Date: 18 July, 2023
Model: gpt-4
Temperature: 0.2
Passing runs: 2
Total runs: 10
Success rate: 20%
Tokens: 422
def minPath(grid, k):
"""
Given a grid with N rows and N columns (N >= 2) and a positive integer k,
each cell of the grid contains a value. Every integer in the range [1, N * N]
inclusive appears exactly once on the cells of the grid.
You have to find the minimum path of length k in the grid. You can start
from any cell, and in each step you can move to any of the neighbor cells,
in other words, you can go to cells which share an edge with you current
cell.
Please note that a path of length k means visiting exactly k cells (not
necessarily distinct).
You CANNOT go off the grid.
A path A (of length k) is considered less than a path B (of length k) if
after making the ordered lists of the values on the cells that A and B go
through (let's call them lst_A and lst_B), lst_A is lexicographically less
than lst_B, in other words, there exist an integer index i (1 <= i <= k)
such that lst_A[i] < lst_B[i] and for any j (1 <= j < i) we have
lst_A[j] = lst_B[j].
It is guaranteed that the answer is unique.
Return an ordered list of the values on the cells that the minimum path go through.
Examples:
Input: grid = [ [1,2,3], [4,5,6], [7,8,9]], k = 3
Output: [1, 2, 1]
Input: grid = [ [5,9,3], [4,1,6], [7,8,2]], k = 1
Output: [1]
"""The above is an incomplete Python code fragment. Return the complete and correct code with no additional text.
def minPath(grid, k):
"""
Given a grid with N rows and N columns (N >= 2) and a positive integer k,
each cell of the grid contains a value. Every integer in the range [1, N * N]
inclusive appears exactly once on the cells of the grid.
You have to find the minimum path of length k in the grid. You can start
from any cell, and in each step you can move to any of the neighbor cells,
in other words, you can go to cells which share an edge with you current
cell.
Please note that a path of length k means visiting exactly k cells (not
necessarily distinct).
You CANNOT go off the grid.
A path A (of length k) is considered less than a path B (of length k) if
after making the ordered lists of the values on the cells that A and B go
through (let's call them lst_A and lst_B), lst_A is lexicographically less
than lst_B, in other words, there exist an integer index i (1 <= i <= k)
such that lst_A[i] < lst_B[i] and for any j (1 <= j < i) we have
lst_A[j] = lst_B[j].
It is guaranteed that the answer is unique.
Return an ordered list of the values on the cells that the minimum path go through.
Examples:
Input: grid = [ [1,2,3], [4,5,6], [7,8,9]], k = 3
Output: [1, 2, 1]
Input: grid = [ [5,9,3], [4,1,6], [7,8,2]], k = 1
Output: [1]
"""n = len(grid)
val = n * n + 1
for i in range(n):
for j in range(n):
if grid[i][j] == 1:
temp = []
if i != 0:
temp.append(grid[i - 1][j])
if j != 0:
temp.append(grid[i][j - 1])
if i != n - 1:
temp.append(grid[i + 1][j])
if j != n - 1:
temp.append(grid[i][j + 1])
val = min(temp)
ans = []
for i in range(k):
if i % 2 == 0:
ans.append(1)
else:
ans.append(val)
return ansdef check(candidate):
# Check some simple cases
print
assert candidate([[1, 2, 3], [4, 5, 6], [7, 8, 9]], 3) == [1, 2, 1]
assert candidate([[5, 9, 3], [4, 1, 6], [7, 8, 2]], 1) == [1]
assert candidate([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16]], 4) == [1, 2, 1, 2]
assert candidate([[6, 4, 13, 10], [5, 7, 12, 1], [3, 16, 11, 15], [8, 14, 9, 2]], 7) == [1, 10, 1, 10, 1, 10, 1]
assert candidate([[8, 14, 9, 2], [6, 4, 13, 15], [5, 7, 1, 12], [3, 10, 11, 16]], 5) == [1, 7, 1, 7, 1]
assert candidate([[11, 8, 7, 2], [5, 16, 14, 4], [9, 3, 15, 6], [12, 13, 10, 1]], 9) == [1, 6, 1, 6, 1, 6, 1, 6, 1]
assert candidate([[12, 13, 10, 1], [9, 3, 15, 6], [5, 16, 14, 4], [11, 8, 7, 2]], 12) == [1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6]
assert candidate([[2, 7, 4], [3, 1, 5], [6, 8, 9]], 8) == [1, 3, 1, 3, 1, 3, 1, 3]
assert candidate([[6, 1, 5], [3, 8, 9], [2, 7, 4]], 8) == [1, 5, 1, 5, 1, 5, 1, 5]
