points    Problem Statement There is a directed graph with N vertices and M edges.
The i -th edge (1≤i≤M) points from vertex a_i to vertex b_i , and has a weight c_i .
We will play the following single-player game using this graph and a piece.  Initially, the piece is placed at vertex 1 , and the score of the player is set to 0 .
The player can move the piece as follows:   When the piece is placed at vertex a_i , move the piece along the i -th edge to vertex b_i . After this move, the score of the player is increased by c_i .   The player can end the game only when the piece is placed at vertex N .
The given graph guarantees that it is possible to traverse from vertex 1 to vertex N .  When the player acts optimally to maximize the score at the end of the game, what will the score be?
If it is possible to increase the score indefinitely, print inf .      Constraints  2≤N≤1000   1≤M≤min(N(N-1),2000)   1≤a_i,b_i≤N (1≤i≤M)   a_i≠b_i (1≤i≤M)   a_i≠a_j or b_i≠b_j (1≤i<j≤M)   -10^9≤c_i≤10^9 (1≤i≤M)  c_i is an integer.  In the given graph, there exists a path from vertex 1 to vertex N .         Input Input is given from Standard Input in the following format:  N  M  a_1  b_1  c_1  a_2  b_2  c_2  :  a_M  b_M  c_M       Output Print the maximum possible score at the end of the game, if it is finite. If it is possible to increase the score indefinitely, print inf .        Sample Input 1 3 3
1 2 4
2 3 3
1 3 5      Sample Output 1 7  There are two ways to move the piece to vertex N=3 :   vertex 1 → vertex 2 → vertex 3 : score 4+3=7  vertex 1 → vertex 3 : score 5   Thus, the maximum possible score at the end of the game is 7 .       Sample Input 2 2 2
1 2 1
2 1 1      Sample Output 2 inf  It is possible to increase the score indefinitely by alternating between vertex 1 and 2 .       Sample Input 3 6 5
1 2 -1000000000
2 3 -1000000000
3 4 -1000000000
4 5 -1000000000
5 6 -1000000000      Sample Output 3 -5000000000

Solution (Python):
n, m = map(int, raw_input().split())
graph = {}
visited = {}

scores = {}
for i in range(n):
    if i == 0:
        scores[i+1] = 0
    else:
        scores[i+1] = float("inf")
    graph[i+1] = {}

for i in range(m):
    a, b, c = map(int, raw_input().split())
    graph[a][b] = -c
    

for i in range(n):
    for v in graph.keys():
        for e in graph[v].keys():
            if scores[e] > scores[v] + graph[v][e]:
                scores[e] = scores[v] + graph[v][e]

ans = -scores[n]
negative = {}
for i in range(n):
    negative[i+1] = False

for i in range(n+1):
    if negative[n]:
        break
    for v in graph.keys():
        for e in graph[v].keys():
            if scores[v] + graph[v][e] < scores[e]:
                scores[e] = scores[v] + graph[v][e]
                negative[e] = True
                if negative[v]:
                    negative[e] = True

if negative[n]:
    print 'inf'
else:
    print ans

Solution (Python):
n,m=map(int,input().split())
e=[tuple(map(int,input().split())) for _ in range(m)]
d=[0]+[-float('inf')]*(n-1)
for _ in range(n-1):
    for a,b,c in e:
        d[b-1]=max(d[b-1],d[a-1]+c)
r=d[n-1]
for _ in range(n-1):
    for a,b,c in e:
        d[b-1]=max(d[b-1],d[a-1]+c)
if d[n-1]==r:
    print(r)
else:
    print('inf')

Solution (Python):
import sys
N,M=map(int, input().split())
a=[]
b=[]
c=[]
for m in range (0,M):
  A,B,C=map(int, input().split() )
  a+=[A]
  b+=[B]
  c+=[C]
V=[0]+[-10**12]*(N-1)
 
for n in range(N-1):
  for m in range(M):
    u=a[m]
    v=b[m]
    if V[b[m]-1]<V[a[m]-1]+c[m]:
      V[b[m]-1]=V[a[m]-1]+c[m]
 
moji2=[0]*N
for n in range(N):
  for m in range(M):
    u=a[m]
    v=b[m]
    if V[b[m]-1]<V[a[m]-1]+c[m]:
      V[b[m]-1]=V[a[m]-1]+c[m]
      moji2[b[m]-1]=1
      if moji2[N-1]:
        print("inf")
        sys.exit()
print(V[N-1])

