Problem:


Score : 700 points

Problem Statement

Tonight, in your favourite cinema they are giving the movie Joker and all seats are occupied. In the cinema there are N rows with N seats each, forming an N\times N square. We denote with 1, 2,\dots, N the viewers in the first row (from left to right); with N+1, \dots, 2N the viewers in the second row (from left to right); and so on until the last row, whose viewers are denoted by N^2-N+1,\dots, N^2.

At the end of the movie, the viewers go out of the cinema in a certain order: the i-th viewer leaving her seat is the one denoted by the number P_i. The viewer P_{i+1} waits until viewer P_i has left the cinema before leaving her seat.
To exit from the cinema, a viewer must move from seat to seat until she exits the square of seats (any side of the square is a valid exit). A viewer can move from a seat to one of its 4 adjacent seats (same row or same column).
While leaving the cinema, it might be that a certain viewer x goes through a seat currently occupied by viewer y; in that case viewer y will hate viewer x forever. Each viewer chooses the way that minimizes the number of viewers that will hate her forever.

Compute the number of pairs of viewers (x, y) such that y will hate x forever.

Constraints

2 \le N \le 500

The sequence P_1, P_2, \dots, P_{N^2} is a permutation of \{1, 2, \dots, N^2\}.

Input

The input is given from Standard Input in the format

N
P_1 P_2 \cdots P_{N^2}

Output

If ans is the number of pairs of viewers described in the statement, you should print on Standard Output

ans

Sample Input 1

3
1 3 7 9 5 4 8 6 2

Sample Output 1

1

Before the end of the movie, the viewers are arranged in the cinema as follows:

1 2 3
4 5 6
7 8 9

The first four viewers leaving the cinema (1, 3, 7, 9) can leave the cinema without going through any seat, so they will not be hated by anybody.

Then, viewer 5 must go through one of the seats where viewers 2, 4, 6, 8 are currently seated while leaving the cinema; hence he will be hated by at least one of those viewers.

Finally the remaining viewers can leave the cinema (in the order 4, 8, 6, 2) without going through any occupied seat (actually, they can leave the cinema without going through any seat at all).

Sample Input 2

4
6 7 1 4 13 16 10 9 5 11 12 14 15 2 3 8

Sample Output 2

3

Sample Input 3

6
11 21 35 22 7 36 27 34 8 20 15 13 16 1 24 3 2 17 26 9 18 32 31 23 19 14 4 25 10 29 28 33 12 6 5 30

Sample Output 3

11



Sample input:
3
1 3 7 9 5 4 8 6 2


Sample output:
1

Submission status: Accepted

Solution code:
#!/usr/bin/env python3
# vim: set fileencoding=utf-8

# pylint: disable=unused-import, invalid-name, missing-docstring, bad-continuation


"""Module docstring
"""

import functools
import heapq
import itertools
import logging
import math
import os
import random
import string
import sys
from argparse import ArgumentParser
from collections import defaultdict, deque
from copy import deepcopy
from io import BytesIO, IOBase
from typing import Dict, List, Optional, Set, Tuple

# sys.setrecursionlimit(pow(2, 31) - 1)

UP = 0
DOWN = 1
LEFT = 2
RIGHT = 3


def solve(values: List[int], nb: int) -> int:
    # min nb of neighbours from here to exit
    grid = [[min(i, nb - i - 1, j, nb - j - 1) for j in range(nb)] for i in range(nb)]
    answer = 0
    still_inside = [[True] * nb for _ in range(nb)]
    # LOG.debug(("\n".join(map(str, grid))))
    for v in values:
        i, j = divmod(v - 1, nb)
        answer += grid[i][j]
        # LOG.debug((i, j, grid[i][j]))
        still_inside[i][j] = False
        dfs(nb, grid, i, j, still_inside)
        # LOG.debug(("\n".join(map(str, grid))))
    return answer


