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



Sample input:
3 3
1 2 4
2 3 3
1 3 5


Sample output:
7

Submission status: Time Limit Exceeded

Solution code:
N, M = map(int, input().split())
edge = []
for i in range(M):
    a,b,c = map(int, input().split())
    edge.append((a-1,b-1, c))
point = [None] * N
point[0] = 0
for i in range(N*2):
    for a,b,c in edge:
        if point[a] is not None:
            if point[b] is None:
                point[b] = point[a] + c
            point[b] = max(point[b], point[a] + c)
current_point = point[N-1]
for i in range(N*2):
    for a,b,c in edge:
        if point[a] is not None:
            if point[b] is None:
                point[b] = point[a] + c
            point[b] = max(point[b], point[a] + c)
if current_point < point[N-1]:
    print("inf")
else:
    print(current_point)

Submission status: Time Limit Exceeded

Solution code:
N, M = map(int, input().split())
a = [0 for i in range(M)]
b = [0 for i in range(M)]
c = [0 for i in range(M)]
for i in range(M):
    a[i], b[i], c[i] = map(int, input().split())
distance = [-10**20 for i in range(N)]
distance[0] = 0
for i in range(1,N):
    for j in range(M):
        u = a[j]-1; v = b[j]-1
        if distance[v] < distance[u] + c[j]:
            distance[v] = distance[u] + c[j]
negative = [False for i in range(N)]
for i in range(N):
    for j in range(M):
        u = a[j]-1; v = b[j]-1
        if distance[v] < distance[u] + c[j]:
            distance[v] = distance[u] + c[j]
            negative[v] = True
        if negative[u]:
            negative[v] = True
if negative[N-1]:
    print("inf")
else:
    print(distance[N-1])

Submission status: Time Limit Exceeded

Solution code:
N, M = map(int, input().split())
a, b, c = [0] * M, [0] * M, [0] * M
d = [-1e20] * N
for i in range(M):
    a[i], b[i], c[i] = map(int, input().split())
    a[i] -= 1
    b[i] -= 1

d[0] = 0
for i in range(N-1):
    for j in range(M):
        d[b[j]] = max((d[b[j]], d[a[j]] + c[j]))

isCycle = False
for i in range(N-1):
    if isCycle:
        break
    for j in range(M):
        if b[j] == N-1 and d[b[j]] < d[a[j]] + c[j]:
            isCycle = True
            break
        d[b[j]] = max((d[b[j]], d[a[j]] + c[j]))
if isCycle:
    print('inf')
else:
    print(d[N-1])

Submission status: Time Limit Exceeded

Solution code:
# -*- coding: utf-8 -*-
"""
http://abc061.contest.atcoder.jp/tasks/abc061_d
TLE
"""
import sys
from sys import stdin
from collections import namedtuple
from heapq import heappush, heappop
input = stdin.readline


def solve(s, N, E):
    best_score = float('-inf')
    count = 0

    d = [float('-inf')] * (N+1)
    d[s] = 0
    while True:
        count += 1
        update = False
        for e in E:
            if d[e.f] != float('-inf') and d[e.t] < d[e.f] + e.c:
                d[e.t] = d[e.f] + e.c
                update = True

                if e.t == N:
                    best_score = max(best_score, d[e.t])
                if count > 50000 and e.f == N:
                    return 'inf'
                if count > 75000:
                    return best_score

        if update is False:
            break
    return d[-1]



edge = namedtuple('edge', ['f', 't', 'c'])
def main(args):
    N, M = map(int, input().split())
    E = []

    for _ in range(M):
        a, b, c = map(int, input().split())
        E.append(edge(a, b, c))

    result = solve(1, N, E)
    print(result)


if __name__ == '__main__':
    main(sys.argv[1:])

Submission status: Time Limit Exceeded

Solution code:
# -*- coding: utf-8 -*-
"""
http://abc061.contest.atcoder.jp/tasks/abc061_d
TLE
"""
import sys
from sys import stdin
from collections import namedtuple
from heapq import heappush, heappop
input = stdin.readline


def solve(s, N, E):
    count = 0
    d = [float('-inf')] * (N+1)
    d[s] = 0
    while True:
        count += 1
        update = False
        for e in E:
            if d[e.f] != float('-inf') and d[e.t] < d[e.f] + e.c:
                d[e.t] = d[e.f] + e.c
                update = True

                if count > 250000 and e.f == N:
                    return 'inf'

        if update is False:
            break
    return d[-1]



edge = namedtuple('edge', ['f', 't', 'c'])
def main(args):
    N, M = map(int, input().split())
    E = []
    for _ in range(M):
        a, b, c = map(int, input().split())
        E.append(edge(a, b, c))

    result = solve(1, N, E)
    print(result)


if __name__ == '__main__':
    main(sys.argv[1:])

