Problem:


Score : 500 points

Problem Statement

There is a directed graph with N vertices numbered 1 to N and M edges.
The i-th edge is directed from Vertex A_i to Vertex B_i, and there are C_i coins placed along that edge.
Additionally, there is a button on Vertex N.

We will play a game on this graph.
You start the game on Vertex 1 with zero coins, and head for Vertex N by traversing the edges while collecting coins.
It takes one minute to traverse an edge, and you can collect the coins placed along the edge each time you traverse it.
As usual in games, even if you traverse an edge once and collect the coins, the same number of coins will reappear next time you traverse that edge, which you can collect again.

When you reach Vertex N, you can end the game by pressing the button. (You can also choose to leave Vertex N without pressing the button and continue traveling.)
However, when you end the game, you will be asked to pay T \times P coins, where T is the number of minutes elapsed since the start of the game. If you have less than T \times P coins, you will have to pay all of your coins instead.

Your score will be the number of coins you have after this payment.
Determine if there exists a maximum value of the score that can be obtained. If the answer is yes, find that maximum value.

Constraints

2 \leq N \leq 2500

1 \leq M \leq 5000

1 \leq A_i, B_i \leq N

1 \leq C_i \leq 10^5

0 \leq P \leq 10^5

All values in input are integers.

Vertex N can be reached from Vertex 1.

Input

Input is given from Standard Input in the following format:

N M P
A_1 B_1 C_1
:
A_M B_M C_M

Output

If there exists a maximum value of the score that can be obtained, print that maximum value; otherwise, print -1.

Sample Input 1

3 3 10
1 2 20
2 3 30
1 3 45

Sample Output 1

35

There are two ways to travel from Vertex 1 to Vertex 3:

Vertex 1 \rightarrow 2 \rightarrow 3: You collect 20 + 30 = 50 coins on the way. After two minutes from the start of the game, you press the button, pay 2 \times 10 = 20 coins, and you have 50 - 20 = 30 coins left.

Vertex 1 \rightarrow 2: You collect 45 coins on the way. After one minute from the start of the game, you press the button, pay 1 \times 10 = 10 coins, and you have 45 - 10 = 35 coins left.

Thus, the maximum score that can be obtained is 35.

Sample Input 2

2 2 10
1 2 100
2 2 100

Sample Output 2

-1

The edge extending from Vertex 1 takes you to Vertex 2. If you then traverse the edge extending from Vertex 2 to itself t times and press the button, your score will be 90 + 90t. Thus, you can infinitely increase your score, which means there is no maximum value of the score that can be obtained.

Sample Input 3

4 5 10
1 2 1
1 4 1
3 4 1
2 2 100
3 3 100

Sample Output 3

0

There is no way to travel from Vertex 1 to Vertex 4 other than traversing the edge leading from Vertex 1 to Vertex 4 directly. You will pick up one coin along this edge, but after being asked to paying 10 coins, your score will be 0.

Note that you can collect an infinite number of coins if you traverse the edge leading from Vertex 1 to Vertex 2, but this is pointless since you can no longer reach Vertex 4 and end the game.



Sample input:
3 3 10
1 2 20
2 3 30
1 3 45


Sample output:
35

Submission status: Runtime Error

Solution code:
import functools
from heapq import*
from collections import deque
import collections
import math
from collections import defaultdict
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10 ** 7)
MOD = 10 ** 9 + 7
inf = float("inf")


def make_divisors(n):
    divisors = []
    for i in range(1, int(n**0.5)+1):
        if n % i == 0:
            divisors.append(i)
            if i != n // i:
                divisors.append(n//i)