def dfs(
    nb: int,
    grid: List[List[int]],
    removed_i: int,
    removed_j: int,
    still_inside: List[List[bool]],
):
    q = deque([(removed_i, removed_j, grid[removed_i][removed_j])])
    while q:
        i, j, cur_cost = q.pop()
        if i > 0 and grid[i - 1][j] > cur_cost:
            grid[i - 1][j] = cur_cost
            q.append((i - 1, j, cur_cost + still_inside[i - 1][j]))
        if j > 0 and grid[i][j - 1] > cur_cost:
            grid[i][j - 1] = cur_cost
            q.append((i, j - 1, cur_cost + still_inside[i][j - 1]))
        if i < nb - 1 and grid[i + 1][j] > cur_cost:
            grid[i + 1][j] = cur_cost
            q.append((i + 1, j, cur_cost + still_inside[i + 1][j]))
        if j < nb - 1 and grid[i][j + 1] > cur_cost:
            grid[i][j + 1] = cur_cost
            q.append((i, j + 1, cur_cost + still_inside[i][j + 1]))


def update_neighbours(nb: int, grid: List[List[int]], i: int, j: int):
    # update neighbours
    if j < nb - 1:
        grid[i][j][RIGHT] = grid[i][j + 1][RIGHT]
    if j > 0:
        grid[i][j][LEFT] = grid[i][j - 1][LEFT]
    if i < nb - 1:
        grid[i][j][UP] = grid[i + 1][j][UP]
    if i > 0:
        grid[i][j][DOWN] = grid[i - 1][j][DOWN]
    for left in range(j):
        grid[i][left][RIGHT] = max(0, grid[i][left][RIGHT])
    for right in range(j + 1, nb):
        grid[i][right][LEFT] = max(0, grid[i][right][LEFT])
    for up in range(i):
        grid[up][j][DOWN] = max(0, grid[up][j][DOWN])
    for down in range(i + 1, nb):
        grid[down][j][UP] = max(0, grid[down][j][UP])


def do_job(stdin, stdout):
    "Do the work"
    LOG.debug("Start working")
    # first line is number of test cases
    N = int(stdin.readline().strip())
    values = list(map(int, stdin.readline().split()))
    # values = []
    # for _ in range(N):
    #     values.append(stdin.readline().split())
    result = solve(values, N)
    print(result, file=stdout)


def print_output(testcase: int, result, stdout) -> None:
    "Formats and print result"
    if result is None:
        result = "IMPOSSIBLE"
    print("Case #{}: {}".format(testcase + 1, result), file=stdout)
    # 6 digits float precision {:.6f} (6 is the default value)
    # print("Case #{}: {:f}".format(testcase + 1, result), file=stdout)


BUFSIZE = 8192


class FastIO(IOBase):
    # pylint: disable=super-init-not-called, expression-not-assigned
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)


class IOWrapper(IOBase):
    # pylint: disable=super-init-not-called
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")


def configure_log() -> None:
    "Configure the log output"
    log_formatter = logging.Formatter("L%(lineno)d - " "%(message)s")
    handler = logging.StreamHandler(IOWrapper(sys.stderr))
    handler.setFormatter(log_formatter)
    LOG.addHandler(handler)


LOG = None
# for interactive call: do not add multiple times the handler
if not LOG:
    LOG = logging.getLogger("template")
    configure_log()


def main(argv=None):
    "Program wrapper."
    if argv is None:
        argv = sys.argv[1:]
    parser = ArgumentParser()
    parser.add_argument(
        "-v",
        "--verbose",
        dest="verbose",
        action="store_true",
        default=False,
        help="run as verbose mode",
    )
    args = parser.parse_args(argv)
    if args.verbose:
        LOG.setLevel(logging.DEBUG)
    stdin = IOWrapper(sys.stdin)
    stdout = IOWrapper(sys.stdout)
    do_job(stdin, stdout)
    stdout.flush()
    for h in LOG.handlers:
        h.flush()
    return 0


if __name__ == "__main__":
    sys.exit(main())