Submission status: Time Limit Exceeded

Solution code:
# -*- coding: utf-8 -*-
"""
http://abc061.contest.atcoder.jp/tasks/abc061_d

"""
import sys
from sys import stdin
from collections import namedtuple
from heapq import heappush, heappop
input = stdin.readline


def dijkstra(s, G):
    count = 0
    d = [float('-inf')] * len(G)
    d[s] = 0

    pq = []
    heappush(pq, (0, s))

    while pq:
        count += 1
        c, v = heappop(pq)
        if v == len(G)-1 and count > 10000 and d[-1] > 0:
            return 'inf'
        if d[v] > c:
            continue

        for e in G[v]:
            if d[e.t] < d[v] + e.c:
                d[e.t] = d[v] + e.c
                heappush(pq, (d[e.t], e.t))
    return d[len(G)-1]


edge = namedtuple('edge', ['t', 'c'])
def main(args):
    N, M = map(int, input().split())


    G = [[] for _ in range(N+1)]

    for _ in range(M):
        a, b, c = map(int, input().split())
        G[a].append(edge(b, c))

    result = dijkstra(1, G)
    print(result)


if __name__ == '__main__':
    main(sys.argv[1:])

Submission status: Time Limit Exceeded

Solution code:
# -*- coding: utf-8 -*-
"""
http://abc061.contest.atcoder.jp/tasks/abc061_d

"""
import sys
from sys import stdin
from collections import namedtuple
from heapq import heappush, heappop
input = stdin.readline


def dijkstra(s, G):
    count = 0
    d = [float('-inf')] * len(G)
    d[s] = 0

    pq = []
    heappush(pq, (0, s))

    while pq:
        count += 1
        c, v = heappop(pq)
        if v == len(G)-1 and count > 100000 and d[-1] > 0:
            return 'inf'
        if d[v] > c:
            continue

        for e in G[v]:
            if d[e.t] < d[v] + e.c:
                d[e.t] = d[v] + e.c
                heappush(pq, (d[e.t], e.t))
    return d[len(G)-1]


edge = namedtuple('edge', ['t', 'c'])
def main(args):
    N, M = map(int, input().split())


    G = [[] for _ in range(N+1)]

    for _ in range(M):
        a, b, c = map(int, input().split())
        G[a].append(edge(b, c))

    result = dijkstra(1, G)
    print(result)


if __name__ == '__main__':
    main(sys.argv[1:])

Submission status: Time Limit Exceeded

Solution code:
N,M = map(int,input().split())
ABC = [tuple(map(int,input().split())) for _ in range(M)]
tree = []
for abc in ABC:
    tree.append([abc[0]-1,abc[1]-1,-1*abc[2]])

def shortest_path(listG, source):
    INF = float("inf")
    d = [INF for _ in range(N)]
    d[source] = 0;
    cnt=0
    while True:
        update = False  #update flag
        for edge in listG:
            if d[edge[0]] != INF and d[edge[1]] > d[edge[0]] + edge[2]:
                d[edge[1]] = d[edge[0]] + edge[2]
                update = True
        if cnt > N-1 and edge[1] == N-1:
            return "inf"
        if not update:
            break
        cnt += 1;
    return d[N-1]*-1

print(shortest_path(tree,0))

Submission status: Time Limit Exceeded

Solution code:
import sys 

N, M = list(map(int, input().split()))
a_list = list()
b_list = list()
c_list = list()

for _ in range(M):
    a, b, c = list(map(int, input().split()))
    a_list.append(a)
    b_list.append(b)
    c_list.append(-c)

inf = sys.maxsize
dist = [inf for _ in range(N)]
dist[0] = 0

for _ in range(N-1):
    for i in range(M):
        if dist[a_list[i]-1] == inf:
            continue
        if dist[b_list[i]-1] > dist[a_list[i]-1] + c_list[i]:
            dist[b_list[i]-1] = dist[a_list[i]-1] + c_list[i]

ans = dist[N-1]
negative = [False for _ in range(N)]

for _ in range(N):
    for i in range(M):
        if dist[a_list[i]-1] == inf:
            continue
        if dist[b_list[i]-1] > dist[a_list[i]-1] + c_list[i]:
            dist[b_list[i]-1] = dist[a_list[i]-1] + c_list[i]
            negative[b_list[i]-1] = True
        if negative[a_list[i]-1]:
            negative[b_list[i]-1] = True

if negative[N-1]:
    print('inf')
else:
    print(str(-ans))