Solution (Python):

n, m = map(int, raw_input().split())
a, b, c = [], [], []
for i in xrange(m):
    at, bt, ct = map(int, raw_input().split())
    a.append(at - 1)
    b.append(bt - 1)
    c.append(ct)

point = [-1e9 * m - 1] * n
point[0] = 0

for i in xrange(n+1):
    for j in xrange(m):
        if point[b[j]] < point[a[j]] + c[j]:
            point[b[j]] = point[a[j]] + c[j]

looped = [False] * n
for i in xrange(n):
    for j in xrange(m):
        if point[b[j]] < point[a[j]] + c[j]:
            looped[b[j]] = True
        if looped[a[j]] == True:
            looped[b[j]] = True
if looped[n-1]:
    print("inf")
else:
    print(point[n-1])

Solution (Python):
import math

INF = float("inf")

V, E = map(int, input().split())
es = []

for _ in range(E):
    a, b, c = map(int, input().split())
    es.append([a-1, b-1, -c])

d = [INF] * V
d[0] = 0
cnt = [0] * V

for _ in range(V):
    updated = False
    for e in es:
        if math.isinf(d[e[0]]):
            continue
        if d[e[1]] > d[e[0]] + e[2]:
            d[e[1]] = d[e[0]] + e[2]
            cnt[e[1]] += 1
            updated = True
    if not updated:
        break

print(-d[V-1] if cnt[V-1] < V else "inf")

Solution (Python):

MAX_N = 10 ** 3 + 10
MAX_M = 2 * (10 ** 3) + 1
INF = 10 ** 13

def bfs(graph, N, M):
    que = []
    que.append([0, 0])
    visited = [-INF for x in range(MAX_N)]
    update_cnt = [0 for x in range(MAX_N)]
    result = -INF
    while (len(que) > 0):
        now = que[0]
        que.pop(0)

        pos = now[0]
        cost = now[1]
        if (visited[pos] > cost):
            continue
        for val in graph[pos]:
            nxt = val[0]
            nxt_cost = val[1]

            if (cost + nxt_cost > visited[nxt] and update_cnt[nxt] < MAX_M):
                visited[nxt] = cost + nxt_cost
                update_cnt[nxt] += 1
                que.append([nxt, nxt_cost + cost])

    if (update_cnt[N - 1] >= MAX_N):
        return (0, False)
    return (visited[N - 1], True)


if __name__ == "__main__":
    N, M = map(int, input().split())
    graph = [[] for x in range(MAX_N)]
    for x in range(M):
        a,b,c = map(int, input().split())
        a -= 1
        b -= 1
        graph[a].append([b, c])
    res,ok = bfs(graph, N, M)
    if (not ok):
        print ('inf')
    else:
        print (res)

Solution (Python):
INF = 10**15
N, M = map(int, raw_input().split())
G = [map(int, raw_input().split()) for _ in range(M)]

def run():
    cost = [-INF for i in range(N+1)]
    cost[1] = 0
    for _ in range(N+1):
        for a, b, c in G:
            if cost[a] == INF:
                continue
            if cost[a] + c > cost[b]:
                cost[b] = cost[a] + c
    looped = [False for i in range(N+1)]
    for _ in range(N+1):
        for a, b, c in G:
            if cost[a] == INF:
                continue
            if cost[a] + c > cost[b]:
                looped[b] = True
            if looped[a]:
                looped[b] = True
    return "inf" if looped[N] else cost[N]
print run()

Solution (Python):
N, M = list(map(int, input().split()))
a = []
b = []
c = []

for o in range(M):
    a_i, b_i, c_i = list(map(int, input().split()))
    a.append(a_i)
    b.append(b_i)
    c.append(c_i)


cost = [-float('inf') for i in range(N + 1)]
cost[1] = 0
flag = True

for _ in range(N - 1):
    for k in range(M):
        cost[b[k]] = max(cost[b[k]], cost[a[k]] + c[k])

cost_n = cost[N]

def check():
    for l in range(M):
        cost[b[l]] = max(cost[b[l]], cost[a[l]] + c[l])
    if cost[N] > cost_n:
        return 'inf'
    return cost[N]


print(check())

Solution (Python):







mozir=input()
hyo=mozir.split(' ')

N=int(hyo[0])
M=int(hyo[1])


tuuro=[]



for idx in range(0,N,1):
    tuuro.append([])