Submission status: Accepted

Solution code:
n = int(input())
P = list(map(int, input().split()))

dist = [[min(i, j, n - i - 1, n - j - 1) for j in range(n)] for i in range(n)]
is_sit = [[True for _ in range(n)] for _ in range(n)]

ans = 0
for p in P:
    i, j = divmod(p - 1, n)
    is_sit[i][j] = False
    ans += dist[i][j]

    q = [(i, j, dist[i][j])]
    while q:
        i, j, cur_cost = q.pop()

        if i > 0 and dist[i - 1][j] > cur_cost:
            dist[i - 1][j] = cur_cost
            q.append((i - 1, j, cur_cost + is_sit[i - 1][j]))

        if j > 0 and dist[i][j - 1] > cur_cost:
            dist[i][j - 1] = cur_cost
            q.append((i, j - 1, cur_cost + is_sit[i][j - 1]))

        if i < n - 1 and dist[i + 1][j] > cur_cost:
            dist[i + 1][j] = cur_cost
            q.append((i + 1, j, cur_cost + is_sit[i + 1][j]))

        if j < n - 1 and dist[i][j + 1] > cur_cost:
            dist[i][j + 1] = cur_cost
            q.append((i, j + 1, cur_cost + is_sit[i][j + 1]))

print(ans)

Submission status: Accepted

Solution code:
import sys
import numpy as np
from numba import njit
 
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines


@njit("i4(i4,i4[:])", cache=True)
def proc(N, P):
    ans = 0
    Removed = np.zeros((500, 500), dtype=np.int8)
    Mat = np.zeros((500, 500), dtype=np.int16)
    Dy, Dx = np.array([1,0,-1,0]), np.array([0,1,0,-1])

    for y in range(N):
        for x in range(N):
            Mat[y, x] = min(y, N-1-y, x, N-1-x)
    #print(Mat)
    Buf = [(0, 0) for _ in range(1<<17)]
    Buf_idx = 0
    for i in range(N*N):
        p = P[i]
        y, x = divmod(p, N)
        ans += Mat[y,x]
        Removed[y,x] = 1
        Buf[Buf_idx] = (y, x)
        Buf_idx += 1
        while Buf_idx:
            Buf_idx -= 1
            vy, vx = Buf[Buf_idx]
            vr = Removed[vy,vx]
            val = Mat[vy,vx]
            #for dy, dx in zip(Dy, Dx):
            for j in range(4):
                uy, ux = vy + Dy[j], vx + Dx[j]
                if not (0<=uy<N and 0<=ux<N):
                    continue
                ur = Removed[uy,ux]
                if vr:
                    if Mat[uy,ux] >= val+1:
                        Mat[uy,ux] = val
                        Buf[Buf_idx] = (uy, ux)
                        Buf_idx += 1
                else:
                    if Mat[uy,ux] >= val+2:
                        Mat[uy,ux] = val+1
                        Buf[Buf_idx] = (uy, ux)
                        Buf_idx += 1
    return ans

N = int(readline())
P = np.array(read().split(), np.int32)-1
 
print(proc(N, P))

Submission status: Accepted

Solution code:
import numba
import numpy as np
N = int(input())
P = np.array([int(c)-1 for c in input().split()])

#from random import shuffle
#N = 500
#P = list(range(N*N))
#shuffle(P)
#P = np.array(P)

@numba.njit("i8(i8,i8[:])", cache=True)
def proc(N, P):
    ans = 0
    Removed = np.zeros((500, 500), dtype=np.int8)
    Mat = np.zeros((500, 500), dtype=np.int16)
    Dy, Dx = np.array([1,0,-1,0]), np.array([0,1,0,-1])

    for y in range(N):
        for x in range(N):
            Mat[y, x] = min(y, N-1-y, x, N-1-x)
    #print(Mat)
    Buf = [(0, 0) for _ in range(1<<17)]
    Buf_idx = 0
    for i in range(N*N):
        p = P[i]
        y, x = divmod(p, N)
        ans += Mat[y,x]
        Removed[y,x] = 1
        Buf[Buf_idx] = (y, x)
        Buf_idx += 1
        while Buf_idx:
            Buf_idx -= 1
            vy, vx = Buf[Buf_idx]
            vr = Removed[vy,vx]
            val = Mat[vy,vx]
            #for dy, dx in zip(Dy, Dx):
            for j in range(4):
                uy, ux = vy + Dy[j], vx + Dx[j]
                if not (0<=uy<N and 0<=ux<N):
                    continue
                ur = Removed[uy,ux]
                if vr:
                    if Mat[uy,ux] >= val+1:
                        Mat[uy,ux] = val
                        Buf[Buf_idx] = (uy, ux)
                        Buf_idx += 1
                else:
                    if Mat[uy,ux] >= val+2:
                        Mat[uy,ux] = val+1
                        Buf[Buf_idx] = (uy, ux)
                        Buf_idx += 1
    # for m in Mat:
    #     print(m)
    return ans
print(proc(N, P))