# Check some edge cases that are easy to work out by hand.
assert candidate([[1, 2], [3, 4]], 10) == [1, 2, 1, 2, 1, 2, 1, 2, 1, 2]
assert candidate([[1, 3], [3, 2]], 10) == [1, 3, 1, 3, 1, 3, 1, 3, 1, 3]Start time: 2023-07-18 18:00:56
Duration: 23.1s
Completion tokens: 202
Result: Fail
from heapq import heappop, heappush
def minPath(grid, k):
N = len(grid)
moves = [(0, 1), (1, 0), (0, -1), (-1, 0)]
visited = set()
heap = [(grid[i][j], i, j, [grid[i][j]]) for i in range(N) for j in range(N)]
while heap:
val, x, y, path = heappop(heap)
if len(path) == k:
return path
for dx, dy in moves:
nx, ny = x + dx, y + dy
if 0 <= nx < N and 0 <= ny < N and (nx, ny) not in visited:
visited.add((nx, ny))
heappush(heap, (grid[nx][ny], nx, ny, path + [grid[nx][ny]]))Start time: 2023-07-18 18:00:29
Duration: 26.59s
Completion tokens: 331
Result: Fail
from heapq import heappop, heappush
def minPath(grid, k):
N = len(grid)
moves = [(0, 1), (1, 0), (0, -1), (-1, 0)]
visited = set()
heap = [(grid[0][0], 0, 0, [grid[0][0]])]
while heap:
val, x, y, path = heappop(heap)
if len(path) == k:
return path
for dx, dy in moves:
nx, ny = x + dx, y + dy
if 0 <= nx < N and 0 <= ny < N and (nx, ny) not in visited:
visited.add((nx, ny))
new_path = path + [grid[nx][ny]]
heappush(heap, (new_path, nx, ny, new_path))
return []Start time: 2023-07-18 18:00:04
Duration: 25.53s
Completion tokens: 300
Result: Fail
from heapq import heappop, heappush
def minPath(grid, k):
N = len(grid)
moves = [(0, 1), (0, -1), (1, 0), (-1, 0)]
heap = [(grid[i][j], i, j, [grid[i][j]]) for i in range(N) for j in range(N)]
heapify(heap)
while heap:
val, x, y, path = heappop(heap)
if len(path) == k:
return path
for dx, dy in moves:
nx, ny = x + dx, y + dy
if 0 <= nx < N and 0 <= ny < N:
heappush(heap, (max(val, grid[nx][ny]), nx, ny, path + [grid[nx][ny]]))Start time: 2023-07-18 17:59:44
Duration: 19.42s
Completion tokens: 228
Result: Fail
from heapq import heappop, heappush
def minPath(grid, k):
N = len(grid)
moves = [(0, 1), (1, 0), (0, -1), (-1, 0)]
heap = [(grid[i][j], i, j, [grid[i][j]]) for i in range(N) for j in range(N)]
visited = set()
while heap:
val, x, y, path = heappop(heap)
if (x, y, len(path)) in visited:
continue
visited.add((x, y, len(path)))
if len(path) == k:
return path
for dx, dy in moves:
nx, ny = x + dx, y + dy
if 0 <= nx < N and 0 <= ny < N and (nx, ny, len(path) + 1) not in visited:
heappush(heap, (grid[nx][ny], nx, ny, path + [grid[nx][ny]]))Start time: 2023-07-18 17:59:25
Duration: 18.78s
Completion tokens: 233
Result: Fail
def minPath(grid, k):
N = len(grid)
directions = [(0, 1), (1, 0), (0, -1), (-1, 0)] # right, down, left, up
min_path = [N * N + 1] * k
visited = set()
def dfs(i, j, path):
nonlocal min_path
if len(path) == k:
min_path = min(min_path, path)
return
for dx, dy in directions:
x, y = i + dx, j + dy
if 0 <= x < N and 0 <= y < N and (x, y) not in visited:
visited.add((x, y))