    # divisors.sort()
    return divisors


def factorize(n):
    fct = []  # prime factor
    b, e = 2, 0  # base, exponent
    while b * b <= n:
        while n % b == 0:
            n = n // b
            e = e + 1
        if e > 0:
            fct.append((b, e))
        b, e = b + 1, 0
    if n > 1:
        fct.append((n, 1))
    return fct


def is_prime(n):
    if n == 1:
        return False

    for k in range(2, int(math.sqrt(n)) + 1):
        if n % k == 0:
            return False

    return True


def primes(n):
    is_prime = [True] * (n + 1)
    is_prime[0] = False
    is_prime[1] = False
    for i in range(2, int(n**0.5) + 1):
        if not is_prime[i]:
            continue
        for j in range(i * 2, n + 1, i):
            is_prime[j] = False
    return [i for i in range(n + 1) if is_prime[i]]


def modpow(a, n, mod):
    res = 1
    while n > 0:
        if n & 1:
            res = res * a % mod
        a = a * a % mod
        n >>= 1
    return res


def modinv(a, mod):
    return modpow(a, mod - 2, mod)


def cnk(a, b):
    MOD = 10**9+7
    ret = 1
    for i in range(b):
        ret *= (a-i)
        ret %= MOD
        ret = ret * modinv(i+1, MOD) % MOD
    return ret


def Dijkstra(n, start, e):
    # input parm e
    # e = [[]for i in range(n)]
    # e[x].append([y, 1])
    # e[y].append([x, 1])
    n += 10

    d = [float("inf") for i in range(n)]
    d[start] = 0

    pathnum = [0 for i in range(n)]
    pathnum[start] = 1

    visited = [False for i in range(n)]
    q = []
    heappush(q, (0, start))
    while len(q):
        now_distance, v = heappop(q)
        if visited[v]:
            continue
        visited[v] = True
        for next_v, next_distance in e[v]:
            if visited[next_v]:
                continue
            dd = now_distance + next_distance
            if d[next_v] > dd:
                d[next_v] = dd
                heappush(q, (dd, next_v))
            if d[next_v] == dd:
                pathnum[next_v] += pathnum[v]
                pathnum[next_v] %= MOD

    return d, pathnum


def warshall_floyd(d):
    for k in range(n):
        for i in range(n):
            for j in range(n):
                d[i][j] = min(d[i][j], d[i][k] + d[k][j])
    return d


class UnionFind:
    def __init__(self, n):
        self.sz = [-1 for i in range(n)]

    # 検索
    def find(self, x):
        if self.sz[x] < 0:
            return x
        else:
            self.sz[x] = self.find(self.sz[x])
            return self.sz[x]

    # 併合

    def union(self, x, y):
        x = self.find(x)
        y = self.find(y)
        if x == y:
            return False
        if self.sz[x] > self.sz[y]:
            x, y = y, x
        self.sz[x] += self.sz[y]
        self.sz[y] = x

    # 同じ集合に属するか判定
    def same(self, x, y):
        return self.find(x) == self.find(y)

    # xが含まれている集合のサイズを求める
    def size(self, x):
        return -self.sz[self.find(x)]


class WeightedUnionFind:
    def __init__(self, n):
        self.par = [i for i in range(n+1)]
        self.rank = [0] * (n+1)
        # 根への距離を管理
        self.weight = [0] * (n+1)

    # 検索
    def find(self, x):
        if self.par[x] == x:
            return x
        else:
            y = self.find(self.par[x])
            # 親への重みを追加しながら根まで走査
            self.weight[x] += self.weight[self.par[x]]
            self.par[x] = y
            return y

    # 併合
    def union(self, x, y, w):
        rx = self.find(x)
        ry = self.find(y)
        # xの木の高さ < yの木の高さ
        if self.rank[rx] < self.rank[ry]:
            self.par[rx] = ry
            self.weight[rx] = w - self.weight[x] + self.weight[y]
        # xの木の高さ ≧ yの木の高さ
        else:
            self.par[ry] = rx
            self.weight[ry] = -w - self.weight[y] + self.weight[x]
            # 木の高さが同じだった場合の処理
            if self.rank[rx] == self.rank[ry]:
                self.rank[rx] += 1