Submission status: Accepted

Solution code:
import numba
import numpy as np
N = int(input())
P = np.array([int(c)-1 for c in input().split()])

#from random import shuffle
#N = 500
#P = list(range(N*N))
#shuffle(P)
#P = np.array(P)

@numba.njit("i8(i8,i8[:])", cache=True)
def proc(N, P):
    ans = 0
    Removed = np.zeros((500, 500), dtype=np.int8)
    Mat = np.zeros((500, 500), dtype=np.int16)
    Dy, Dx = [1,0,-1,0], [0,1,0,-1]

    for y in range(N):
        for x in range(N):
            Mat[y, x] = min(y, N-1-y, x, N-1-x)
    #print(Mat)
    Buf = [(0, 0) for _ in range(1<<17)]
    Buf_idx = 0
    for i in range(N*N):
        p = P[i]
        y, x = divmod(p, N)
        ans += Mat[y,x]
        Removed[y,x] = 1
        Buf[Buf_idx] = (y, x)
        Buf_idx += 1
        while Buf_idx:
            Buf_idx -= 1
            vy, vx = Buf[Buf_idx]
            vr = Removed[vy,vx]
            val = Mat[vy,vx]
            #for dy, dx in zip(Dy, Dx):
            for j in range(4):
                uy, ux = vy + Dy[j], vx + Dx[j]
                if not (0<=uy<N and 0<=ux<N):
                    continue
                ur = Removed[uy,ux]
                if vr:
                    if Mat[uy,ux] >= val+1:
                        Mat[uy,ux] = val
                        Buf[Buf_idx] = (uy, ux)
                        Buf_idx += 1
                else:
                    if Mat[uy,ux] >= val+2:
                        Mat[uy,ux] = val+1
                        Buf[Buf_idx] = (uy, ux)
                        Buf_idx += 1
    # for m in Mat:
    #     print(m)
    return ans
print(proc(N, P))

Submission status: Accepted

Solution code:
import numba
import numpy as np
N = int(input())
P = np.array([int(c)-1 for c in input().split()])

#from random import shuffle
#N = 500
#P = list(range(N*N))
#shuffle(P)
#P = np.array(P)

@numba.njit("i8(i8,i8[:])")
def proc(N, P):
    ans = 0
    Removed = np.zeros((500, 500), dtype=np.int8)
    Mat = np.zeros((500, 500), dtype=np.int16)
    Dy, Dx = [1,0,-1,0], [0,1,0,-1]

    for y in range(N):
        for x in range(N):
            Mat[y, x] = min(y, N-1-y, x, N-1-x)
    #print(Mat)
    Buf = [(0, 0) for _ in range(1<<17)]
    Buf_idx = 0
    for i in range(N*N):
        p = P[i]
        y, x = divmod(p, N)
        ans += Mat[y,x]
        Removed[y,x] = 1
        Buf[Buf_idx] = (y, x)
        Buf_idx += 1
        while Buf_idx:
            Buf_idx -= 1
            vy, vx = Buf[Buf_idx]
            vr = Removed[vy,vx]
            val = Mat[vy,vx]
            #for dy, dx in zip(Dy, Dx):
            for j in range(4):
                uy, ux = vy + Dy[j], vx + Dx[j]
                if not (0<=uy<N and 0<=ux<N):
                    continue
                ur = Removed[uy,ux]
                if vr:
                    if Mat[uy,ux] >= val+1:
                        Mat[uy,ux] = val
                        Buf[Buf_idx] = (uy, ux)
                        Buf_idx += 1
                else:
                    if Mat[uy,ux] >= val+2:
                        Mat[uy,ux] = val+1
                        Buf[Buf_idx] = (uy, ux)
                        Buf_idx += 1
    # for m in Mat:
    #     print(m)
    return ans
print(proc(N, P))

Submission status: Accepted

Solution code:
import numba
import numpy as np
N = int(input())
P = np.array([int(c)-1 for c in input().split()])

