Problem:


Score : 600 points

Problem Statement

Snuke, a water strider, lives in a rectangular pond that can be seen as a grid with H east-west rows and W north-south columns. Let (i,j) be the square at the i-th row from the north and j-th column from the west.

Some of the squares have a lotus leaf on it and cannot be entered.
The square (i,j) has a lotus leaf on it if c_{ij} is @, and it does not if c_{ij} is ..

In one stroke, Snuke can move between 1 and K squares (inclusive) toward one of the four directions: north, east, south, and west.
The move may not pass through a square with a lotus leaf. Moving to such a square or out of the pond is also forbidden.

Find the minimum number of strokes Snuke takes to travel from the square (x_1,y_1) to (x_2,y_2).
If the travel from (x_1,y_1) to (x_2,y_2) is impossible, point out that fact.

Constraints

1 \leq H,W,K \leq 10^6

H \times W \leq 10^6

1 \leq x_1,x_2 \leq H

1 \leq y_1,y_2 \leq W

x_1 \neq x_2 or y_1 \neq y_2.

c_{i,j} is . or @.

c_{x_1,y_1} = .

c_{x_2,y_2} = .

All numbers in input are integers.

Input

Input is given from Standard Input in the following format:

H W K
x_1 y_1 x_2 y_2
c_{1,1}c_{1,2} .. c_{1,W}
c_{2,1}c_{2,2} .. c_{2,W}
:
c_{H,1}c_{H,2} .. c_{H,W}

Output

Print the minimum number of strokes Snuke takes to travel from the square (x_1,y_1) to (x_2,y_2), or print -1 if the travel is impossible.

Sample Input 1

3 5 2
3 2 3 4
.....
.@..@
..@..

Sample Output 1

5

Initially, Snuke is at the square (3,2).
He can reach the square (3, 4) by making five strokes as follows:

From (3, 2), go west one square to (3, 1).

From (3, 1), go north two squares to (1, 1).

From (1, 1), go east two squares to (1, 3).

From (1, 3), go east one square to (1, 4).

From (1, 4), go south two squares to (3, 4).

Sample Input 2

1 6 4
1 1 1 6
......

Sample Output 2

2

Sample Input 3

3 3 1
2 1 2 3
.@.
.@.
.@.

Sample Output 3

-1



Sample input:
3 5 2
3 2 3 4
.....
.@..@
..@..


Sample output:
5

Submission status: Time Limit Exceeded

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

def update(x, y, k, cost, pt, vec, pond, row, hq, fs):
    hpush = heapq.heappush
    i = 1
    while i <= k:
        nx, ny = x, y
        nc = cost+1
        if vec == 0:
            nx -= i
        elif vec == 1:
            ny += i
        elif vec == 2:
            nx += i
        else:
            ny -= i
        if pond[nx][ny] == 1:
            return
        if row[nx][ny][vec] > nc:
            row[nx][ny][vec] = nc
            if i == k:
                hpush(hq, [nc, nx, ny, i, vec])
            if fs[nx][ny]:
                for j in range(1, 4):
                    if row[nx][ny][(vec+j)%4] > nc:
                        row[nx][ny][(vec+j)%4] = nc
                        hpush(hq, [nc, nx, ny, k, (vec+j)%4])
                fs[nx][ny] = False
        else:
            return
        i += 1

def main():
    h, w, k = map(int, input().split())
    x1, y1, x2, y2 = map(int, input().split())
    pond = [[1]*(w+2) for _ in range(h+2)]
    for i in range(1, h+1):
        s = input()
        for j in range(w):
            if s[j] == ".":
                pond[i][j+1] = 0
    hq = []
    row = [[[float("inf")]*4 for j in range(w+2)] for i in range(h+2)]
    fs = [[True]*(w+2) for _ in range(h+2)]
    hpop = heapq.heappop
    for i in range(4):
        row[x1][y1][i] = 0
        heapq.heappush(hq, [0, x1, y1, k, i])
    while len(hq) > 0:
        cost, x, y, pt, vec = hpop(hq)
        if cost > row[x][y][vec]:
            continue
        update(x, y, k, cost, pt, vec, pond, row, hq, fs)
    ans = min(row[x2][y2])
    if ans == float("inf"):
        print(-1)
    else:
        print(ans)

if __name__ == "__main__":
    main()

