There is an N × N square mesh-shaped grid of wires, as shown in a figure below. Nodes of the grid are at points (X, Y), where X and Y are integers from 0 to N−1. An electric current flows through the grid, between the nodes at (0, 0) and (N−1, N−1).
Initially, all the wires conduct the current, but the wires burn out at a rate of one per second. The burnouts are described by three arrays of integers, A, B and C, each of size M. For each moment T (0 ≤ T < M), in the T-th second the wire between nodes (A[T], B[T]) and:
- (A[T], B[T] + 1), if C[T] = 0 or
- (A[T] + 1, B[T]), if C[T] = 1
burns out. You can assume that the arrays describe existing wires, and that no wire burns out more than once. Your task is to determine when the current stops flowing between the nodes at (0,0) and (N−1,N−1).
Write a function:
def solution(N, A, B, C)
that, given integer N and arrays A, B and C, returns the number of seconds after which the current stops flowing between the nodes at (0, 0) and (N−1, N−1). If the current keeps flowing even after all M wires burn out, the function should return −1.
For example, given N = 4, M = 9 and the following arrays:
A[0] = 0 B [0] = 0 C[0] = 0 A[1] = 1 B [1] = 1 C[1] = 1 A[2] = 1 B [2] = 1 C[2] = 0 A[3] = 2 B [3] = 1 C[3] = 0 A[4] = 3 B [4] = 2 C[4] = 0 A[5] = 2 B [5] = 2 C[5] = 1 A[6] = 1 B [6] = 3 C[6] = 1 A[7] = 0 B [7] = 1 C[7] = 0 A[8] = 0 B [8] = 0 C[8] = 1your function should return 8, because just after the eighth wire burns out, there is no connection between the nodes at (0, 0) and (N−1, N−1). This situation is shown in the following figure:
Given N = 4, M = 1 and the following arrays:
A[0] = 0 B [0] = 0 C[0] = 0your function should return −1, because burning out a single wire cannot break the connection between the nodes at (0, 0) and (N−1, N−1).
Write an efficient algorithm for the following assumptions:
- N is an integer within the range [1..400];
- M is an integer within the range [0..2*N*(N-1)];
- each element of arrays A and B is an integer within the range [0..N-1];
- each element of array C is an integer that can have one of the following values: 0, 1.
'''
Problem statement can be viewed at:
http://codility.com/cert/view/certMK3AUD-D2PXDA6P779BVATT/details
'''
def wire_burnouts ( N,A,B,C ):
hori = [[True] * (N - 1) for _ in range(N)]
verti = [[True] * (N) for _ in range(N - 1)]
for i, c in enumerate(C):
x, y = A[i], B[i]
horizontal_burn = bool(c)
if horizontal_burn:
arr = hori
else:
arr = verti
arr[y][x] = False
walkable = dfs(hori, verti, N - 1)
if not walkable:
return i + 1
return -1
def dfs(hori, verti, N):
visited = set()
goal = N - 1
stack = [(0,0)]
while stack:
x, y = stack.pop()
if (x,y) in visited:
return
else:
visited.add((x,y))
if x == goal and y == goal:
return True
move_up = y < goal
move_right = x < goal
move_left = x > 0
move_down = y > 0
if move_left and hori[y][x-1]:
stack.append(x-1, y)
if move_down and verti[y-1][x]:
stack.append(x, y-1)
if move_right and hori[y][x]:
stack.append(x+1, y)
if move_up and verti[y][x]:
stack.append(x, y+1)
return False
example from the problem statement
tested program terminated unexpectedly
Traceback (most recent call last): File "user.py", line 147, in <module> result = wire_burnouts ( N,A,B,C ) File "user.py", line 19, in wire_burnouts walkable = dfs(hori, verti, N - 1) File "user.py", line 46, in dfs stack.append(x+1, y) TypeError: append() takes exactly one argument (2 given)
example from the problem statement
tested program terminated unexpectedly
Traceback (most recent call last): File "user.py", line 147, in <module> result = wire_burnouts ( N,A,B,C ) File "user.py", line 19, in wire_burnouts walkable = dfs(hori, verti, N - 1) File "user.py", line 46, in dfs stack.append(x+1, y) TypeError: append() takes exactly one argument (2 given)
'''
Problem statement can be viewed at:
http://codility.com/cert/view/certMK3AUD-D2PXDA6P779BVATT/details
'''
def wire_burnouts ( N,A,B,C ):
hori = [[True] * (N - 1) for _ in range(N)]
verti = [[True] * (N) for _ in range(N - 1)]
for i, c in enumerate(C):
x, y = A[i], B[i]