#from random import shuffle
#N = 500
#P = list(range(N*N))
#shuffle(P)
#P = np.array(P)

@numba.njit("i8(i8,i8[:])")
def proc(N, P):
    ans = 0
    Removed = np.zeros((500, 500), dtype=np.int8)
    Mat = np.zeros((500, 500), dtype=np.int16)
    Dy, Dx = [1,0,-1,0], [0,1,0,-1]

    for y in range(N):
        for x in range(N):
            Mat[y, x] = min(y, N-1-y, x, N-1-x)
    #print(Mat)
    for i in range(N*N):
        p = P[i]
        y, x = divmod(p, N)
        ans += Mat[y,x]
        Removed[y,x] = 1
        st = [(y, x)]
        while st:
            vy, vx = st.pop()
            vr = Removed[vy,vx]
            val = Mat[vy,vx]
            #for dy, dx in zip(Dy, Dx):
            for j in range(4):
                uy, ux = vy + Dy[j], vx + Dx[j]
                if not (0<=uy<N and 0<=ux<N):
                    continue
                ur = Removed[uy,ux]
                if vr:
                    if Mat[uy,ux] >= val+1:
                        Mat[uy,ux] = val
                        st.append((uy, ux))
                else:
                    if Mat[uy,ux] >= val+2:
                        Mat[uy,ux] = val+1
                        st.append((uy, ux))
    # for m in Mat:
    #     print(m)
    return ans
print(proc(N, P))

Submission status: Accepted

Solution code:
import numba
import numpy as np
N = int(input())
P = np.array([int(c)-1 for c in input().split()])

#from random import shuffle
#N = 500
#P = list(range(N*N))
#shuffle(P)
#P = np.array(P)

@numba.njit("void(i8,i8[:])")
def proc(N, P):
    ans = 0
    Removed = np.zeros((500, 500), dtype=np.int8)
    Mat = np.zeros((500, 500), dtype=np.int16)
    Dy, Dx = [1,0,-1,0], [0,1,0,-1]

    for y in range(N):
        for x in range(N):
            Mat[y, x] = min(y, N-1-y, x, N-1-x)
    #print(Mat)
    for i in range(N*N):
        p = P[i]
        y, x = divmod(p, N)
        ans += Mat[y,x]
        Removed[y,x] = 1
        st = [(y, x)]
        while st:
            vy, vx = st.pop()
            vr = Removed[vy,vx]
            val = Mat[vy,vx]
            #for dy, dx in zip(Dy, Dx):
            for j in range(4):
                uy, ux = vy + Dy[j], vx + Dx[j]
                if not (0<=uy<N and 0<=ux<N):
                    continue
                ur = Removed[uy,ux]
                if vr:
                    if Mat[uy,ux] >= val+1:
                        Mat[uy,ux] = val
                        st.append((uy, ux))
                else:
                    if Mat[uy,ux] >= val+2:
                        Mat[uy,ux] = val+1
                        st.append((uy, ux))
    # for m in Mat:
    #     print(m)
    print(ans)
proc(N, P)

Submission status: Accepted

Solution code:
import numba
import numpy as np
N = int(input())
P = np.array([int(c)-1 for c in input().split()])

#from random import shuffle
#N = 500
#P = list(range(N*N))
#shuffle(P)
#P = np.array(P)

@numba.njit("void(i8,i8[:])")
def proc(N, P):
    ans = 0
    Removed = np.zeros((500, 500), dtype=np.int8)
    Mat = np.zeros((500, 500), dtype=np.int16)
    Dy, Dx = [1,0,-1,0], [0,1,0,-1]

    for y in range(N):
        for x in range(N):
            Mat[y, x] = min(y, N-1-y, x, N-1-x)
    #print(Mat)
    for i in range(N*N):
        p = P[i]
        y, x = divmod(p, N)
        ans += Mat[y,x]
        Removed[y,x] = 1
        st = [(y, x)]
        while st:
            vy, vx = st.pop()
            vr = Removed[vy,vx]
            val = Mat[vy,vx]
            #for dy, dx in zip(Dy, Dx):
            for j in range(4):
                dy,dx = Dy[j],Dx[j]
                uy = vy + dy
                ux = vx + dx
                if not (0<=uy<N and 0<=ux<N):
                    continue
                ur = Removed[uy,ux]
                if vr:
                    if Mat[uy,ux] >= val+1:
                        Mat[uy,ux] = val
                        st.append((uy, ux))
                else:
                    if Mat[uy,ux] >= val+2:
                        Mat[uy,ux] = val+1
                        st.append((uy, ux))
    # for m in Mat:
    #     print(m)
    print(ans)
proc(N, P)