Submission status: Time Limit Exceeded

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

def update(x, y, k, cost, pt, vec, pond, row, q, fs):
    i = 1
    while i <= k:
        nx, ny = x, y
        nc = cost+1
        if vec == 0:
            nx -= i
        elif vec == 1:
            ny += i
        elif vec == 2:
            nx += i
        else:
            ny -= i
        if pond[nx][ny] == 1:
            return
        if row[nx][ny][vec] > nc:
            row[nx][ny][vec] = nc
            if i == k:
                q.put([nc, nx, ny, i, vec])
            if fs[nx][ny]:
                for j in range(1, 4):
                    if row[nx][ny][(vec+j)%4] > nc:
                        row[nx][ny][(vec+j)%4] = nc
                        q.put([nc, nx, ny, k, (vec+j)%4])
                fs[nx][ny] = False
        else:
            return
        i += 1

def main():
    h, w, k = map(int, input().split())
    x1, y1, x2, y2 = map(int, input().split())
    pond = [[1]*(w+2) for _ in range(h+2)]
    for i in range(1, h+1):
        s = input()
        for j in range(w):
            if s[j] == ".":
                pond[i][j+1] = 0
    q = queue.Queue()
    row = [[[float("inf")]*4 for j in range(w+2)] for i in range(h+2)]
    fs = [[True]*(w+2) for _ in range(h+2)]
    for i in range(4):
        row[x1][y1][i] = 0
        q.put([0, x1, y1, k, i])
    while not q.empty():
        cost, x, y, pt, vec = q.get()
        if cost > row[x][y][vec]:
            continue
        update(x, y, k, cost, pt, vec, pond, row, q, fs)
    ans = min(row[x2][y2])
    if ans == float("inf"):
        print(-1)
    else:
        print(ans)

if __name__ == "__main__":
    main()

Submission status: Time Limit Exceeded

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

def main():
    h, w, k = map(int, input().split())
    x1, y1, x2, y2 = map(int, input().split())
    pond = [[1]*(w+2) for _ in range(h+2)]
    for i in range(1, h+1):
        s = input()
        for j in range(w):
            if s[j] == ".":
                pond[i][j+1] = 0
    q = queue.Queue()
    row = [[float("inf")]*(w+2) for _ in range(h+2)]
    row[x1][y1] = 0
    ans = -1
    for i in range(4):
        q.put([0, x1, y1, i])
    while not q.empty():
        cost, x, y, vec = q.get()
        if cost > row[x][y]:
            continue
        if x == x2 and y == y2:
            ans = cost
            break
        for i in range(1, k+1):
            nx, ny = x, y
            if vec == 0:
                nx -= i
            elif vec == 1:
                ny += i
            elif vec == 2:
                nx += i
            else:
                ny -= i
            if pond[nx][ny] == 1 or row[nx][ny] < cost + 1:
                break
            row[nx][ny] = cost + 1
            if i < k:
                for j in range(4):
                    if j != vec:
                        row[nx][ny] = cost+1
                        q.put([cost+1, nx, ny, j])
            else:
                for j in range(4):
                    row[nx][ny] = cost+1
                    q.put([cost+1, nx, ny, j])
    print(ans)

if __name__ == "__main__":
    main()