A=[]
B=[]

for idx in range(0,M,1):
    mozir=input()
    hyo=mozir.split(' ')
    tuuro[int(hyo[0])-1].append((int(hyo[1])-1,int(hyo[2])))




tmp_score=[None]*N 
tmp_score[0]=0
tansaku=[0]
loopconut=0
while len(tansaku) > 0:
    loopconut=loopconut+1
    next_tansaku=[]
    for mono in tansaku:
        for deru in tuuro[mono]:
            kouho_ten=tmp_score[mono]+deru[1]
            if tmp_score[deru[0]] == None or kouho_ten > tmp_score[deru[0]]:
                tmp_score[deru[0]]=kouho_ten
                next_tansaku.append(deru[0])

    tansaku=list(set(next_tansaku))
    if loopconut==N-1:
        tmp_ans=tmp_score[N-1] 
    elif loopconut==2*N-1:
        
        if tmp_score[N-1] > tmp_ans:
            print('inf')
            break
        else:
            
            print(tmp_score[N-1])
            break
else:
    print(tmp_score[N-1])

Solution (Python):
import sys
from math import sqrt

inf = 1<<60

def solve():
    N, M = map(int, sys.stdin.readline().split())

    edges = [None] * M
    
    Adjr = [[] for i in range(N)]

    for i in range(M):
        ai, bi, ci = map(int, sys.stdin.readline().split())
        edges[i] = (ai - 1, bi - 1, -ci)
        
        Adjr[bi - 1].append(ai - 1)

    reachable = [False] * N
    dfs(N, M, Adjr, reachable, N - 1)

    edges = [(u, v, c) for (u, v, c) in edges if reachable[u] and reachable[v]]

    ans = BellmanFord(N, M, edges)

    if ans is None:
        print('inf')
    else:
        print(-ans)

def dfs(N, M, Adj, visited, u):
    visited[u] = True

    for v in Adj[u]:
        if not visited[v]:
            dfs(N, M, Adj, visited, v)

def BellmanFord(N, M, edges):
    d = [inf] * N
    d[0] = 0

    for i in range(N):
        flag = False

        for (u, v, c) in edges:
            if d[u] != inf and d[u] + c < d[v]:
                d[v] = d[u] + c
                flag = True

        if not flag:
            break

        if flag and i == N - 1:
            return None

    return d[N - 1]

if __name__ == '__main__':
    solve()

Solution (Python):
import sys
from math import sqrt

inf = 1<<60

def solve():
    N, M = map(int, sys.stdin.readline().split())

    edges = [None] * M
    Adj = [[] for i in range(N)]
    Adjr = [[] for i in range(N)]

    for i in range(M):
        ai, bi, ci = map(int, sys.stdin.readline().split())
        edges[i] = (ai - 1, bi - 1, -ci)
        Adj[ai - 1].append(bi - 1)
        Adjr[bi - 1].append(ai - 1)

    visitable = [False] * N
    dfs(N, M, Adj, visitable, 0)

    reachable = [False] * N
    dfs(N, M, Adjr, reachable, N - 1)

    valid = [visitable[i] and reachable[i] for i in range(N)]

    edges = [(u, v, c) for (u, v, c) in edges if valid[u] and valid[v]]

    ans = BellmanFord(N, M, edges, valid)

    if ans is None:
        print('inf')
    else:
        print(-ans)

def dfs(N, M, Adj, visited, u):
    visited[u] = True

    for v in Adj[u]:
        if not visited[v]:
            dfs(N, M, Adj, visited, v)

def BellmanFord(N, M, edges, valid):
    d = [inf] * N
    d[0] = 0

    for i in range(N):
        flag = False

        for (u, v, c) in edges:
            if d[u] != inf and d[u] + c < d[v]:
                d[v] = d[u] + c
                flag = True

        if not flag:
            break

        if flag and i == N - 1:
            return None

    return d[N - 1]

if __name__ == '__main__':
    solve()

Solution (Python):
import sys
sys.setrecursionlimit(100000)

def set_enable_goal(cur_node, back_paths, enable_goal):
    if cur_node in back_paths:
        for next_node in back_paths[cur_node]:
            if enable_goal[next_node - 1] == 0:
                enable_goal[next_node - 1] = 1
                set_enable_goal(next_node, back_paths, enable_goal)