    # 同じ集合に属するか
    def same(self, x, y):
        return self.find(x) == self.find(y)

    # xからyへのコスト
    def diff(self, x, y):
        return self.weight[x] - self.weight[y]

#
# kruskal
#


@functools.lru_cache(maxsize=None)
class UNION_FIND(object):
    def __init__(self, n):
        self.parent = [-1 for i in range(n)]

    def root(self, x):
        if self.parent[x] < 0:
            return x
        else:
            self.parent[x] = self.root(self.parent[x])
            return self.parent[x]

    def size(self, x):
        return -self.parent[self.root(x)]

    def union(self, x, y):
        x = self.root(x)
        y = self.root(y)
        if x == y:
            return False
        if self.size(x) < self.size(y):
            x, y = y, x
        self.parent[x] += self.parent[y]
        self.parent[y] = x
        return True


def compute_mst_kruskal(max_v, edges):
    edges.sort(key=lambda x: x[2], reverse=1)
    uf = UNION_FIND(max_v)
    mst = []
    for (a, b, c, d) in edges:
        if uf.root(a-1) != uf.root(b-1):
            uf.union(a-1, b-1)
            mst += [d+1]
    return mst


# max_v, max_e = map(int, input().split())
# edges = []
# for i in range(max_e):
#     a, b, c = map(int, input().split())
#     heappush(edges, (a, b, c, i))

# mst = compute_mst_kruskal(max_v, edges)
# mst.sort()
# for i in mst:
#   print(i)

#
# Dinic
#

class Dinic:
    def __init__(self, N):
        self.N = N
        self.G = [[] for i in range(N)]

    def add_edge(self, fr, to, cap):
        forward = [to, cap, None]
        forward[2] = backward = [fr, 0, forward]
        self.G[fr].append(forward)
        self.G[to].append(backward)

    def add_multi_edge(self, v1, v2, cap1, cap2):
        edge1 = [v2, cap1, None]
        edge1[2] = edge2 = [v1, cap2, edge1]
        self.G[v1].append(edge1)
        self.G[v2].append(edge2)

    def bfs(self, s, t):
        self.level = level = [None]*self.N
        deq = deque([s])
        level[s] = 0
        G = self.G
        while deq:
            v = deq.popleft()
            lv = level[v] + 1
            for w, cap, _ in G[v]:
                if cap and level[w] is None:
                    level[w] = lv
                    deq.append(w)
        return level[t] is not None

    def dfs(self, v, t, f):
        if v == t:
            return f
        level = self.level
        for e in self.it[v]:
            w, cap, rev = e
            if cap and level[v] < level[w]:
                d = self.dfs(w, t, min(f, cap))
                if d:
                    e[1] -= d
                    rev[1] += d
                    return d
        return 0

    def flow(self, s, t):
        flow = 0
        INF = 10**9 + 7
        G = self.G
        while self.bfs(s, t):
            *self.it, = map(iter, self.G)
            f = INF
            while f:
                f = self.dfs(s, t, INF)
                flow += f
        return flow

# V, E, r = map(int, input().split())
# edges = []
# for i in range(E):
#     s, t, d = map(int, input().split())
#     edges.append([s, t, d])

# d = BellmanFord(edges, V, r)
# if d == -1:
#     print("NEGATIVE CYCLE")
#     exit()

# for i in range(V):
#     if d[i] == float("inf"):
#         print("INF")
#     else:
#         print(d[i])


# def BellmanFord(edges, n, s):
#     # グラフの初期化
#     dist = [float("inf") for i in range(n)]
#     dist[s] = 0

#     # 辺の緩和
#     for i in range(n):
#         for edge in edges:
#             if edge[0] != float("inf") and dist[edge[1]] > dist[edge[0]] + edge[2]:
#                 dist[edge[1]] = dist[edge[0]] + edge[2]
#                 if i == n-1 and edge[1] == n - 1:
#                     return -1

#     return dist


def Bellmanford(e, n, s):
    d = [float("inf") for i in range(n)]
    d[s] = 0
    while True:
        update = False
        for i in range(n):
            if e[i][0] != float("inf") and d[e[i][1]] > d[e[i][0]] + e[i][2]:
                d[e[i][1]] = d[e[i][0]] + e[i][2]
                update = True
                if i == n - 1:
                    return d
        if not update:
            break
    return d


def main():
    n, m, p = map(int, input().split())
    e = []

    for i in range(m):
        a, b, c = map(int, input().split())
        e.append([a - 1, b - 1, -(c - 10)])

    d = Bellmanford(e, n, 0)
    if d == -1:
        print(-1)
        exit()

    if -d[n - 1] <= 0:
        print(0)
    else:
        print(-d[n - 1])


if __name__ == '__main__':
    main()