Submission status: Time Limit Exceeded

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

def update(x, y, k, cost, pt, vec, pond, row, q, fs):
    for i in range(1, k+1):
        nx, ny = x, y
        nc = cost+1
        if vec == 0:
            nx -= i
        elif vec == 1:
            ny += i
        elif vec == 2:
            nx += i
        else:
            ny -= i
        if pond[nx][ny] == 1:
            return
        if row[nx][ny][vec] > nc:
            row[nx][ny][vec] = nc
            if i == k:
                q.put([nc, nx, ny, i, vec])
            if fs[nx][ny]:
                for j in range(1, 4):
                    if row[nx][ny][(vec+j)%4] > nc:
                        row[nx][ny][(vec+j)%4] = nc
                        q.put([nc, nx, ny, k, (vec+j)%4])
                fs[nx][ny] = False
        else:
            return

def main():
    h, w, k = map(int, input().split())
    x1, y1, x2, y2 = map(int, input().split())
    pond = [[1]*(w+2) for _ in range(h+2)]
    for i in range(1, h+1):
        s = input()
        for j in range(w):
            if s[j] == ".":
                pond[i][j+1] = 0
    q = queue.Queue()
    row = [[[float("inf")]*4 for j in range(w+2)] for i in range(h+2)]
    fs = [[True]*(w+2) for _ in range(h+2)]
    for i in range(4):
        row[x1][y1][i] = 0
        q.put([0, x1, y1, k, i])
    while not q.empty():
        cost, x, y, pt, vec = q.get()
        if cost > row[x][y][vec]:
            continue
        update(x, y, k, cost, pt, vec, pond, row, q, fs)
    ans = min(row[x2][y2])
    if ans == float("inf"):
        print(-1)
    else:
        print(ans)

if __name__ == "__main__":
    main()

Submission status: Time Limit Exceeded

Solution code:
import heapq

def main():
    h, w, k = map(int, input().split())
    x1, y1, x2, y2 = map(int, input().split())
    pond = [[1]*(w+2) for _ in range(h+2)]
    for i in range(1, h+1):
        s = input()
        for j in range(w):
            if s[j] == ".":
                pond[i][j+1] = 0
    hq = []
    row = [[float("inf")]*(w+2) for _ in range(h+2)]
    row[x1][y1] = 0
    ans = -1
    for i in range(4):
        heapq.heappush(hq, [0, x1, y1, i])
    while len(hq) > 0:
        cost, x, y, vec = heapq.heappop(hq)
        if cost > row[x][y]:
            continue
        if x == x2 and y == y2:
            ans = cost
            break
        for i in range(1, k+1):
            nx, ny = x, y
            if vec == 0:
                nx -= i
            elif vec == 1:
                ny += i
            elif vec == 2:
                nx += i
            else:
                ny -= i
            if pond[nx][ny] == 1 or row[nx][ny] < cost + 1:
                break
            row[nx][ny] = cost + 1
            if i < k:
                for j in range(4):
                    if j != vec:
                        row[nx][ny] = cost+1
                        heapq.heappush(hq, [cost+1, nx, ny, j])
            else:
                for j in range(4):
                    row[nx][ny] = cost+1
                    heapq.heappush(hq, [cost+1, nx, ny, j])
    print(ans)

if __name__ == "__main__":
    main()

Submission status: Time Limit Exceeded

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

def update(x, y, k, cost, pt, vec, pond, row, hq, fs):
    hpush = heapq.heappush
    for i in range(1, k+1):
        nx, ny = x, y
        nc = cost+1
        if vec == 0:
            nx -= i
        elif vec == 1:
            ny += i
        elif vec == 2:
            nx += i
        else:
            ny -= i
        if pond[nx][ny] == 1:
            return
        if row[nx][ny][vec] > nc:
            row[nx][ny][vec] = nc
            if i == k:
                hpush(hq, [nc, nx, ny, i, vec])
            if fs[nx][ny]:
                for j in range(1, 4):
                    if row[nx][ny][(vec+j)%4] > nc:
                        row[nx][ny][(vec+j)%4] = nc
                        hpush(hq, [nc, nx, ny, k, (vec+j)%4])
                fs[nx][ny] = False
        else:
            return