Submission status: Time Limit Exceeded

Solution code:
N, M = map(int,input().split())
dist = [0] + [float('inf')] * (N - 1)

a = []
b = []
c = []

for i in range(M):
    i,j,k = map(int,input().split())
    a.append(i)
    b.append(j)
    c.append(-1*k)

INF = float('inf')

for i in range(N-1):
    for j in range(M):
        if dist[a[j] - 1] == INF: continue
        if dist[b[j] - 1] > dist[a[j] - 1] + c[j]:
            dist[b[j] - 1] = dist[a[j] - 1] + c[j]
        
ans = dist[N -1]

negative = [False] * N

for i in range(N):
    for j in range(M):
        if dist[a[j] - 1] == INF: continue
        if dist[b[j] - 1] > dist[a[j] - 1] + c[j]:
            dist[b[j] - 1] = dist[a[j] - 1] + c[j]
            negative[b[j] - 1] = True

        if negative[a[j] - 1] == True:
            negative[b[j] - 1] = True

if negative[N - 1]:
    print('inf')
else:
    print(-1 * ans)

Submission status: Time Limit Exceeded

Solution code:
import sys

# sys.stdin = open('d1.in')

n, m = map(int, input().split())
weights = {}
for i in range(m):
    a, b, c = map(int, input().split())
    a -= 1
    b -= 1
    weights[(a, b)] = c

score = [-10 ** 50] * n
score[0] = 0
pred = [-1] * n
for i in range(n):
    for edge, c in weights.items():
        a, b = edge
        if score[b] < score[a] + c:
            score[b] = score[a] + c
            pred[b] = a
res = score[n - 1]

b = n - 1
while b != 0:
    a = pred[b]
    c = weights[(a, b)]
    if score[b] < score[a] + c:
        res = 'inf'
    b = a

print(res)

Submission status: Time Limit Exceeded

Solution code:
n, m = map(int, input().split())
abc = [list(map(int, input().split())) for x in range(m)]
nodes = [[] for x in range(n + 1)]

for a, b, c in abc:
    nodes[a].append([a, b, -c])

costs = [None for x in range(n + 1)]
costs[1] = 0
flg = True
for i in range(n - 1):
    for a, b, c in abc:
        if costs[a] == None:
            continue
        if costs[b] == None or costs[b] < costs[a] + c:
            flg = False
            costs[b] = costs[a] + c
    # for node in nodes[1:]:
    #     for a, b, c in node:
    #         if costs[a] == None:
    #             continue
    #         if costs[b] == None or costs[b] > costs[a] + c:
    #             flg = False
    #             costs[b] = costs[a] + c

ans = costs[n]
negative = [False for x in range(n + 1)]
for i in range(n - 1):
    for a, b, c in abc:
        if costs[a] == None:
            continue
        if costs[b] == None or costs[b] < costs[a] + c:
            costs[b] = costs[a] + c
            negative[b] = True

        if negative[a] == True:
            negative[b] = True

print(negative[n] and "inf" or ans)
#     if flg:
#         print(costs[n])
#         break
#     flg = True
# else:
#     print("inf")
#

Submission status: Time Limit Exceeded

Solution code:
n, m = map(int, raw_input().split())
graph = {}
visited = {}
# 0: not visited, 1: 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
    # {1: {2: 4, 3: 5}, 2: {3: 4}}

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):
    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