N, M = map(int, input().split())
MIN = float('-inf')
INF_LIMIT = -MIN

back_paths = {}
all_paths = {}
for i in range(M):
    a, b, c = map(int, input().split())
    if a in all_paths:
        all_paths[a].append((b, c))
    else:
        all_paths[a] = [(b, c)]

    if b in back_paths:
        back_paths[b].append(a)
    else:
        back_paths[b] = [a]



enable_goal= [0 for i in range(N)]
enable_goal[N - 1] = 1
set_enable_goal(N, back_paths, enable_goal)

scores = [MIN for i in range(N)]
scores[0] = 0

is_inf = False
for n in range(N):
    for a in all_paths.keys():
        if not enable_goal[a - 1]:
            continue
        for b, c in all_paths[a]:
            if not enable_goal[b - 1]:
                continue
            scores[b - 1] = max(scores[b - 1], scores[a - 1] + c)


if not is_inf:
    prev_score = scores[N - 1]
    for a in all_paths.keys():
        if not enable_goal[a - 1]:
            continue
        for b, c in all_paths[a]:
            if not enable_goal[b - 1]:
                continue
            scores[b - 1] = max(scores[b - 1], scores[a - 1] + c)
    if prev_score != scores[N - 1]:
        is_inf = True


if is_inf:
    print('inf')
else:
    print(scores[N - 1])

Solution (Python):
import sys
sys.setrecursionlimit(100000)

def set_enable_goal(cur_node, back_paths, enable_goal):
    if cur_node in back_paths:
        for next_node in back_paths[cur_node]:
            if enable_goal[next_node - 1] == 0:
                enable_goal[next_node - 1] = 1
                set_enable_goal(next_node, back_paths, enable_goal)


N, M = map(int, input().split())
MIN = float('-inf')
INF_LIMIT = -MIN

back_paths = {}
all_paths = {}
for i in range(M):
    a, b, c = map(int, input().split())
    if a in all_paths:
        all_paths[a].append((b, c))
    else:
        all_paths[a] = [(b, c)]

    if b in back_paths:
        back_paths[b].append(a)
    else:
        back_paths[b] = [a]



enable_goal= [0 for i in range(N)]
enable_goal[N - 1] = 1
set_enable_goal(N, back_paths, enable_goal)

for a, paths in all_paths.items():
    if not enable_goal[a - 1]:
        all_paths[a] = []
    else:
        valid_paths = []
        for b, c in paths:
            if enable_goal[b - 1]:
                valid_paths.append((b, c))
        all_paths[a] = valid_paths


scores = [MIN for i in range(N)]
scores[0] = 0

is_inf = False
for n in range(N):
    for a in all_paths.keys():
        for b, c in all_paths[a]:
            scores[b - 1] = max(scores[b - 1], scores[a - 1] + c)


if not is_inf:
    prev_score = scores[N - 1]
    for a in all_paths.keys():
        for b, c in all_paths[a]:
            scores[b - 1] = max(scores[b - 1], scores[a - 1] + c)
    if prev_score != scores[N - 1]:
        is_inf = True


if is_inf:
    print('inf')
else:
    print(scores[N - 1])

Solution (Python):


import numpy as np
N, M = map(int, raw_input().split())
R = [map(int, raw_input().split()) for i in xrange(M)] 

score = [None for _ in xrange(N+1)]
score[1] = 0
for _ in xrange(N):
    for  a, b, c in R:
        if score[a] != None:
          score[b] = max(score[b], score[a] + c) 
v1 = score[-1]

for _ in xrange(N):
    for  a, b, c in R:
          if score[a] != None:
            score[b] = max(score[b], score[a] + c)
v2 = score[-1]

if v1 != v2:
    print "inf"
else:
    print v2

Solution (Python):
import sys

inf = 1<<60

def solve():
    N, M = map(int, input().split())
    edges = [None] * M

    for i in range(M):
        ai, bi, ci = map(int, sys.stdin.readline().split())
        ai, bi = ai - 1, bi - 1
        edges[i] = (ai, bi, -ci)

    ans = BellmanFord(N, M, edges)

    if ans is None:
        print('inf')
    else:
        print(-ans)

def BellmanFord(N, M, edges):
    d = [inf] * N
    d[0] = 0

    for i in range(N - 1):
        for (u, v, c) in edges:
            if d[u] + c < d[v]:
                d[v] = d[u] + c

    for i in range(N):
        for (u, v, c) in edges:
            if d[u] + c < d[v]:
                if v == N - 1:
                    return None

                d[v] = d[u] + c

    return d[N - 1]

if __name__ == '__main__':
    solve()