Submission status: Runtime Error

Solution code:
import sys
input = sys.stdin.readline

sys.setrecursionlimit(10000000)

N,M,P=map(int,input().split())
INF = 1000000000
edge = []
to = [[] for _ in range(N)]
rto = [[] for _ in range(N)]
reachable_from1 = [False]*N
reachable_fromN = [False]*N
for i in range(M):
    a,b,c = map(int,input().split())
    a-=1
    b-=1
    c=-c
    to[a].append(b)
    rto[b].append(a)
    edge.append([a,b,c])

def dfs(v):
    if reachable_from1[v] == True:
        return
    reachable_from1[v] = True
    for u in to[v]:
        dfs(u)

def rdfs(v):
    if reachable_fromN[v] == True:
        return
    reachable_fromN[v] = True
    for u in rto[v]:
        rdfs(u)

dfs(0)
rdfs(N-1)
ok = [False]*N
for i in range(N):
    ok[i] = reachable_from1[i]&reachable_fromN[i]

d = [INF]*N
d[0] = 0
update = True
step=0
while update:
    update = False
    for i in range(N):
        a,b,c=edge[i]
        if not(ok[a]): continue
        newD = d[a]+c+P
        if newD < d[b]:
            d[b] = newD
            update = True
    step+=1
    if step > N:
        print(-1)
        sys.exit()
print(max(0,-d[N-1]))

Submission status: Runtime Error

Solution code:
from collections import defaultdict


def p_e():
    N, M, P = map(int, input().split())
    abc = [tuple(map(int, input().split())) for _ in range(M)]
    li = defaultdict(set)

    for i in range(M):
        li[abc[i][0]].append((abc[i][1], -(abc[i][2] - P)))

    li_ans = defaultdict()
    li_ans[1] = 0
    li_top = [1]
    lt = []
    bf_n = -1
    while li_top and li_top != lt:
        lt = li_top.copy()
        li_top = []
        if N in li_ans.keys():
            bf_n = li_ans[N]

        for i in lt:
            for e in li[i]:
                if not e[0] in li_ans.keys():
                    li_ans[e[0]] = e[1] + li_ans[i]
                    li_top.append(e[0])
                else:
                    if li_ans[e[0]] > e[1] + li_ans[i]:
                        li_ans[e[0]] = e[1] + li_ans[i]
                        li_top.append(e[0])

    if li_top == lt and bf_n != li_ans[N]:
        print(-1)
    else:
        print(max(0, -li_ans[N]))


if __name__ == '__main__':
    p_e()

Submission status: Runtime Error

Solution code:
def is_reachable(edges,start,end):
  g = {}
  for f,t,w in edges:
    if f in g: g[f].append(t)
    else: g[f] = [t]
  visiting = [start]
  visited = {}
  while visiting:
    v = visiting.pop()
    if v in visited: continue
    if v == end: return True
    visited[v] = True
    for v2 in g.get(v, ()):
      if v2 in visited or v2 in visiting: continue
      visiting.append(v2)
  return False

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

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

neg_inf = float("-Inf")
no_answer = False

start = 1
end = N

distance = {}
for i in range(1,N+1):
  distance[i] = neg_inf
distance[start] = 0

for i in range(N-1):
    for f,t,w in edges:
        if distance[f] + w - P > distance[t]:
            distance[t] = distance[f] + w - P

for f,t,w in edges:
    if distance.get[f] + w - P > distance[t] and is_reachable(edges,t,end):
        no_answer = True
        break

if no_answer:
    print(-1)
else:
    print(max(0,distance[end]))

Submission status: Runtime Error

Solution code:
def is_reachable(edges,start,end):
  g = {}
  for f,t,w in edges:
    if f in g: g[f].append(t)
    else: g[f] = [t]
  visiting = [start]
  visited = []
  while visiting:
    v = visiting.pop()
    if v in visited: continue
    if v == end: return True
    visited[v] = True
    for v2 in g.get(v, ()):
      if v2 in visited or v2 in visiting: continue
      visiting.append(v2)
  return False