def main():
    h, w, k = map(int, input().split())
    x1, y1, x2, y2 = map(int, input().split())
    pond = [[1]*(w+2) for _ in range(h+2)]
    for i in range(1, h+1):
        s = input()
        for j in range(w):
            if s[j] == ".":
                pond[i][j+1] = 0
    hq = []
    row = [[[float("inf")]*4 for j in range(w+2)] for i in range(h+2)]
    fs = [[True]*(w+2) for _ in range(h+2)]
    hpop = heapq.heappop
    for i in range(4):
        row[x1][y1][i] = 0
        heapq.heappush(hq, [0, x1, y1, k, i])
    while len(hq) > 0:
        cost, x, y, pt, vec = hpop(hq)
        if cost > row[x][y][vec]:
            continue
        update(x, y, k, cost, pt, vec, pond, row, hq, fs)
    ans = min(row[x2][y2])
    if ans == float("inf"):
        print(-1)
    else:
        print(ans)

if __name__ == "__main__":
    main()

Submission status: Time Limit Exceeded

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

def update(x, y, k, cost, pt, vec, pond, row, hq, fs):
    for i in range(1, k+1):
        nx, ny = x, y
        nc = cost+1
        if vec == 0:
            nx -= i
        elif vec == 1:
            ny += i
        elif vec == 2:
            nx += i
        else:
            ny -= i
        if pond[nx][ny] == 1:
            return
        if row[nx][ny][vec] > nc:
            row[nx][ny][vec] = nc
            if i == k:
                heapq.heappush(hq, [nc, nx, ny, i, vec])
            if fs[nx][ny]:
                for j in range(1, 4):
                    if row[nx][ny][(vec+j)%4] > nc:
                        row[nx][ny][(vec+j)%4] = nc
                        heapq.heappush(hq, [nc, nx, ny, k, (vec+j)%4])
                fs[nx][ny] = False
        else:
            return

def main():
    h, w, k = map(int, input().split())
    x1, y1, x2, y2 = map(int, input().split())
    pond = [[1]*(w+2) for _ in range(h+2)]
    for i in range(1, h+1):
        s = input()
        for j in range(w):
            if s[j] == ".":
                pond[i][j+1] = 0
    hq = []
    row = [[[float("inf")]*4 for j in range(w+2)] for i in range(h+2)]
    fs = [[True]*(w+2) for _ in range(h+2)]
    for i in range(4):
        row[x1][y1][i] = 0
        heapq.heappush(hq, [0, x1, y1, k, i])
    st = set()
    while len(hq) > 0:
        cost, x, y, pt, vec = heapq.heappop(hq)
        if (x, y, vec) in st:
            continue
        else:
            st.add((x, y, vec))
        update(x, y, k, cost, pt, vec, pond, row, hq, fs)
    ans = min(row[x2][y2])
    if ans == float("inf"):
        print(-1)
    else:
        print(ans)

if __name__ == "__main__":
    main()

Submission status: Time Limit Exceeded

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

def update(x, y, k, cost, pt, vec, pond, row, hq, fs):
    for i in range(1, k+1):
        nx, ny = x, y
        nc = cost+1
        if vec == 0:
            nx -= i
        elif vec == 1:
            ny += i
        elif vec == 2:
            nx += i
        else:
            ny -= i
        if pond[nx][ny] == 1:
            return
        if row[nx][ny][vec] > nc:
            row[nx][ny][vec] = nc
            if i == k:
                heapq.heappush(hq, [nc, nx, ny, i, vec])
            if fs[nx][ny]:
                for j in range(1, 4):
                    if row[nx][ny][(vec+j)%4] > nc:
                        row[nx][ny][(vec+j)%4] = nc
                        heapq.heappush(hq, [nc, nx, ny, k, (vec+j)%4])
                fs[nx][ny] = False
        else:
            return

def main():
    h, w, k = map(int, input().split())
    x1, y1, x2, y2 = map(int, input().split())
    pond = [[1]*(w+2) for _ in range(h+2)]
    for i in range(1, h+1):
        s = input()
        for j in range(w):
            if s[j] == ".":
                pond[i][j+1] = 0
    hq = []
    row = [[[float("inf")]*4 for j in range(w+2)] for i in range(h+2)]
    fs = [[True]*(w+2) for _ in range(h+2)]
    for i in range(4):
        row[x1][y1][i] = 0
        heapq.heappush(hq, [0, x1, y1, k, i])
    while len(hq) > 0:
        cost, x, y, pt, vec = heapq.heappop(hq)
        if cost > row[x][y][vec]:
            continue
        update(x, y, k, cost, pt, vec, pond, row, hq, fs)
    ans = min(row[x2][y2])
    if ans == float("inf"):
        print(-1)
    else:
        print(ans)

if __name__ == "__main__":
    main()