Submission status: Time Limit Exceeded

Solution code:
import sys

sys.setrecursionlimit(10000000)

def solve(node, sc, ps, inf_check, goal_cnt):
    global inf
    if goal_cnt == 0 and sc > max_score[node]:
        max_score[node] = sc
    if node == N:
        goal_cnt += 1
        if inf_check:
            inf = True
        if goal_cnt >= 2:
            return
    for n in path[node]:
        if n in ps:
            if max_score[n] < sc + score["{} {}".format(node, n)]:
                inf_check = True
                if node == N:
                    inf = True
        else:
            ps.add(n)
            solve(n, sc + score["{} {}".format(node, n)], ps, inf_check, goal_cnt)
            ps.remove(n)
            
    return
            

N, M = map(int, input().split())
a, b, c = [0], [0], [0]
max_score = [0, 0]
path = {}
score = {}
inf = False

for num in range(1, N+1):
    path[num] = []
    max_score.append(-10000000000000)

for num in range(M):
    t1, t2, t3 = map(int, input().split())
    a.append(t1)
    b.append(t2)
    c.append(t3)
    path[t1].append(t2)
    score["{} {}".format(t1, t2)] = t3

solve(1, 0, set([1]), False, 0)

if inf:
    print('inf')
else:
    print(max_score[N])

Submission status: Time Limit Exceeded

Solution code:
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')

Submission status: Time Limit Exceeded

Solution code:
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)# iに到達するときの最大得点
 
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]:#共に有限の時はやる
      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]:#共に有限の時はやる
        V[b[m]-1]=V[a[m]-1]+c[m]
        moji2[b[m]-1]=1
if moji2[N-1]:
  print("inf")
else:
  print(V[N-1])

Submission status: Time Limit Exceeded

Solution code:

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]

        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)

Submission status: Time Limit Exceeded

Solution code:
from collections import defaultdict
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]

        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 = defaultdict(list)
    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)

Submission status: Time Limit Exceeded

Solution code:
from collections import defaultdict
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
        if (pos == N - 1):
            result = max(result, cost)

        for val in graph[pos]:
            nxt = val[0]
            nxt_cost = val[1]
            if (cost + nxt_cost > visited[nxt]):
                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 (result, True)


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

Submission status: Time Limit Exceeded

Solution code:
from collections import defaultdict
MAX_N = 10 ** 3 + 10
MAX_M = 2 * (10 ** 3) + 1
INF = 10 ** 13

def bfs(graph, N, M):
    que = []

    visited = [-INF for x in range(MAX_N)]
    update_cnt = [0 for x in range(MAX_N)]

    que.append(0)
    visited[0] = 0
    while (len(que) > 0):
        now = que[0]
        que.pop(0)

        pos = now
        cost = visited[pos]

        if (visited[pos] > cost):
            continue
        if (update_cnt[pos] >= MAX_M):
            continue
        for val in graph[pos]:
            nxt = val[0]
            nxt_cost = val[1]
            if (cost + nxt_cost > visited[nxt]):
                visited[nxt] = cost + nxt_cost
                update_cnt[nxt] += 1
                que.append(nxt)

    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 = defaultdict(list)
    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)

Submission status: Time Limit Exceeded

Solution code:
from collections import defaultdict
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 (pos == N - 1):
            result = max(result, cost)
            if (update_cnt[N - 1] >= MAX_N):
                return (0, False)

        for val in graph[pos]:
            nxt = val[0]
            nxt_cost = val[1]
            if (cost + nxt_cost > visited[nxt]):
                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 (result, True)


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

Submission status: Time Limit Exceeded

Solution code:
from collections import defaultdict
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] != -INF):
            if (visited[pos] >= cost):
                continue
            if (update_cnt[pos] >= MAX_N):
                continue
            visited[pos] = cost
            update_cnt[pos] += 1
        else:
            visited[pos] = cost
            update_cnt[pos] += 1

        if (pos == N - 1):
            result = max(result, cost)
            if (update_cnt[N - 1] >= MAX_N):
                return (0, False)

        for val in graph[pos]:
            nxt = val[0]
            nxt_cost = val[1]
            if (cost + nxt_cost > visited[nxt]):
                que.append([nxt, nxt_cost + cost])

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


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

Submission status: Time Limit Exceeded

Solution code:
from collections import defaultdict
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] != -INF):
            if (visited[pos] >= cost):
                continue
            if (update_cnt[pos] >= MAX_N):
                continue
            visited[pos] = cost
            update_cnt[pos] += 1
        else:
            visited[pos] = cost
            update_cnt[pos] += 1

        if (pos == N - 1):
            result = max(result, cost)

        for val in graph[pos]:
            nxt = val[0]
            nxt_cost = val[1]
            if (cost + nxt_cost > visited[nxt]):
                que.append([nxt, nxt_cost + cost])