Submission status: Accepted

Solution code:
#!/usr/bin/env python3

import sys
import math
from bisect import bisect_right as br
from bisect import bisect_left as bl
sys.setrecursionlimit(2147483647)
from heapq import heappush, heappop,heappushpop
from collections import defaultdict
from itertools import accumulate
from collections import Counter
from collections import deque
from operator import itemgetter
from itertools import permutations
mod = 10**9 + 7
inf = float('inf')
def I(): return int(sys.stdin.readline())
def LI(): return list(map(int,sys.stdin.readline().split()))

n = I()
p = LI()
p = [((i-1)%n, (i-1)//n) for i in p]
ans = 0
dp = [[min(i, j, n - (i + 1), n - (j + 1)) for j in range(n)] for i in range(n)]
dp2 = [[False]*n for _ in range(n)]
for (q, r) in p:
    ans += dp[r][q]
    dp2[r][q] = True
    h = [(dp[r][q], r, q)]
    while h:
        d, y, x = h.pop()
        if not dp2[y][x]:
            d += 1
        if x != 0:
            if dp[y][x-1] > d:
                dp[y][x-1] = d
                h.append((d, y, x-1))
        if x != n-1:
            if dp[y][x+1] > d:
                dp[y][x+1] = d
                h.append((d, y, x+1))
        if y != 0:
            if dp[y-1][x] > d:
                dp[y-1][x] = d
                h.append((d, y-1, x))
        if y != n-1:
            if dp[y+1][x] > d:
                dp[y+1][x] = d
                h.append((d, y+1, x))
print(ans)

Submission status: Accepted

Solution code:
import numba
import numpy as np
N = int(input())
P = np.array([int(c)-1 for c in input().split()])

#from random import shuffle
#N = 500
#P = list(range(N*N))
#shuffle(P)
#P = np.array(P)

@numba.njit("void(i8,i8[:])")
def proc(N, P):
    ans = 0
    Removed = np.zeros((500, 500), dtype=np.int8)
    Mat = np.zeros((500, 500), dtype=np.int16)
    Dy, Dx = [1,0,-1,0], [0,1,0,-1]

    for y in range(N):
        for x in range(N):
            Mat[y, x] = min(y, N-1-y, x, N-1-x)
    #print(Mat)
    for i in range(N*N):
        p = P[i]
        y, x = divmod(p, N)
        ans += Mat[y,x]
        Removed[y,x] = 1
        st = [(y, x)]
        while st:
            vy, vx = st.pop()
            vr = Removed[vy,vx]
            val = Mat[vy,vx]
            #for dy, dx in zip(Dy, Dx):
            for j in range(4):
                dy = Dy[j]
                dx = Dx[j]
                uy = vy + dy
                ux = vx + dx
                if not (0<=uy<N and 0<=ux<N):
                    continue
                ur = Removed[uy,ux]
                if vr:
                    if Mat[uy,ux] >= val+1:
                        Mat[uy,ux] = val
                        st.append((uy, ux))
                else:
                    if Mat[uy,ux] >= val+2:
                        Mat[uy,ux] = val+1
                        st.append((uy, ux))
    # for m in Mat:
    #     print(m)
    print(ans)
proc(N, P)