Submission status: Time Limit Exceeded

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

def update(x, y, k, cost, pt, vec, pond, row, hq, fs):
    for i in range(1, k+1):
        nx, ny = x, y
        nc = cost+1
        if vec == 0:
            nx -= i
        elif vec == 1:
            ny += i
        elif vec == 2:
            nx += i
        else:
            ny -= i
        if pond[nx][ny] == 1:
            return
        if row[nx][ny][vec] > nc:
            row[nx][ny][vec] = nc
            if i == k:
                heapq.heappush(hq, [nc, nx, ny, i, vec])
            if fs[nx][ny]:
                for j in range(1, 4):
                    if row[nx][ny][(vec+j)%4] > nc:
                        row[nx][ny][(vec+j)%4] = nc
                        heapq.heappush(hq, [nc, nx, ny, k, (vec+j)%4])
                fs[nx][ny] = False
        else:
            return

def main():
    h, w, k = map(int, input().split())
    x1, y1, x2, y2 = map(int, input().split())
    pond = [[1]*(w+2) for _ in range(h+2)]
    for i in range(1, h+1):
        s = input()
        for j in range(w):
            if s[j] == ".":
                pond[i][j+1] = 0
    hq = []
    row = [[[float("inf")]*4 for j in range(w+2)] for i in range(h+2)]
    fs = [[True]*(w+2) for _ in range(h+2)]
    for i in range(4):
        row[x1][y1][i] = 0
        heapq.heappush(hq, [0, x1, y1, k, i])
    while len(hq) > 0:
        cost, x, y, pt, vec = heapq.heappop(hq)
        if cost > row[x][y][vec]:
            continue
        if pt == k:
            update(x, y, k, cost, pt, vec, pond, row, hq, fs)
    ans = min(row[x2][y2])
    if ans == float("inf"):
        print(-1)
    else:
        print(ans)

if __name__ == "__main__":
    main()

Submission status: Time Limit Exceeded

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

def update(x, y, k, cost, pt, vec, pond, row, hq, fs):
    for i in range(1, k+1):
        nx, ny = x, y
        nc = cost+1
        if vec == 0:
            nx -= i
        elif vec == 1:
            ny += i
        elif vec == 2:
            nx += i
        else:
            ny -= i
        if pond[nx][ny] == 1:
            return
        if row[nx][ny][vec] > nc:
            row[nx][ny][vec] = nc
            heapq.heappush(hq, [nc, nx, ny, i, vec])
            if fs[nx][ny]:
                for j in range(1, 4):
                    if row[nx][ny][(vec+j)%4] > nc:
                        row[nx][ny][(vec+j)%4] = nc
                        heapq.heappush(hq, [nc, nx, ny, k, (vec+j)%4])
                fs[nx][ny] = False
        else:
            return

def main():
    h, w, k = map(int, input().split())
    x1, y1, x2, y2 = map(int, input().split())
    pond = [[1]*(w+2) for _ in range(h+2)]
    for i in range(1, h+1):
        s = input()
        for j in range(w):
            if s[j] == ".":
                pond[i][j+1] = 0
    hq = []
    row = [[[float("inf")]*4 for j in range(w+2)] for i in range(h+2)]
    fs = [[True]*(w+2) for _ in range(h+2)]
    for i in range(4):
        row[x1][y1][i] = 0
        heapq.heappush(hq, [0, x1, y1, k, i])
    while len(hq) > 0:
        cost, x, y, pt, vec = heapq.heappop(hq)
        if cost > row[x][y][vec]:
            continue
        if pt == k:
            update(x, y, k, cost, pt, vec, pond, row, hq, fs)
    ans = min(row[x2][y2])
    if ans == float("inf"):
        print(-1)
    else:
        print(ans)

if __name__ == "__main__":
    main()

