Problem:


Score : 500 points

Problem Statement

There are N towns numbered 1 to N and M roads. The i-th road connects Town A_i and Town B_i bidirectionally and has a length of C_i.

Takahashi will travel between these towns by car, passing through these roads. The fuel tank of his car can contain at most L liters of fuel, and one liter of fuel is consumed for each unit distance traveled. When visiting a town while traveling, he can full the tank (or choose not to do so). Travel that results in the tank becoming empty halfway on the road cannot be done.

Process the following Q queries:

The tank is now full. Find the minimum number of times he needs to full his tank while traveling from Town s_i to Town t_i. If Town t_i is unreachable, print -1.

Constraints

All values in input are integers.

2 \leq N \leq 300

0 \leq M \leq \frac{N(N-1)}{2}

1 \leq L \leq 10^9

1 \leq A_i, B_i \leq N

A_i \neq B_i

\left(A_i, B_i\right) \neq \left(A_j, B_j\right) (if i \neq j)

\left(A_i, B_i\right) \neq \left(B_j, A_j\right) (if i \neq j)

1 \leq C_i \leq 10^9

1 \leq Q \leq N\left(N-1\right)

1 \leq s_i, t_i \leq N

s_i \neq t_i

\left(s_i, t_i\right) \neq \left(s_j, t_j\right) (if i \neq j)

Input

Input is given from Standard Input in the following format:

N M L
A_1 B_1 C_1
:
A_M B_M C_M
Q
s_1 t_1
:
s_Q t_Q

Output

Print Q lines.

The i-th line should contain the minimum number of times the tank needs to be fulled while traveling from Town s_i to Town t_i. If Town t_i is unreachable, the line should contain -1 instead.

Sample Input 1

3 2 5
1 2 3
2 3 3
2
3 2
1 3

Sample Output 1

0
1

To travel from Town 3 to Town 2, we can use the second road to reach Town 2 without fueling the tank on the way.

To travel from Town 1 to Town 3, we can first use the first road to get to Town 2, full the tank, and use the second road to reach Town 3.

Sample Input 2

4 0 1
1
2 1

Sample Output 2

-1

There may be no road at all.

Sample Input 3

5 4 4
1 2 2
2 3 2
3 4 3
4 5 2
20
2 1
3 1
4 1
5 1
1 2
3 2
4 2
5 2
1 3
2 3
4 3
5 3
1 4
2 4
3 4
5 4
1 5
2 5
3 5
4 5

Sample Output 3

0
0
1
2
0
0
1
2
0
0
0
1
1
1
0
0
2
2
1
0



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


Sample output:
0
1

Submission status: Accepted

Solution code:
from scipy.sparse.csgraph import csgraph_from_dense
from scipy.sparse import csr_matrix
from scipy.sparse.csgraph import floyd_warshall
import numpy as np
N,M,L=map(int,input().split())
A=[0]*M
B=[0]*M
C=[0]*M
for i in range(M):
    A[i],B[i],C[i] = map(int,input().split())
    A[i] -=1
    B[i] -=1
Q=int(input())
ST=[list(map(int,input().split())) for _ in range(Q)]


G = csr_matrix((C, (A, B)), shape=(N, N))
d = floyd_warshall(G, directed=False)
G=np.full((N,N), np.inf)
G[d<=L]=1
G = csr_matrix(G)
E = floyd_warshall(G, directed=False)

for s,t in ST:
    if E[s-1][t-1]==float('inf'):
        print(-1)
    else:
        print(int(E[s-1][t-1]-1))

Submission status: Accepted

Solution code:
# coding: utf-8
from scipy.sparse.csgraph import floyd_warshall

N,M,L=map(int, input().split())
RG=[[0 for i in range(N)] for j in range(N)]

for i in range(M):
    f,t,c = map(int, input().split())
    if c <= L:
        RG[f-1][t-1] = c
        RG[t-1][f-1] = c

Rd = floyd_warshall(RG, directed=False)

FG=[[0 for i in range(N)] for j in range(N)]
for i in range(N):
    for j in range(i+1, N):
        if Rd[i][j] <= L:
            FG[i][j] = 1
            FG[j][i] = 1