Solution (Python):
import sys

inf = 1<<60

def solve():
    N, M = map(int, input().split())
    edges = [None] * M

    for i in range(M):
        ai, bi, ci = map(int, sys.stdin.readline().split())
        ai, bi = ai - 1, bi - 1
        edges[i] = (ai, bi, -ci)

    ans = BellmanFord(N, M, edges)

    if ans is None:
        print('inf')
    else:
        print(-ans)

def BellmanFord(N, M, edges):
    d = [inf] * N
    d[0] = 0

    for i in range(N - 1):
        for (u, v, c) in edges:
            if d[u] + c < d[v]:
                d[v] = d[u] + c

    for i in range(N):
        for (u, v, c) in edges:
            if d[u] + c < d[v]:
                if v == N - 1:
                    return None

                d[v] = d[u] + c

    return d[N - 1]

if __name__ == '__main__':
    solve()

Solution (Python):
N,M = map(int, input().split())

from collections import defaultdict
E = []

for i in range(M):
  a,b,c = map(int, input().split())
  a,b = a-1, b-1
  E += [(a,b,c)]

def reachable_vertices(neighbor, s):
  V = set()
  V.add(s)
  stack=[s]
  while stack:
    v = stack.pop()
    for u in neighbor[v]:
      if u not in V:
        V.add(u)
        stack.append(u)
  return V

def neighbor_dict(E):
  neighbor = defaultdict(list)
  for a,b,c in E:
    neighbor[a].append(b)
  return neighbor

def rev_neighbor_dict(E):
  neighbor = defaultdict(list)
  for a,b,c in E:
    neighbor[b].append(a)
  return neighbor

def degenerate_graph(V, E):
  d = {v:i for i,v in enumerate(sorted(V))}
  return len(V), [(d[a],d[b],c) for a,b,c in E if a in V and b in V]


N,E = degenerate_graph(reachable_vertices(neighbor_dict(E), 0), E)
N,E = degenerate_graph(reachable_vertices(rev_neighbor_dict(E), N-1), E)
score = [float('-inf')]*N
score[0] = 0


i = 0
updated=True
while updated:
  if i == N:
    print('inf')
    break

  updated = False
  for a,b,w in E:
    if score[b] < score[a] + w:
      score[b] = score[a] + w
      updated = True
  i += 1
else:
  print(score[N-1])

Solution (Python):


import sys
from collections import defaultdict

if __name__ == "__main__":
    N, M = map(int, input().split(" "))

    V = set()
    E = []
    for i in range(M):
        a, b, c = map(int, input().split(" "))
        V.add(a)
        V.add(b)
        E.append((a, b, -c))

    dist = defaultdict(lambda :10**20 + 1)
    pre = {}
    dist[1] = 0


    for i in range(1, len(V)):
        for edge in E:
            u = edge[0]
            v = edge[1]

            if dist[v] > dist[u] + edge[2]:
                dist[v] = dist[u] + edge[2]
                pre[v] = u

    is_cycle = False
    cycle_node = []
    for edge in E:
        u = edge[0]
        v = edge[1]
        if dist[u] + edge[2] < dist[v]:
            is_cycle = True
            cycle_node.append(u)

    is_inf = False
    if is_cycle:
        route_node = N
        while route_node != 1:
            route_node = pre[route_node]
            if route_node in cycle_node:
                is_inf = True
                break


    if is_inf:
        print ("inf")
    else:
        print (-dist[N])

Solution (Python):
n, m = map(int, input().split())
dist = [-10**18] * n
edge = []
for i in range(m):
    a, b, c = map(int, input().split())
    edge.append((a - 1, b - 1, c))
dist[0] = 0
for i in range(n):
    for i in edge:
        a, b, c = i
        if dist[a] + c > dist[b]:
            dist[b] = dist[a] + c
            updated = True
ans = dist[n - 1]
for i in range(n):
    for i in edge:
        a, b, c = i
        if dist[a] + c > dist[b]:
            dist[b] = dist[a] + c
            updated = True
if ans == dist[n - 1]:
    print(dist[n - 1])
else:
    print("inf")

Solution (Python):
import math 
from collections import defaultdict as dd
def main():
    N, M = map(int, input().split())