Submission status: Time Limit Exceeded

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

def update(x, y, k, cost, pt, vec, pond, row, hq):
    for i in range(1, k+1):
        nx, ny = x, y
        nc = cost+1
        if vec == 0:
            nx -= i
        elif vec == 1:
            ny += i
        elif vec == 2:
            nx += i
        else:
            ny -= i
        if pond[nx][ny] == 1:
            return
        if row[nx][ny][vec] > nc:
            row[nx][ny][vec] = nc
            heapq.heappush(hq, [nc, nx, ny, i, vec])
            for j in range(1, 4):
                if row[nx][ny][(vec+j)%4] > nc:
                    row[nx][ny][(vec+j)%4] = nc
                    heapq.heappush(hq, [nc, nx, ny, k, (vec+j)%4])
        else:
            return

def main():
    h, w, k = map(int, input().split())
    x1, y1, x2, y2 = map(int, input().split())
    pond = [[1]*(w+2) for _ in range(h+2)]
    for i in range(1, h+1):
        s = input()
        for j in range(w):
            if s[j] == ".":
                pond[i][j+1] = 0
    hq = []
    row = [[[float("inf")]*4 for j in range(w+2)] for i in range(h+2)]
    for i in range(4):
        row[x1][y1][i] = 0
        heapq.heappush(hq, [0, x1, y1, k, i])
    while len(hq) > 0:
        cost, x, y, pt, vec = heapq.heappop(hq)
        if cost > row[x][y][vec]:
            continue
        if pt == k:
            update(x, y, k, cost, pt, vec, pond, row, hq)
    ans = min(row[x2][y2])
    if ans == float("inf"):
        print(-1)
    else:
        print(ans)

if __name__ == "__main__":
    main()

Submission status: Time Limit Exceeded

Solution code:
import heapq

def update(x, y, k, cost, pt, vec, pond, row, hq):
    for i in range(1, k+1):
        nx, ny = x, y
        nc = cost+1
        if vec == 0:
            nx -= i
        elif vec == 1:
            ny += i
        elif vec == 2:
            nx += i
        else:
            ny -= i
        if pond[nx][ny] == 1:
            return
        if row[nx][ny][vec] > nc:
            row[nx][ny][vec] = nc
            heapq.heappush(hq, [nc, nx, ny, i, vec])
            for j in range(1, 4):
                if row[nx][ny][(vec+j)%4] > nc:
                    row[nx][ny][(vec+j)%4] = nc
                    heapq.heappush(hq, [nc, nx, ny, k, (vec+j)%4])
        else:
            return

def main():
    h, w, k = map(int, input().split())
    x1, y1, x2, y2 = map(int, input().split())
    pond = [[1]*(w+2) for _ in range(h+2)]
    for i in range(1, h+1):
        s = input()
        for j in range(w):
            if s[j] == ".":
                pond[i][j+1] = 0
    hq = []
    row = [[[float("inf")]*4 for j in range(w+2)] for i in range(h+2)]
    for i in range(4):
        row[x1][y1][i] = 0
        heapq.heappush(hq, [0, x1, y1, k, i])
    while len(hq) > 0:
        cost, x, y, pt, vec = heapq.heappop(hq)
        if cost > row[x][y][vec]:
            continue
        if pt == k:
            update(x, y, k, cost, pt, vec, pond, row, hq)
    ans = min(row[x2][y2])
    if ans == float("inf"):
        print(-1)
    else:
        print(ans)

if __name__ == "__main__":
    main()