Fd = floyd_warshall(FG, directed=False)

Q=int(input())
for i in range(Q):
    s, t = map(int, input().split())
    v = Fd[s-1][t-1]
    if s == t:
        print (str(0))
    if v == float('inf'):
        print (str(-1))
    else:
        print (str(int(v-1)))

Submission status: Accepted

Solution code:
from scipy.sparse.csgraph import floyd_warshall as fw

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

S = [[float("inf") for i in range(N)] for i in range(N)]

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

Sdist = fw(S)

Ssup_init = [[float("inf") for i in range(N)] for i in range(N)]

for i in range(N):
    for j in range(N):
        if Sdist[i][j]<=L:
            Ssup_init[i][j] = 1

Ssup = fw(Ssup_init)

Q = int(input())

for i in range(Q):
    s, t = map(int, input().split())
    if Ssup[s-1][t-1]==float("inf"):
        print(-1)
    else:
        print(int(Ssup[s-1][t-1]-1))

Submission status: Accepted

Solution code:

from scipy.sparse.csgraph import floyd_warshall as fw
N, M, L = map(int, input().split())

# 町間の道の長さのマトリックスを初期値無限で作成
S = [[float("INF") for i in range(N)] for i in range(N)]

# 町間の道の長さ情報をマトリックスに入力
for i in range(M):
    a, b, c = map(int,input().split())
    S[a-1][b-1] = c
    S[b-1][a-1] = c


# ワーシャルフロイド法で最短距離のマップを生成
Sf = fw(S)

T = [[float("INF")for i in range(N)] for i in range(N)]

# 町間を補給なしで通行可能な場合は1、不可能な場合はINFとしてマトリックスを作成
# （町間距離がタンク容量より大きい場合は通行不可）
for i in range(N):
    for j in range(N):
        if Sf[i][j] <= L:
            T[i][j] = 1

# ワーシャルフロイド法で町間移動可否のマップを生成
# すぐ上のfor文で、補給なしで移動できない町間の移動コストはINFにしたが、
# この処理で複数回の補給を行えば移動できる距離を
Tf = fw(T)

for i in range(int(input())):
    a, b = map(int, input().split())
    if Tf[a-1][b-1] != float("INF"):
        print(int(Tf[a-1][b-1])-1)
    else:
        print(-1)

Submission status: Accepted

Solution code:
def w(d):
    n=len(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
N,M,L = map(int, input().split())
inf=float('inf')
fuel=[[inf]*N for _ in range(N)]
for i in range(N):
    fuel[i][i]=0
for _ in range(M):
    a,b,c=map(int,input().split())
    fuel[a-1][b-1]=fuel[b-1][a-1]=c
Q=int(input())
ST=[list(map(int, input().split())) for _ in range(Q)]
fuel = w(fuel)
for i in range(N):
    for j in range(N):
        if 0 < fuel[i][j] <= L:
            fuel[i][j]=1
        elif fuel[i][j] != 0:
            fuel[i][j] = inf
fuel = w(fuel)
for st in ST:
    print(fuel[st[0]-1][st[1]-1]-1 if fuel[st[0]-1][st[1]-1] != inf else -1)

Submission status: Accepted

Solution code:
def warshal(d):
    n=len(d)
    for k in range(1,n):
        for i in range(1,n):
            for j in range(1,n):
                d[i][j]=min(d[i][j],d[i][k]+d[k][j])
    return d
n,m,l=map(int,input().split())
abc=[list(map(int,input().split())) for i in range(m)]
q=int(input())
st=[list(map(int,input().split())) for i in range(q)]
inf=float("inf")
dp=[[inf]*(n+1) for i in range(n+1)]
for i in range(1,n+1):
    dp[i][i]=0
for u in abc:
    a,b,c=u
    dp[a][b]=c
    dp[b][a]=c
dp=warshal(dp)
data=[[inf]*(n+1) for i in range(n+1)]
for i in range(1,n+1):
    for j in range(1,n+1):
        if 0<dp[i][j]<=l:
            data[i][j]=1
        elif dp[i][j]==0:
            data[i][j]=0
data=warshal(data)
for u in st:
    s,t=u
    if data[s][t]!=inf:
        print(data[s][t]-1)
    else:
        print(-1)