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


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

Submission status: Time Limit Exceeded

Solution code:
from collections import defaultdict
MAX_N = 10 ** 3 + 10
MAX_M = 2 * (10 ** 3) + 1
INF = 10 ** 100

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] != -INF):
            if (visited[pos] >= cost):
                continue
            if (update_cnt[pos] >= MAX_N):
                continue
            visited[pos] = cost
            update_cnt[pos] += 1
        else:
            visited[pos] = cost
            update_cnt[pos] += 1

        if (pos == N - 1):
            result = max(result, cost)

        for val in graph[pos]:
            nxt = val[0]
            nxt_cost = val[1]
            que.append([nxt, nxt_cost + cost])

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


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

Submission status: Time Limit Exceeded

Solution code:
from collections import defaultdict
MAX_N = 10 ** 3 + 1
MAX_M = 2 * (10 ** 3) + 1
INF = -(10 ** 100)

def bfs(graph, N, M):
    que = []
    que.append([0, 0])
    visited = defaultdict(list)
    result = INF
    while (len(que) > 0):
        now = que[0]
        que.pop(0)

        pos = now[0]
        cost = now[1]

        if (pos in visited):
            visited_cost = visited[pos][0]
            visited_cnt = visited[pos][1]
            if (visited_cost >= cost):
                continue
            if (visited_cnt >= MAX_N):
                continue
            visited[pos] = [cost, visited_cnt + 1]
        else:
            visited[pos] = [cost, 0]

        if (pos == N - 1):
            result = max(result, cost)
            if (visited[pos][1] >= MAX_N):
                return (0, False)

        for val in graph[pos]:
            nxt = val[0]
            nxt_cost = val[1]
            if (nxt not in visited):
                que.append([nxt, nxt_cost + cost])
            elif(nxt_cost + cost > visited[nxt][0]):
                que.append([nxt, nxt_cost + cost])
    return (result, True)


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

Submission status: Time Limit Exceeded

Solution code:
from collections import defaultdict
MAX_N = 10 ** 3 + 1
MAX_M = 2 * (10 ** 3) + 1
INF = -(10 ** 100)

def bfs(graph, N, M):
    que = []
    que.append([0, 0])
    visited = defaultdict(list)
    result = INF
    while (len(que) > 0):
        now = que[0]
        que.pop(0)

        pos = now[0]
        cost = now[1]

        if (pos in visited):
            visited_cost = visited[pos][0]
            visited_cnt = visited[pos][1]
            if (visited_cost >= cost):
                continue
            if (visited_cnt >= MAX_N):
                continue
            visited[pos] = [cost, visited_cnt + 1]
        else:
            visited[pos] = [cost, 0]

        if (pos == N - 1):
            result = max(result, cost)

        for val in graph[pos]:
            nxt = val[0]
            nxt_cost = val[1]
            if (nxt not in visited):
                que.append([nxt, nxt_cost + cost])
            elif(nxt_cost + cost > visited[nxt][0]):
                que.append([nxt, nxt_cost + cost])
    if (visited[N - 1][1] >= MAX_N):
        return (0, False)
    return (result, True)


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

Submission status: Time Limit Exceeded

Solution code:
from collections import defaultdict
MAX_N = 10 ** 3 + 10
MAX_M = 2 * (10 ** 3) + 1
INF = -(10 ** 100)

def bfs(graph, N, M):
    que = []
    que.append([0, 0])
    visited = defaultdict(list)
    result = INF
    while (len(que) > 0):
        now = que[0]
        que.pop(0)

        pos = now[0]
        cost = now[1]

        if (pos in visited):
            visited_cost = visited[pos][0]
            visited_cnt = visited[pos][1]
            if (visited_cost >= cost):
                continue
            if (visited_cnt >= MAX_N):
                continue
            visited[pos] = [cost, visited_cnt + 1]
        else:
            visited[pos] = [cost, 0]

        if (pos == N - 1):
            result = max(result, cost)

        for val in graph[pos]:
            nxt = val[0]
            nxt_cost = val[1]
            if (nxt not in visited):
                que.append([nxt, nxt_cost + cost])
            elif(nxt_cost + cost > visited[nxt][0]):
                que.append([nxt, nxt_cost + cost])
    if (visited[N - 1][1] >= MAX_N):
        return (0, False)
    return (result, True)


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