    MAP = [[]*N for x in range(N)]
    E = []
    for m in range(M):
        a,b,c = map(int, input().split())
        MAP[a-1].append((b-1, c))
        E.append((a-1,b-1,c))

    dp = [-float('inf')]*N
    dp[0] = 0
    updated = set([0])
    for count in range(1, 2*N+1):  
        preupdated = list(updated)
        updated = set([])
        for a in preupdated:
            for b,c in MAP[a]:
                if max(dp[b], dp[b]) < dp[a] + c:
                    updated.add(b)
                    dp[b] = dp[a] + c
        if count == N-1:
            tmp = dp[N-1]

    
    if dp[N-1] == tmp:
        print(tmp)
    else:
        print('inf')


if __name__ == "__main__":
    
    
    main()

Solution (Python):
N, M = map(int, raw_input().split())
D = [map(int, raw_input().split()) for _ in range(M)]
 
score = [None for _ in range(N+1)]
score[1] = 0
 
for _ in range(N):
    for a, b, c in D:
        if score[a] != None:
            score[b] = max(score[b], score[a] + c)
v1 = score[-1]
for _ in range(N):
    for a, b, c in D:
        if score[a] != None:
            score[b] = max(score[b], score[a] + c)
v2 = score[-1]
 
if v1 != v2:
    print "inf"
else:
    print v2

Solution (Python):
N, M = map(int, raw_input().split())
D = [map(int, raw_input().split()) for _ in range(M)]
 
score = [None for _ in range(N+1)]
score[1] = 0
 
for _ in range(N):
    for a, b, c in D:
        if score[a] != None:
            score[b] = max(score[b], score[a] + c)
v1 = score[-1]
for _ in range(N):
    for a, b, c in D:
        if score[a] != None:
            score[b] = max(score[b], score[a] + c)
v2 = score[-1]
 
if v1 != v2:
    print "inf"
else:
    print v2

Solution (Python):
N,M = map(int, input().split())

from collections import defaultdict
neighbor = defaultdict(list)
rev_neighbor = defaultdict(list)
E = []

for i in range(M):
  a,b,c = map(int, input().split())
  a,b = a-1, b-1
  E += [(a,b,c)]
  neighbor[a].append(b)
  rev_neighbor[b].append(a)

def reachable_vertices(neighbor, s):
  V = set()
  V.add(s)
  stack=[s]
  while stack:
    v = stack.pop()
    for u in neighbor[v]:
      if u not in V:
        V.add(u)
        stack.append(u)
  return V


V = reachable_vertices(neighbor, 0) & reachable_vertices(rev_neighbor, N-1)

E = [(a,b,c) for a,b,c in E if a in V or b in V]
score = defaultdict(lambda: float('-inf'))
score[0] = 0


i = 0
updated=True
while updated:
  if i == len(V):
    print('inf')
    break

  updated = False
  for a,b,w in E:
    if score[b] < score[a] + w:
      score[b] = score[a] + w
      updated = True
  i += 1
else:
  print(score[N-1])

Solution (Python):


N,M = map(int, input().split())

from collections import defaultdict
neighbor = defaultdict(list)
Rneighbor = defaultdict(list)
edges = []
for i in range(M):
  a,b,c = map(int, input().split())
  a,b = a-1, b-1
  edges += [(a,b,c)]
  neighbor[a].append(b)
  Rneighbor[b].append(a)


v1 = set()
v1.add(0)
stack = [0]
while stack:
  v = stack.pop()
  for u in neighbor[v]:
    if u not in v1:
      v1.add(u)
      stack.append(u)

vn = set()
vn.add(N-1)
stack = [N-1]
while stack:
  v = stack.pop()
  for u in Rneighbor[v]:
    if u not in vn:
      vn.add(u)
      stack.append(u)

V = v1 & vn

edges = [(a,b,c) for a,b,c in edges if a in V and b in V]
score = [float('-inf')]*N
score[0] = 0

updated = True
i = 0

positive_cycle = False

while updated:
  if i == len(V):
    positive_cycle = True
    break

  updated = False
  for a,b,w in edges:
    if score[b] < score[a] + w:
      score[b] = score[a] + w
      updated = True
  i += 1

if positive_cycle:
  print('inf')
else:
  print(score[N-1])