Submission status: Time Limit Exceeded

Solution code:
import heapq

def update(x, y, k, cost, pt, vec, pond, row, hq):
    for i in range(1, k+1):
        nx, ny = x, y
        nc = cost+1
        if vec == 0:
            nx -= i
        elif vec == 1:
            ny += i
        elif vec == 2:
            nx += i
        else:
            ny -= i
        if pond[nx][ny] == 1:
            return
        if row[nx][ny][vec] > nc:
            row[nx][ny][vec] = nc
            heapq.heappush(hq, [nc, nx, ny, i, vec])
            for j in range(1, 4):
                if row[nx][ny][(vec+j)%4] > nc:
                    row[nx][ny][(vec+j)%4] = nc
                    heapq.heappush(hq, [nc, nx, ny, k, (vec+j)%4])

def main():
    h, w, k = map(int, input().split())
    x1, y1, x2, y2 = map(int, input().split())
    pond = [[1]*(w+2) for _ in range(h+2)]
    for i in range(1, h+1):
        s = input()
        for j in range(w):
            if s[j] == ".":
                pond[i][j+1] = 0
    hq = []
    row = [[[float("inf")]*4 for j in range(w+2)] for i in range(h+2)]
    for i in range(4):
        row[x1][y1][i] = 0
        heapq.heappush(hq, [0, x1, y1, k, i])
    while len(hq) > 0:
        cost, x, y, pt, vec = heapq.heappop(hq)
        if cost > row[x][y][vec]:
            continue
        if pt == k:
            update(x, y, k, cost, pt, vec, pond, row, hq)
    ans = min(row[x2][y2])
    if ans == float("inf"):
        print(-1)
    else:
        print(ans)

if __name__ == "__main__":
    main()

Submission status: Time Limit Exceeded

Solution code:
import heapq
from numba import jit

@jit
def update(x, y, k, cost, pt, vec, pond, row, hq):
    for i in range(1, k+1):
        nx, ny = x, y
        nc = cost+1
        if vec == 0:
            nx -= i
        elif vec == 1:
            ny += i
        elif vec == 2:
            nx += i
        else:
            ny -= i
        if pond[nx][ny] == 1:
            return
        if row[nx][ny][vec] > nc:
            row[nx][ny][vec] = nc
            heapq.heappush(hq, [nc, nx, ny, i, vec])
            for j in range(1, 4):
                if row[nx][ny][(vec+j)%4] > nc:
                    row[nx][ny][(vec+j)%4] = nc
                    heapq.heappush(hq, [nc, nx, ny, k, (vec+j)%4])

def main():
    h, w, k = map(int, input().split())
    x1, y1, x2, y2 = map(int, input().split())
    pond = [[1]*(w+2) for _ in range(h+2)]
    for i in range(1, h+1):
        s = input()
        for j in range(w):
            if s[j] == ".":
                pond[i][j+1] = 0
    hq = []
    row = [[[float("inf")]*4 for j in range(w+2)] for i in range(h+2)]
    for i in range(4):
        row[x1][y1][i] = 0
        heapq.heappush(hq, [0, x1, y1, k, i])
    while len(hq) > 0:
        cost, x, y, pt, vec = heapq.heappop(hq)
        if cost > row[x][y][vec]:
            continue
        if pt == k:
            update(x, y, k, cost, pt, vec, pond, row, hq)
    ans = min(row[x2][y2])
    if ans == float("inf"):
        print(-1)
    else:
        print(ans)

if __name__ == "__main__":
    main()

Submission status: Time Limit Exceeded

Solution code:
import heapq

def main():
    h, w, k = map(int, input().split())
    x1, y1, x2, y2 = map(int, input().split())
    pond = [[1]*(w+2) for _ in range(h+2)]
    for i in range(1, h+1):
        s = input()
        for j in range(w):
            if s[j] == ".":
                pond[i][j+1] = 0
    hq = []
    row = [[[float("inf")]*4 for j in range(w+2)] for i in range(h+2)]
    for i in range(4):
        row[x1][y1][i] = 0
        heapq.heappush(hq, [0, x1, y1, k, i])
    while len(hq) > 0:
        cost, x, y, pt, vec = heapq.heappop(hq)
        if cost > row[x][y][vec]:
            continue
        if pt == k:
            i = 1
            while True:
                nx, ny = x, y
                nc = cost+((i+k-1)//k)
                if vec == 0:
                    nx -= i
                elif vec == 1:
                    ny += i
                elif vec == 2:
                    nx += i
                else:
                    ny -= i
                if pond[nx][ny] == 1:
                    break
                if row[nx][ny][vec] > nc:
                    row[nx][ny][vec] = nc
                    heapq.heappush(hq, [nc, nx, ny, i, vec])
                    for j in range(1, 4):
                        if row[nx][ny][(vec+j)%4] > nc:
                            row[nx][ny][(vec+j)%4] = nc
                            heapq.heappush(hq, [nc, nx, ny, k, (vec+j)%4])
                i += 1
    ans = min(row[x2][y2])
    if ans == float("inf"):
        print(-1)
    else:
        print(ans)