horizontal_burn = bool(c)
if horizontal_burn:
arr = hori
else:
arr = verti
arr[y][x] = False
walkable = dfs(hori, verti, N)
if not walkable:
return i + 1
return -1
def dfs(hori, verti, N):
visited = set()
goal = N - 1
stack = [(0,0)]
while stack:
x, y = stack.pop()
if (x,y) in visited:
continue
else:
visited.add((x,y))
if x == goal and y == goal:
return True
move_up = y < goal
move_right = x < goal
move_left = x > 0
move_down = y > 0
if move_left and hori[y][x-1]:
stack.append((x-1, y))
if move_down and verti[y-1][x]:
stack.append((x, y-1))
if move_right and hori[y][x]:
stack.append((x+1, y))
if move_up and verti[y][x]:
stack.append((x, y+1))
return False
'
example from the problem statement
tested program terminated unexpectedly
File "user.py", line 50 ' ^ SyntaxError: EOL while scanning string literal
example from the problem statement
tested program terminated unexpectedly
File "user.py", line 50 ' ^ SyntaxError: EOL while scanning string literal
'''
Problem statement can be viewed at:
http://codility.com/cert/view/certMK3AUD-D2PXDA6P779BVATT/details
'''
def wire_burnouts ( N,A,B,C ):
hori = [[True] * (N - 1) for _ in range(N)]
verti = [[True] * (N) for _ in range(N - 1)]
for i, c in enumerate(C):
x, y = A[i], B[i]
horizontal_burn = bool(c)
if horizontal_burn:
arr = hori
else:
arr = verti
arr[y][x] = False
walkable = dfs(hori, verti, N)
if not walkable:
return i + 1
return -1
def dfs(hori, verti, N):
visited = set()
goal = N - 1
stack = [(0,0)]
while stack:
x, y = stack.pop()
if (x,y) in visited:
continue
else:
visited.add((x,y))
if x == goal and y == goal:
return True
move_up = y < goal
move_right = x < goal
move_left = x > 0
move_down = y > 0
if move_left and hori[y][x-1]:
stack.append((x-1, y))
if move_down and verti[y-1][x]:
stack.append((x, y-1))
if move_right and hori[y][x]:
stack.append((x+1, y))
if move_up and verti[y][x]:
stack.append((x, y+1))
return False
'''
Problem statement can be viewed at:
http://codility.com/cert/view/certMK3AUD-D2PXDA6P779BVATT/details
'''
def wire_burnouts ( N,A,B,C ):
hori = [[True] * (N - 1) for _ in range(N)]
verti = [[True] * (N) for _ in range(N - 1)]
for i, c in enumerate(C):
x, y = A[i], B[i]
horizontal_burn = bool(c)
if horizontal_burn:
arr = hori
else:
arr = verti
arr[y][x] = False
walkable = dfs(hori, verti, N)
if not walkable:
return i + 1
return -1
def dfs(hori, verti, N):
visited = set()
goal = N - 1
stack = [(0,0)]
while stack:
x, y = stack.pop()
if (x,y) in visited:
continue
else:
visited.add((x,y))
if x == goal and y == goal:
return True
move_up = y < goal
move_right = x < goal
move_left = x > 0
move_down = y > 0
if move_left and hori[y][x-1]:
stack.append((x-1, y))
if move_down and verti[y-1][x]:
stack.append((x, y-1))
if move_right and hori[y][x]:
stack.append((x+1, y))
if move_up and verti[y][x]:
stack.append((x, y+1))
return False
'''
Problem statement can be viewed at:
http://codility.com/cert/view/certMK3AUD-D2PXDA6P779BVATT/details
'''
def wire_burnouts ( N,A,B,C ):
hori = [[True] * (N - 1) for _ in range(N)]
verti = [[True] * (N) for _ in range(N - 1)]
for i, c in enumerate(C):
x, y = A[i], B[i]
horizontal_burn = bool(c)
if horizontal_burn:
arr = hori
else:
arr = verti
arr[y][x] = False
walkable = dfs(hori, verti, N)
if not walkable:
return i + 1
return -1
def dfs(hori, verti, N):
visited = set()
goal = N - 1
stack = [(0,0)]
while stack:
x, y = stack.pop()
if (x,y) in visited:
continue
else:
visited.add((x,y))
if x == goal and y == goal:
return True
move_up = y < goal
move_right = x < goal
move_left = x > 0
move_down = y > 0
if move_left and hori[y][x-1]:
stack.append((x-1, y))
if move_down and verti[y-1][x]:
stack.append((x, y-1))
if move_right and hori[y][x]:
stack.append((x+1, y))
if move_up and verti[y][x]:
stack.append((x, y+1))
return False
The following issues have been detected: timeout errors.
N=200, erase all connections in random order
running time: >2.02 sec., time limit: 1.56 sec.
N=342, parallel trees
running time: >4.05 sec., time limit: 3.52 sec.
N=400, erase all connections in random order
running time: >11.03 sec., time limit: 10.60 sec.