Submission status: Accepted

Solution code:
#!/usr/bin/env python3
import sys
input = sys.stdin.readline
def INT(): return int(input())
def MAP(): return map(int,input().split())
def LI(): return list(map(int,input().split()))

def main():
    n = INT()
    P = LI()
    cost = [[min(i, n-i-1, j, n-j-1) for j in range(n)] for i in range(n)]
    issit = [[True for _ in range(n)] for _ in range(n)]
    ans = 0

    for p in P:
        i,j = divmod(p-1,n)
        issit[i][j] = False
        ans += cost[i][j]

        q = [(i, j, cost[i][j])]
        while q:
            n_i, n_j, cur_cost = q.pop()

            if n_i > 0 and cost[n_i-1][n_j] > cur_cost:
                cost[n_i-1][n_j] = cur_cost
                q.append((n_i-1,n_j,cur_cost+issit[n_i-1][n_j]))

            if n_i < n-1 and cost[n_i+1][n_j] > cur_cost:
                cost[n_i+1][n_j] = cur_cost
                q.append((n_i+1,n_j,cur_cost+issit[n_i+1][n_j]))

            if n_j > 0 and cost[n_i][n_j-1] > cur_cost:
                cost[n_i][n_j-1] = cur_cost
                q.append((n_i,n_j-1,cur_cost+issit[n_i][n_j-1]))
 
            if n_j < n-1 and cost[n_i][n_j+1] > cur_cost:
                cost[n_i][n_j+1] = cur_cost
                q.append((n_i,n_j+1,cur_cost+issit[n_i][n_j+1]))
    print(ans)

if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
import os

import itertools
import sys

if os.getenv("LOCAL"):
    sys.stdin = open("_in.txt", "r")

sys.setrecursionlimit(10 ** 9)
INF = float("inf")
IINF = 10 ** 18
MOD = 10 ** 9 + 7


# MOD = 998244353


def test():
    ans_hist = [INF] * (N ** 2)

    ans = 0
    dist = [INF] * (N ** 2)
    for i, p in enumerate(P):
        p -= 1
        ph, pw = p // N, p % N
        d = min(ph, pw, N - ph - 1, N - pw - 1)

        j = i - 1
        while j >= 0:
            q = P[j] - 1
            qh, qw = q // N, q % N
            d = min(d, dist[q] + abs(ph - qh) + abs(pw - qw) - 1)
            j -= 1

        dist[p] = d
        ans_hist[p] = d

        j = i - 1
        while j >= 0:
            q = P[j] - 1
            qh, qw = q // N, q % N
            dist[q] = min(dist[q], dist[p] + abs(ph - qh) + abs(pw - qw) - 1)
            j -= 1

        ans += d
        # print(p, dist)
    print(ans)
    # print(dist)
    # print(np.array(ans_hist, dtype=int).reshape(N, N))
    return ans


N = int(sys.stdin.buffer.readline())
P = list(map(int, sys.stdin.buffer.readline().split()))

# 解説
dist = [INF] * len(P)
for h, w in itertools.product(range(N), range(N)):
    dist[h * N + w] = min(h, w, N - h - 1, N - w - 1)
present = [1] * len(P)

ans = 0
for p in P:
    p -= 1
    h, w = p // N, p % N
    present[p] = 0

    ans += dist[p]
    stack = [(p, dist[p])]
    while stack:
        p, d = stack.pop()
        h, w = p // N, p % N
        d += present[p]
        for dh, dw in ((0, 1), (1, 0), (0, -1), (-1, 0)):
            if 0 <= h + dh < N and 0 <= w + dw < N:
                q = (h + dh) * N + w + dw
                if d < dist[q]:
                    dist[q] = d
                    stack.append((q, d))
print(ans)
# test()

Submission status: Accepted

Solution code:
import sys
from collections import deque

readline = sys.stdin.readline
ni = lambda: int(readline().rstrip())
nl = lambda: list(map(int, readline().split()))

def solve():
    n = ni()
    p = nl()
    diag = [-1, 1, n, -n]
    st = [1]*(n+2)**2
    gr = [0]*(n+2)**2
    ans = 0
    for i in range(n):
        for j in range(n):
            gr[i*n + j + n + 1] = min(min(i, j), n-1-max(i, j))
    for v in p:
        v += n
        ans += gr[v]
        st[v] = 0
        c = gr[v]
        for dv in diag:
            nv = v + dv
            c = min(c, gr[nv] + st[nv])
        gr[v]= c
        q = deque()
        q.append(v)
        while q:
            v = q.popleft()
            for dv in diag:
                nv = v + dv
                if gr[nv] > gr[v] + st[v]:
                    gr[nv] = gr[v] + st[v]
                    if st[v]:
                        q.append(nv)
                    else:
                        q.appendleft(nv)
    print(ans)
    return

if __name__ == '__main__':
    solve()

