Problem: Takahashi is locked within a building.  This building consists of H×W rooms, arranged in H rows and W columns. We will denote the room at the i-th row and j-th column as (i,j). The state of this room is represented by a character A_{i,j}. If A_{i,j}= `#`, the room is locked and cannot be entered; if A_{i,j}= `.`, the room is not locked and can be freely entered. Takahashi is currently at the room where A_{i,j}= `S`, which can also be freely entered.  Each room in the 1-st row, 1-st column, H-th row or W-th column, has an exit. Each of the other rooms (i,j) is connected to four rooms: (i-1,j), (i+1,j), (i,j-1) and (i,j+1).  Takahashi will use his magic to get out of the building. In one cast, he can do the following:    * Move to an adjacent room at most K times, possibly zero. Here, locked rooms cannot be entered.   * Then, select and unlock at most K locked rooms, possibly zero. Those rooms will remain unlocked from then on.  His objective is to reach a room with an exit. Find the minimum necessary number of casts to do so.  It is guaranteed that Takahashi is initially at a room without an exit.

Submission attempts (in order):
from collections import deque

INF = float("inf")

H, W, K = map(int, input().split())
A = [list(input()) for _ in range(H)]

Si, Sj = (0, 0)
for i, a in enumerate(A):
    if "S" in a:
        Si, Sj = (i, a.index("S"))
        break

dist = [[INF] * W for _ in range(H)]
dist[Si][Sj] = 0

ans = INF

Q = deque([(Si, Sj)])
while Q:
    i, j = Q.popleft()

    ans = min(
        1 + (i + K - 1) // K,
        1 + (j + K - 1) // K,
        1 + (H - 1 - i + K - 1) // K,
        1 + (W - 1 - j + K - 1) // K
    )

    if dist[i][j] == K:
        continue

    distance = dist[i][j] + 1

    for di, dj in ((1, 0), (0, 1), (-1, 0), (0, -1)):
        ni, nj = i + di, j + dj

        if not (0 <= ni < H or 0 <= nj < W) and A[ni][nj] == "#":
            continue

        if dist[ni][nj] > distance:
            dist[ni][nj] = distance
            Q.append((ni, nj))

print(ans)


from collections import deque

INF = float("inf")

H, W, K = map(int, input().split())
A = [list(input()) for _ in range(H)]

Si, Sj = (0, 0)
for i, a in enumerate(A):
    if "S" in a:
        Si, Sj = (i, a.index("S"))
        break

dist = [[INF] * W for _ in range(H)]
dist[Si][Sj] = 0


ans = INF

Q = deque([(Si, Sj)])
while Q:
    i, j = Q.popleft()

    ans = min(
        ans,
        1 + (i + K - 1) // K,
        1 + (j + K - 1) // K,
        1 + (H - 1 - i + K - 1) // K,
        1 + (W - 1 - j + K - 1) // K
    )

    if dist[i][j] == K:
        continue

    distance = dist[i][j] + 1

    for di, dj in ((1, 0), (0, 1), (-1, 0), (0, -1)):
        ni, nj = i + di, j + dj

        if not (0 <= ni < H or 0 <= nj < W) and A[ni][nj] == "#":
            continue

        if dist[ni][nj] > distance:
            dist[ni][nj] = distance
            Q.append((ni, nj))

print(ans)


from collections import deque

INF = float("inf")

H, W, K = map(int, input().split())
A = [list(input()) for _ in range(H)]

Si, Sj = (0, 0)
for i, a in enumerate(A):
    if "S" in a:
        Si, Sj = (i, a.index("S"))
        break

dist = [[INF] * W for _ in range(W)]
dist[Si][Sj] = 0


ans = INF

Q = deque([(Si, Sj)])
while Q:
    i, j = Q.popleft()

    ans = min(
        1 + (i + K - 1) // K,
        1 + (j + K - 1) // K,
        1 + (H - 1 - i + K - 1) // K,
        1 + (W - 1 - j + K - 1) // K
    )

    if dist[i][j] == K:
        continue

    distance = dist[i][j] + 1

    for di, dj in ((1, 0), (0, 1), (-1, 0), (0, -1)):
        ni, nj = i + di, j + dj

        if not (0 <= ni < H or 0 <= nj < W) and A[ni][nj] == "#":
            continue

        if dist[ni][nj] > distance:
            dist[ni][nj] = distance
            Q.append((ni, nj))

print(ans)


from collections import deque

INF = float("inf")

H, W, K = map(int, input().split())
A = [list(input()) for _ in range(H)]

Si, Sj = (0, 0)
for i, a in enumerate(A):
    if "S" in a:
        Si, Sj = (i, a.index("S"))
        break

dist = [[INF] * W for _ in range(W)]
dist[Si][Sj] = 0


ans = INF

Q = deque([(Si, Sj)])
while Q:
    i, j = Q.popleft()

    ans = min(
        1 + (i + K - 1) // K,
        1 + (j + K - 1) // K,
        1 + (H - 1 - i + K - 1) // K,
        1 + (W - 1 - j + K - 1) // K
    )

    if dist[i][j] == K:
        continue

    distance = dist[i][j] + 1

    for di, dj in ((1, 0), (0, 1), (-1, 0), (0, -1)):
        ni, nj = i + di, j + dj

        if not (0 <= ni < H or 0 <= nj < W) or A[ni][nj] == "#":
            continue

        if dist[ni][nj] > distance:
            dist[ni][nj] = distance
            Q.append((ni, nj))

print(ans)


from collections import deque

H, W, K = map(int, input().split())
A = [list(input()) for _ in range(H)]

Si, Sj = (0, 0)
for i, a in enumerate(A):
	if "S" in a:
		Si, Sj = (i, a.index("S"))
		break

dist = float("inf")

Q = deque([(0, Si, Sj)])
while Q:
	cnt, i, j = Q.popleft()

	dist = min(dist, i, j, H - i - 1, W - j - 1)
	if dist == 0:
		break

	if cnt >= K:
		continue

	for ni, nj in ((i + 1, j), (i, j + 1), (i - 1, j), (i, j - 1)):
		if 0 <= ni < H and 0 <= nj < W and A[ni][nj] == ".":
			A[ni][nj] = "#"
			Q.append((cnt + 1, ni, nj))

print(-(-dist // K) + 1)

Verdicts: Runtime Error

Runtime Error

Runtime Error

Runtime Error

Accepted