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

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

neg_inf = float("-Inf")
no_answer = False

start = 1
end = N

distance = {}
for i in range(1,N+1):
  distance[i] = neg_inf
distance[start] = 0
previous = {}

for i in range(N-1):
    for f,t,w in edges:
        if distance[f] + w - P > distance[t]:
            distance[t] = distance[f] + w - P
            previous[t] = f

path = []
node = end
while node != start:
    path.append(node)
    node = previous[node]
path.append(start)

for f,t,w in edges:
    if distance[f] + w - P > distance[t] and is_reachable(edges,t,end):
        no_answer = True
        break

if no_answer:
    print(-1)
else:
    print(max(0,distance[end]))

Submission status: Runtime Error

Solution code:
def is_reachable(edges,start,end):
  g = {}
  for f,t,w in edges:
    if f in g: g[f].append(t)
    else: g[f] = [t]
  visiting = [start]
  visited = []
  while visiting:
    v = visiting.pop()
    if v in visited: continue
    if v == end: return True
    visited[v] = True
    for v2 in g.get(v, ()):
      if v2 in visited or v2 in visiting: continue
      visiting.append(v2)
  return False

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

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

neg_inf = float("-Inf")
no_answer = False

start = 1
end = N

distance = {}
for i in range(1,N+1):
  distance[i] = neg_inf
distance[start] = 0
previous = {}

for i in range(N-1):
    for f,t,w in edges:
        if distance[f] + w - P > distance[t]:
            distance[t] = distance[f] + w - P
            previous[t] = f

path = []
node = end
while node != start:
    path.append(node)
    node = previous[node]
path.append(start)

for f,t,w in edges:
    if distance.get[f] + w - P > distance[t] and is_reachable(edges,t,end):
        no_answer = True
        break

if no_answer:
    print(-1)
else:
    print(max(0,distance[end]))

Submission status: Runtime Error

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

edges = []
for _ in range(N):
    edges.append(map(int, input().split()))

neg_inf = float("-Inf")
no_answer = False

start = 1
end = M

distance = {}
distance[start] = 0
previous = {}

for i in range(M-1):
    for f,t,w in edges:
        if distance.get(f,neg_inf) + w - P > distance.get(t,neg_inf):
            distance[t] = distance[f] + w - P
            previous[t] = f

path = []
node = end
if node in previous:
    while node != start:
        path.append(node)
        node = previous[node]
        if node in path:
            no_answer = True
            break
    path.append(start)

for f,t,w in edges:
    if distance.get(f,neg_inf) + w - P > distance.get(t,neg_inf) and t in path:
        no_answer = True
        break

if no_answer:
    print(-1)
else:
    print(max(0,distance[end]))

Submission status: Runtime Error

Solution code:
M,N,P = map(int, input().split())
# M: number of V
# N: number of edges
# P: P x edges to pay

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

neg_inf = float("-Inf")
no_answer = False

start = 1
end = M

distance = {}
distance[start] = 0
previous = {}

for i in range(M-1):
    for f,t,w in edges:
        if distance.get(f,neg_inf) + w - P > distance.get(t,neg_inf):
            distance[t] = distance[f] + w - P
            previous[t] = f

path = []
node = end
if node in previous:
    cnt = 0
    while node != start:
        path.append(node)
        node = previous[node]
        cnt += 1
        if cnt > M:
            no_answer = True
            break
    path.append(start)

    for f,t,w in edges:
    if distance.get(f,neg_inf) + w - P > distance.get(t,neg_inf) and t in path:
        no_answer = True
        break

if no_answer:
    print(-1)
else:
    print(max(0,distance[end]))

Submission status: Runtime Error

Solution code:
ef find_negative_loop(s,n,w,es):
  # s: start
  # n: number of nodes
  # w: number of edges
  # es[i]: from, to, cost
  