Submission status: Accepted

Solution code:
import sys

N,M,L=map(int, sys.stdin.readline().split())

d=[  [ float("inf") for j in range(N+1) ]  for i in range(N+1) ]

for _ in range(M):
    a,b,c=map(int, sys.stdin.readline().split())
    d[a][b]=c
    d[b][a]=c
    d[a][a]=0
    d[b][b]=0

for k in range(1,N+1):
	for i in range(1,N+1):
		for j in range(1,N+1):
			d[i][j]=min(d[i][j], d[i][k]+d[k][j])

e=[  [ float("inf") for j in range(N+1) ]  for i in range(N+1) ]
for i in range(1,N+1):
    for j in range(i,N+1):
        if i==j:
            e[i][j]=0
            e[j][i]=0
        elif d[i][j]<=L:
            e[i][j]=1
            e[j][i]=1

for k in range(1,N+1):
	for i in range(1,N+1):
		for j in range(1,N+1):
			e[i][j]=min(e[i][j], e[i][k]+e[k][j])


Q=input()
for _ in range(Q):
    s,t=map(int, sys.stdin.readline().split())
    if e[s][t]==float("inf"):
        print -1
    else:
        print e[s][t]-1

Submission status: Accepted

Solution code:
from scipy.sparse.csgraph import floyd_warshall

N, M, L = map(int, input().split())
INF = 10**9 + 1
dist = [[0 if i == j else INF for i in range(N+1)] for j in range(N+1)]
for i in range(M):
  a, b, c = map(int, input().split())
  dist[a][b] = c
  dist[b][a] = c

dist = floyd_warshall(dist)

dist_2 = [[INF for i in range(N+1)] for j in range(N+1)]
for i in range(1, N+1):
  for j in range(i+1, N+1):
    if dist[i][j] <= L:
      dist_2[i][j] = 1
      dist_2[j][i] = 1

dist_2 = floyd_warshall(dist_2)

Q = int(input())
for i in range(Q):
  s, t = map(int, input().split())
  print(-1 if dist_2[s][t] == INF else int(dist_2[s][t]-1))

Submission status: Accepted

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

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


N, M, L = map(int, input().split())
INF = 10 ** 10
d = [[INF for _ in range(N)] for _ in range(N)]
D = [[INF for _ in range(N)] for _ in range(N)]

for i in range(N):
    d[i][i] = 0
for i in range(M):
    A, B, C = map(int, input().split())
    A -= 1
    B -= 1
    d[A][B] = C
    d[B][A] = C
d = warshall_floyd(d)

for i in range(N):
    for j in range(N):
        if 0 < d[i][j] <= L:
            D[i][j] = 1
        elif d[i][j] == 0:
            D[i][j] = 0
D = warshall_floyd(D)

Q = int(input())
for _ in range(Q):
    s, t = map(int, input().split())
    s -= 1
    t -= 1
    print(D[s][t] - 1 if D[s][t] != INF else -1)

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline
N,M,L = map(int, input().split())
INF = float("inf")
dist1 = [[INF]*N for i in range(N)]
dist2 = [[INF]*N for i in range(N)]

for i in range(M):
  A,B,C = map(int, input().split())
  A -= 1
  B -= 1
  dist1[A][B] = C
  dist1[B][A] = C

for i in range(N):
  dist1[i][i] = 0
  dist2[i][i] = 0
  
for k in range(N):
  for i in range(N):
    for j in range(N):
      d = dist1[i][k]+dist1[k][j]
      if dist1[i][j] <= d:
        continue
      dist1[i][j] = d
for i in range(N):
  for j in range(N):
    if dist1[i][j] > L or i==j:
      continue
    dist2[i][j] = 1
  
for k in range(N):
  for i in range(N):
    for j in range(N):
      d = dist2[i][k]+dist2[k][j]
      if dist2[i][j] <= d:
        continue
      dist2[i][j] = d
Q = int(input())
for i in range(Q):
  s,t = map(int, input().split())
  print(dist2[s-1][t-1]-1 if dist2[s-1][t-1]<=L else -1)