dfs(x, y, path + [grid[x][y]])
visited.remove((x, y))
for i in range(N):
for j in range(N):
visited.add((i, j))
dfs(i, j, [grid[i][j]])
visited.remove((i, j))
return min_pathStart time: 2023-07-18 17:59:02
Duration: 23.57s
Completion tokens: 303
Result: Pass
def minPath(grid, k):
N = len(grid)
directions = [(0, 1), (0, -1), (1, 0), (-1, 0)]
min_path = [float('inf')] * k
for i in range(N):
for j in range(N):
def dfs(x, y, path, k):
nonlocal min_path
if k == 0:
min_path = min(min_path, path)
return
for dx, dy in directions:
nx, ny = x + dx, y + dy
if 0 <= nx < N and 0 <= ny < N:
dfs(nx, ny, path + [grid[nx][ny]], k - 1)
dfs(i, j, [grid[i][j]], k - 1)
return min_pathStart time: 2023-07-18 17:58:36
Duration: 25.45s
Completion tokens: 335
Result: Fail
from heapq import heappop, heappush
def minPath(grid, k):
N = len(grid)
moves = [(0, 1), (1, 0), (0, -1), (-1, 0)]
heap = [(grid[i][j], i, j, [grid[i][j]]) for i in range(N) for j in range(N)]
visited = set()
while heap:
val, x, y, path = heappop(heap)
if len(path) == k:
return path
for dx, dy in moves:
nx, ny = x + dx, y + dy
if 0 <= nx < N and 0 <= ny < N and (nx, ny) not in visited:
visited.add((nx, ny))
heappush(heap, (grid[nx][ny], nx, ny, path + [grid[nx][ny]]))Start time: 2023-07-18 17:58:18
Duration: 18.18s
Completion tokens: 202
Result: Fail
from heapq import heappop, heappush
def minPath(grid, k):
N = len(grid)
moves = [(0, 1), (1, 0), (0, -1), (-1, 0)]
visited = set()
heap = [(grid[i][j], i, j, [grid[i][j]]) for i in range(N) for j in range(N)]
while heap:
val, x, y, path = heappop(heap)
if len(path) == k:
return path
for dx, dy in moves:
nx, ny = x + dx, y + dy
if 0 <= nx < N and 0 <= ny < N and (nx, ny) not in visited:
visited.add((nx, ny))
heappush(heap, (grid[nx][ny], nx, ny, path + [grid[nx][ny]]))Start time: 2023-07-18 17:57:56
Duration: 21.99s
Completion tokens: 218
Result: Fail
from heapq import heappop, heappush
def minPath(grid, k):
n = len(grid)
moves = [(0, 1), (1, 0), (0, -1), (-1, 0)]
heap = [(grid[i][j], i, j, [grid[i][j]]) for i in range(n) for j in range(n)]
visited = set()
while heap:
val, x, y, path = heappop(heap)
if (x, y) in visited:
continue
visited.add((x, y))
if len(path) == k:
return path
for dx, dy in moves:
nx, ny = x + dx, y + dy
if 0 <= nx < n and 0 <= ny < n and (nx, ny) not in visited:
heappush(heap, (grid[nx][ny], nx, ny, path + [grid[nx][ny]]))
return []Start time: 2023-07-18 17:57:31
Duration: 24.87s
Completion tokens: 330
Result: Pass
def minPath(grid, k):
N = len(grid)
min_path = [N*N]*k
directions = [(0, 1), (1, 0), (0, -1), (-1, 0)] # right, down, left, up
def dfs(i, j, depth, path):
nonlocal min_path
if depth == k:
min_path = min(min_path, path)
return
for dx, dy in directions:
x, y = i + dx, j + dy
if 0 <= x < N and 0 <= y < N:
dfs(x, y, depth + 1, path + [grid[x][y]])
for i in range(N):
for j in range(N):
dfs(i, j, 1, [grid[i][j]])
return min_path