  # d: shortest dist of s -> i
  d = [float('inf')]*n
  d[s] = 0
  for i in range(2*n):
    for j in range(w):
      p, q, r = es[j]
      if d[p] != float('inf') and (d[q] > d[p] + r):
        d[q] = d[p] + r
        if i >= n:
          d[q] = -float('inf')
      if i == n-1:
        temp = d[-1]
  return temp, d[-1]
         
n, w, p = map(int, input().split())
es = []
for i in range(w):
  x, y, z = map(int, input().split())
  x, y = x-1, y-1
  z = (z-p)*(-1)
  es.append([x, y, z])
  
temp, d = find_negative_loop(0, n, w ,es)
if temp == d:
  print(min(0, d)*(-1))
else:
  print('-1')

Submission status: Runtime Error

Solution code:
n, m, p = map(int, input().split())
edge = []
for i in range(n):
    ai, bi, ci = map(int, input().split())
    edge.append((bi-1,ai-1,-ci+p))
dist = [float("inf") for i in range(n)]
dist[n-1] = 0
h = False
for i in range(n):
    updated = False
    for e in edge:
        if dist[e[1]] > dist[e[0]] + e[2]:
            dist[e[1]] = dist[e[0]] + e[2]
            updated = True
    if not updated:
        break
else:
    h = True

if h:
    print(-1)
else:
    print(max(0, -dist[0]))

Submission status: Runtime Error

Solution code:
from collections import deque
n,m,p = map(int,input().split())
d = {}
cost = [[float("inf") for i in range(n)] for j in range(n)]
for i in range(n):
    ai,bi,ci = map(int, input().split())
    if not bi-1 in d:
        d[bi-1] = []
    d[bi-1] += [ai-1]
    cost[bi-1][ai-1] = min(cost[bi-1][ai-1], -(ci-p))
dist = [float("inf") for i in range(n)]
dist[n-1] = 0
h = False
for i in range(n):
    v = [True for j in range(n)]
    q = deque([n-1])
    v[n-1] = False
    while len(q) > 0:
        x = q.popleft()
        if x in d:
            for xi in d[x]:
                if dist[xi] > dist[x] + cost[x][xi]:
                    dist[xi] = dist[x] + cost[x][xi]
                    if v[xi]:
                        v[xi] = False
                        q.append(xi)
                    if i == n-1:
                        h = True
if h:
    print(-1)
else:
    print(max(0,-dist[0]))

Submission status: Runtime Error

Solution code:
inf = float('inf')

# 計算量O(VE) V:頂点数, E:辺の数
# True - >正常に更新, False -> startからendまでの経路において負閉路有り
def bellmanford(start, end):
    global dist
    dist = [inf] * N
    dist[start] = 0
    # 頂点数Nなら更新は高々N-1回で済む
    for _ in range(N-1):
        for v ,nv, w in edges:
            if dist[nv] > dist[v] + w:
                dist[nv] = dist[v] + w
    # 負閉路の検出部分
    # N回目で更新があった場合、負閉路を含む
    for v, nv, w in edges:
        if dist[nv] > dist[v] + w:
            return False
    return True

# 頂点vが1を始点にNにたどり着けるならばTrueを返す
def dfs(v):
    visited[v] = True
    res = False
    if v == N-1:
        res = True
        bit[v] = res
        return res
    for nv, w in ad[v]:
        if not visited[nv]:
            res |= dfs(nv)
    bit[v] = res
    return res

N, M, P = map(int,input().split())
ad = [[] for _ in range(N)]
edges = []
for _ in range(M):
    A, B, C = map(int,input().split())
    A -= 1
    B -= 1
    ad[A].append((B, C))
    edges.append((A, B, -C+P))

visited = [False] * N
bit = [False] * N
dfs(0)
# 頂点1から頂点Nのパスに含まれない頂点を削除
edges = [(v, nv, w) for v, nv, w in edges if bit[v] and bit[nv]]

flag = bellmanford(0,N-1)
ans = max(-dist[N-1],0) if flag else -1
print(ans)