Solution (Python):
import sys
from collections import Counter

sys.setrecursionlimit(10**7)
 
inf = 1<<100
 
def solve():
    N, M = map(int, input().split())
    edges = [None]*M
    Adj = [[] for i in range(N)]
 
    for i in range(M):
        ui, vi, ci = map(int, sys.stdin.readline().split())
        ui, vi = ui - 1, vi - 1
        edges[i] = (ui, vi, -ci)
        Adj[ui].append(vi)

    visitable = [False]*N

    dfs(N, M, Adj, visitable, 0)

    reachable = [False]*N
    reachable[0] = True
    reachable[N - 1] = True

    for u in range(1, N - 1):
        visited = [False]*N

        dfs(N, M, Adj, visited, u)

        if visited[N - 1]:
            reachable[u] = True
 
    ans = Bellmanford(N, M, edges, visitable, reachable)
 
    if ans is not None:
        print(-ans)
    else:
        print('inf')

def dfs(N, M, Adj, visitable, u):
    visitable[u] = True

    for v in Adj[u]:
        if not visitable[v]:
            dfs(N, M, Adj, visitable, v)

def Bellmanford(N, M, edges, visitable, reachable):
    dist = [inf]*N
    dist[0] = 0
    flag = True

    cnt = 0
 
    for i in range(N):
        flag = False

        for (u, v, c) in edges:
            if dist[u] != inf and dist[v] > dist[u] + c:
                dist[v] = dist[u] + c

                if visitable[v] and reachable[v]:
                    flag = True

        

        if not flag:
            break

        if flag and i == N - 1:
            return None

    return dist[N - 1]
 
if __name__ == '__main__':
    solve()

Solution (Python):
def read_data():
    N, M = map(int, input().split())
    Es = [[] for _ in range(N)]
    Cs = [[float('inf')] * N for n in range(N)]
    for m in range(M):
        a, b, c = map(int, input().split())
        Es[a - 1].append(b - 1)
        Cs[a - 1][b - 1] = -c
    return N, M, Es, Cs

def solve(N, M, Es, Cs):
    dist = [float('inf')] * N
    dist[0] = 0
    for i in range(N + 1):
        for v in range(N):
            Cv = Cs[v]
            for e in Es[v]:
                c = Cv[e]
                if dist[v] != float('inf') and dist[e] > dist[v] + c:
                    dist[e] = dist[v] + c
                    if (i == N - 1):
                        d = dist[N - 1]
                    if (i == N):
                        if d != dist[N - 1]:
                            return 'inf'
    return -dist[N - 1]

N, M, Es, Cs = read_data()
print(solve(N, M, Es, Cs))

Solution (Python):

N,M = map(int,input().split())

class Bellman_Ford(object):
	"""
	ベルマンフォード法, O(EV)
	ステータス:distance(list),prev(list),length(int)
	edge=[i, j, cost] のリスト
	"""
	def __init__(self, edge, start, length):
		self.start=start
		self.length=length
		self.distance=[float("inf") for x in range(self.length)]
		self.distance[start]=0
		self.prev=[0 for x in range(self.length)]
		self.prev[start]=-1
		self.solvable=True
		def update():
			for i in edge:
				d=self.distance[i[0]]+i[2]
				if d<self.distance[i[1]]:
					self.distance[i[1]]=d 
					self.prev[i[1]]=i[0]
		for i in range(length-1):
			update()
		memo=self.distance[-1]
		for i in range(length-1):
			update()
		if memo!=self.distance[-1]:
			self.solvable=False

	def route(self,goal):
		route=[]
		while(True):
			route.append(self.prev[goal])
			goal=self.prev[goal]
			if goal==self.start:
				break
		route.reverse()
		return(route)

edges = []
for i in range(M):
	a,b,c = map(int,input().split())
	edges.append([a-1,b-1,-c])

B = Bellman_Ford(edges,0,N)
if (not B.solvable):
	print("inf")
else:
	print(-B.distance[-1])

Solution (Python):
n,m = map(int, input().split())
g = [[] for i in range(n)]
for i in range(m):
    a,b,c = map(int, input().split())
    a -= 1
    b -= 1
    g[a].append((b, -c))


dist = [float('inf') for i in range(n)]
dist[0] = 0
prev = [-1 for i in range(n)]
negative_cycle = False
for k in range(n*2):
    for i in range(n):
        for dst, cst in g[i]:
            src = i
            if dist[dst] > dist[src] + cst:
                dist[dst] = dist[src] + cst
                prev[dst] = src
                if k >= n-1 and dst == n-1:
                    dist[dst] = -float('inf')
                    negative_cycle = True

if negative_cycle:
    print('inf')
else:
    print(-dist[n-1])