if __name__ == "__main__":
    main()

Submission status: Time Limit Exceeded

Solution code:
import heapq

def main():
    h, w, k = map(int, input().split())
    x1, y1, x2, y2 = map(int, input().split())
    pond = [[1]*(w+2) for _ in range(h+2)]
    for i in range(1, h+1):
        s = input()
        for j in range(w):
            if s[j] == ".":
                pond[i][j+1] = 0
    hq = []
    row = [[[float("inf")]*4 for j in range(w+2)] for i in range(h+2)]
    for i in range(4):
        row[x1][y1][i] = 0
        heapq.heappush(hq, [0, x1, y1, k, i])
    while len(hq) > 0:
        cost, x, y, pt, vec = heapq.heappop(hq)
        if cost > row[x][y][vec]:
            continue
        if pt == k:
            for i in range(1, k+1):
                nx, ny = x, y
                nc = cost+1
                if vec == 0:
                    nx -= i
                elif vec == 1:
                    ny += i
                elif vec == 2:
                    nx += i
                else:
                    ny -= i
                if pond[nx][ny] == 1:
                    break
                if row[nx][ny][vec] > nc:
                    row[nx][ny][vec] = nc
                    heapq.heappush(hq, [nc, nx, ny, i, vec])
                    for j in range(1, 4):
                        if row[nx][ny][(vec+j)%4] > nc:
                            row[nx][ny][(vec+j)%4] = nc
                            heapq.heappush(hq, [nc, nx, ny, k, (vec+j)%4])
    ans = min(row[x2][y2])
    if ans == float("inf"):
        print(-1)
    else:
        print(ans)

if __name__ == "__main__":
    main()

Submission status: Time Limit Exceeded

Solution code:
import heapq

def main():
    h, w, k = map(int, input().split())
    x1, y1, x2, y2 = map(int, input().split())
    pond = [[1]*(w+2) for _ in range(h+2)]
    for i in range(1, h+1):
        s = input()
        for j in range(w):
            if s[j] == ".":
                pond[i][j+1] = 0
    hq = []
    row = [[[float("inf")]*4 for j in range(w+2)] for i in range(h+2)]
    for i in range(4):
        row[x1][y1][i] = 1
        heapq.heappush(hq, [1, x1, y1, 0, i])
    while len(hq) > 0:
        cost, x, y, pt, vec = heapq.heappop(hq)
        if cost > row[x][y][vec]:
            continue
        if pt == 0 or pt == k:
            for i in range(1, k+1):
                nx, ny = x, y
                nc = cost
                if pt == k:
                    nc += 1
                if vec == 0:
                    nx -= i
                elif vec == 1:
                    ny += i
                elif vec == 2:
                    nx += i
                else:
                    ny -= i
                if pond[nx][ny] == 1:
                    break
                if row[nx][ny][vec] > nc:
                    row[nx][ny][vec] = nc
                    heapq.heappush(hq, [nc, nx, ny, i, vec])
        for i in range(1, 4):
            if row[x][y][(vec+i)%4] > cost+1:
                row[x][y][(vec+i)%4] = cost+1
                heapq.heappush(hq, [cost+1, x, y, 0, (vec+i)%4])
    ans = min(row[x2][y2])
    if ans == float("inf"):
        print(-1)
    else:
        print(ans)

if __name__ == "__main__":
    main()