Submission status: Runtime Error

Solution code:
import sys
sys.setrecursionlimit(1000000000000)

def dfs(i):
	if i in use:
		return 
	use.add(i)
	for e in edges_r[i]:
		dfs(e)

def bf():
	d = [float('inf') for _ in range(n + 1)]
	d[1] = 0
	for _ in range(n):
		f = False
		for e in edges_f:
			if d[e[1]] > d[e[0]] + e[2]:
				d[e[1]] = d[e[0]] + e[2]
				f = True	
		if not f:
			return max(0, -1 * d[n])
	return -1

n, m, p = list(map(int, input().split()))

edges_f = []
edges_r = [[] for i in range(n + 1)]
for _ in range(m):
	a, b, c = list(map(int, input().split()))
	edges_f.append([a, b, -1 * (c - p)])
	edges_r[b].append(a)

use = set()
dfs(n)

edges_f = [e for e in edges_f if e[0] in use and e[1] in use]
print(bf())

Submission status: Runtime Error

Solution code:
def dfs(i):
	if i in use:
		return 
	use.add(i)
	for e in edges_r[i]:
		dfs(e)

def bf():
	d = [float('inf') for _ in range(n + 1)]
	d[1] = 0
	for _ in range(n):
		f = False
		for e in edges_f:
			if d[e[1]] > d[e[0]] + e[2]:
				d[e[1]] = d[e[0]] + e[2]
				f = True
		if not f:
			return max(0, -1 * d[n])
	return -1

n, m, p = list(map(int, input().split()))

edges_f = []
edges_r = [[] for i in range(n + 1)]
for _ in range(m):
	a, b, c = list(map(int, input().split()))
	edges_f.append([a, b, -1 * (c - p)])
	edges_r[b].append(a)

use = set()
dfs(n)

edges_f = [e for e in edges_f if e[0] in use and e[1] in use]
print(bf())

Submission status: Runtime Error

Solution code:
# E - Coins Respawn
from collections import defaultdict

_input = list(map(int, input().split()))
n = _input[0]
m = _input[1]
p = _input[2]

# aから伸びるルート＋点数をマッピング
routes = defaultdict(list)
for i in range(m):
    __input = list(map(int, input().split()))
    routes[__input[0] - 1].append([__input[1] - 1, __input[2] - p])

# 1から到達できる点を求める
def dfs(start):
    stack = [start]
    use = {start, }
    while len(stack) > 0:
        a = stack.pop()
        for route in routes[a]:
            if route[0] not in use:
                use.add(route[0])
                stack.append(route[0])
    return use
        

# 重み付け経路探索(ベルマンフォード)
def berman(targets, points, before):
    for target in targets:
        for route in routes[target]:
            b = route[0]
            c = route[1]
            if points[b] is None or points[target] + c >= points[b]:
                points[b] = points[target] + c

use = dfs(0)
pre = [None] * n
pre[0] = 0
points = pre[:]
cnt = -1
for j in range(n):
    berman(use, points, pre)
    ret = (points == pre)
    if ret or (j == n - 1 and points[n - 1] == pre[n - 1]):
        cnt = points[n - 1] if points[n - 1] > 0 else 0
        break
    pre = points[:]
    
print(cnt)

Submission status: Runtime Error

Solution code:
# E - Coins Respawn
from collections import defaultdict

_input = list(map(int, input().split()))
n = _input[0]
m = _input[1]
p = _input[2]

# aから伸びるルート＋点数をマッピング
routes = defaultdict(list)
for i in range(m):
    __input = list(map(int, input().split()))
    routes[__input[0] - 1].append([__input[1] - 1, __input[2] - p])
    
# 重み付け経路探索(ベルマンフォード)
def berman(start, points, before):
    nowPoint = points[start] if points[start] is not None else 0
    for route in routes[start]:
        b = route[0]
        c = route[1]
        if points[b] is None or nowPoint + c >= points[b]:
            points[b] = nowPoint + c
        if start != b:
            berman(b, points, pre)

pre = [None] * n
pre[0] = 0
points = pre[:]
cnt = -1
for j in range(n):
    berman(0, points, pre)
    ret = (points == pre)
    if ret or (j == n - 1 and points[n - 1] == pre[n - 1]):
        cnt = points[n - 1] if points[n - 1] > 0 else 0
        break
    pre = points[:]
    
print(cnt)

Submission status: Runtime Error

Solution code:
import collections
from scipy.sparse import lil_matrix
from scipy.sparse.csgraph import bellman_ford