Solution (Python):
import sys
import random

def rd():
        return sys.stdin.readline().rstrip()

def rdi():
        return [ long(x) for x in rd().split() ]

INF = 1000000000 * 2000 + 1

N, M = rdi()
a = []
b = []
c = []
for i in range(M):
        ai, bi, ci = rdi()
        a.append(ai)
        b.append(bi)
        c.append(ci)

t = {}
for i in range(N):
        t[i+1] = []
for i in range(M):
        ai = a[i]
        bi = b[i]
        ci = c[i]
        t[ai].append( (bi, ci) )


w = { 1: (0, []) }
q = [ 1 ]
while q:
        ai = q.pop()
        s = w[ai][0]
        p = w[ai][1]
        for bi, ci in t[ai]:
                if s == INF:
                        s2 = INF
                else:
                        s2 = s + ci
                if bi not in w:
                        w[bi] = (s2, p+[bi])
                        q.append(bi)
                else:
                        if s2 > w[bi][0]:
                                if bi in p:
                                        s2 = INF
                                w[bi] = (s2, p+[bi])
                                q.append(bi)

sn = w[N][0]
if sn == INF:
        print "inf"
else:
        print sn

Solution (Python):
import sys

stdin = sys.stdin


def na(): return map(int, stdin.readline().split())


def ns(): return stdin.readline().strip()

def bf(es, n, start, ved):
    I = 999999999999999999
    d = [I] * n
    d[start] = 0

    for i in range(n-1):
        updated = False
        for e in es:
            if not ved[e[0]]: continue
            if not ved[e[1]]: continue
            if d[e[0]] + e[2] < d[e[1]]:
                d[e[1]] = d[e[0]] + e[2]
                updated = True
        if not updated: break
    for e in es:
        if not ved[e[0]]: continue
        if not ved[e[1]]: continue
        if d[e[0]] + e[2] < d[e[1]]:
            return None
    return d

def go(start, g, ind):
    n = len(g)
    ved = [False] * n
    q = [start]
    j = 0
    ved[start] = True
    while(j < len(q)):
        cur = q[j]
        for e in g[cur]:
            if not ved[e[ind]]:
                ved[e[ind]] = True
                q.append(e[ind])
        j += 1
    return ved

n,m = na()
es = []

for i in range(m):
    a,b,c = na()
    es.append([a-1,b-1,-c])

g = [[] for _ in range(n)]
for e in es:
    g[e[0]].append(e)

ig = [[] for _ in range(n)]
for e in es:
    ig[e[1]].append(e)


ved = go(0, g, 1)
ived = go(n-1, ig, 0)

for i in range(n):
    ved[i] &= ived[i]

res = bf(es, n, 0, ved)
if res:
    print(-res[n-1])
else:
    print("inf")

Solution (Python):
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools

sys.setrecursionlimit(10**7)
inf = 10**20
mod = 10**9 + 7

def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()


def main():
    n,m = LI()
    e = collections.defaultdict(list)
    for _ in range(m):
        a,b,c = LI_()
        e[a].append((b,c+1))

    t = [0] * n

    def search(s):
        d = collections.defaultdict(lambda: -inf)
        d[s] = 0
        q = []
        heapq.heappush(q, (0, s, -1))
        v = [{} for _ in range(n)]
        while len(q):
            k, u, mu = heapq.heappop(q)
            if mu in v[u] and v[u][mu] >= -k:
                continue
            if mu in v[u]:
                v[u][mu] = inf
            else:
                v[u][mu] = -k

            for uv, ud in e[u]:
                vd = -k + ud
                if u in v[uv] and v[uv][u] >= vd:
                    continue
                heapq.heappush(q, (-vd, uv, u))

        return v

    d = search(0)
    if max(d[n-1].values()) == inf:
        return 'inf'
    return max(d[n-1].values())


print(main())

Solution (Python):
N, M = map(int, raw_input().split())
D = [map(int, raw_input().split()) for _ in range(M)]

score = [None for _ in range(N+1)]
score[1] = 0

for _ in range(N):
    for a, b, c in D:
        if score[a] != None:
            score[b] = max(score[b], score[a] + c)
v1 = score[-1]
for _ in range(N):
    for a, b, c in D:
        if score[a] != None:
            score[b] = max(score[b], score[a] + c)
v2 = score[-1]

if v1 != v2:
    print "inf"
else:
    print v2