N, M, P = [int(_) for _ in input().split()]
#for multiple edges
ABC = sorted([[int(_) for _ in input().split()] for _ in range(M)], key=lambda xs:xs[2])
cd = collections.defaultdict
Ga = cd(set)
Gb = cd(set)
ok = cd(int)
for a, b, c in ABC:
    Ga[a].add(b)
    Gb[b].add(a)
#dfs
for pair in [[1, Ga], [N, Gb]]:
    S = pair
    Gn = pair.pop()
    visited = [0] * (N + 1)
    while S:
        s = S.pop()
        if not visited[s]:
            visited[s] = 1
            ok[s] += 1
            for ns in Gn[s]:
                S += [ns]
G = lil_matrix((N + 1, N + 1))
for a, b, c in ABC:
    if ok[a] == ok[b] == 2:
        G[a, b] = P - c

dist_matrix = bellman_ford(G, directed=True, indices=[1])
print(max(-int(dist_matrix[0][-1]), 0))

Submission status: Runtime Error

Solution code:
import collections
from scipy.sparse import lil_matrix
from scipy.sparse.csgraph import bellman_ford

N, M, P = [int(_) for _ in input().split()]
ABC = [[int(_) for _ in input().split()] for _ in range(M)]
cd = collections.defaultdict
Ga = cd(set)
Gb = cd(set)
ok = cd(int)
for a, b, c in ABC:
    Ga[a].add(b)
    Gb[b].add(a)
#dfs
for pair in [[1, Ga], [N, Gb]]:
    S = pair
    Gn = pair.pop()
    visited = [0] * (N + 1)
    while S:
        s = S.pop()
        if not visited[s]:
            visited[s] = 1
            ok[s] += 1
            for ns in Gn[s]:
                S += [ns]
G = lil_matrix((N + 1, N + 1))
for a, b, c in ABC:
    if ok[a] == ok[b] == 2:
        G[a, b] = P - c
dist_matrix = bellman_ford(G, directed=True, indices=[1])
try:
    print(max(-int(dist_matrix[0][-1]), 0))
except:
    print(-1)

Submission status: Runtime Error

Solution code:
# -*- coding: utf-8 -*-
from sys import stdin
# from collections import deque
# import numpy as np
# import sys
# sys.setrecursionlimit(10**4)

def _li(): return list(map(int, stdin.readline().split()))
def _li_(): return list(map(lambda x: int(x)-1, stdin.readline().split()))
def _lf(): return list(map(float, stdin.readline().split()))
def _ls(): return stdin.readline().split()
def _i(): return int(stdin.readline())
def _f(): return float(stdin.readline())
def _s(): return stdin.readline()[:-1]


N, M, P = _li()

edge_cost = []
edge_from = [[] for _ in range(N)]
edge_to = [[] for _ in range(N)]

for _ in range(M):
    a, b, c = _li()
    a -= 1
    b -= 1
    edge_cost.append((a, b, -(c-P)))
    edge_to[a].append(b)
    edge_from[b].append(a)


ok_from_start = [False] * N
ok_from_end = [False] * N


def reachable_start(node):
    if not ok_from_start[node]:
        ok_from_start[node] = True
        for n in edge_to[node]:
            reachable_start(n)


def reachable_end(node):
    if not ok_from_end[node]:
        ok_from_end[node] = True
        for n in edge_from[node]:
            reachable_end(n)


reachable_start(0)
reachable_end(N-1)


shortest_path = [float('inf')] * N
shortest_path[0] = 0

# Bellman-Ford
contain_negative_loop = False
for i in range(N):
    update_flag = False
    for ec in edge_cost:
        if ok_from_start[ec[1]] and ok_from_end[ec[1]]:
            if shortest_path[ec[1]] > shortest_path[ec[0]] + ec[2]:
                shortest_path[ec[1]] = shortest_path[ec[0]] + ec[2]
                update_flag = True
    if not update_flag:
        break
if i == N - 1:
    contain_negative_loop = True

if contain_negative_loop:
    print(-1)
else:
    print(max(0, -shortest_path[-1]))