Submission status: Accepted

Solution code:
import sys
import numpy as np
from numba import njit

read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

@njit('(i4,i4[::1])', cache=True)
def solve(N, P):
    W = N + 2
    dp = np.zeros((W, W), np.int32)
    for _ in range(4):
        dp = dp.T[::-1]
        for n in range(1, (N + 1) // 2 + 1):
            dp[n, n:-n] = n
    filled = np.zeros_like(dp)
    filled[1:-1, 1:-1] = 1
    dp = dp.ravel()
    filled = filled.ravel()
    stack = np.empty_like(dp)
    ans = 0
    for n in P:
        n -= 1
        h, w = divmod(n, N)
        v = (h + 1) * W + (w + 1)
        ans += dp[v] - 1
        filled[v] = 0
        k = min(dp[v - 1], dp[v + 1], dp[v - W], dp[v + W])
        if dp[v] == k:
            return ans
        p = 0
        stack[0] = v
        dp[v] = k
        while p >= 0:
            v = stack[p]
            p -= 1
            for dx in (-1, 1, -W, W):
                w = v + dx
                k = dp[v] + filled[w]
                if dp[w] > k:
                    dp[w] = k
                    p += 1
                    stack[p] = w
    return ans

N = int(readline())
P = np.array(read().split(), np.int32)

print(solve(N, P))

Submission status: Runtime Error

Solution code:
n=int(input())
*p,=map(int, input().split())
#n=3
#p=[1, 3, 7, 9, 5, 4, 8, 6, 2]

for i in range(n*n):p[i]-=1
seats=[
    [min(i,j,n-i-1,n-j-1)for i in range(n)] 
    for j in range(n)
    ]

check=[[False]*n for _ in range(n)]
exist=[[1]*n for _ in range(n)]
dxy=[(0,1),(1,0),(-1,0),(0,-1)]
def dfs(pi):
    global check,exist
    i=pi%n
    j=pi//n
    res=seats[i][j]
    check[i][j]=True
    for dx,dy in dxy:
        idx,jdy=i+dx,j+dy
        if 0<=idx<n and 0<=jdy<n and (not check[idx][jdy]):
            res=min(res,dfs(idx+jdy*n)+exist[idx][jdy])
        if res==0:
            return res
    seats[i][j]=res
    return res
ans=0
for pi in p:
    check=[[False]*n for _ in range(n)]
    ans+=dfs(pi)
    exist[pi%n][pi//n]=0
print(ans)

Submission status: Runtime Error

Solution code:
def dfs(c,v,sheet,space,n):
  x,y=divmod(v,n)
  for dx,dy in ((0,1),(0,-1),(1,0),(-1,0)):
    if 0<=x+dx<n and 0<=y+dy<n:
      nv=(x+dx)+(y+dy)*n
      if sheet[nv]>c:
        sheet[nv]=c
        dfs(c+space[nv],nv,sheet,space,n)

def main(n,p):
  sheet=[min(i%n,i//n,n-i%n-1,n-i//n-1) for i in range(n**2)]
  space=[1]*(n**2)
  #for i in range(n):
  #  print(sheet[i*n:(i+1)*n])
  ans=0
  for x in p:
    x-=1
    ans+=sheet[x]
    space[x]=0
    dfs(sheet[x],x,sheet,space,n)
  print(ans)

n=int(input())
p=list(map(int,input().split()))
main(n,p)

Submission status: Runtime Error

Solution code:
import sys
import numpy as np

if sys.argv[-1] == 'ONLINE_JUDGE':
    from numba.pycc import CC
    cc = CC('my_module')

    @cc.export('dfs', '(i4, i4, i4, i4[:,:], i4[:,:])')
    def dfs(N, h, w, minDist, isFilled):
        dist = minDist[h][w] + isFilled[h][w]

        if h + 1 < N and minDist[h + 1][w] > dist:
            minDist[h + 1][w] = dist
            dfs(N, h + 1, w, minDist, isFilled)
        if h - 1 >= 0 and minDist[h - 1][w] > dist:
            minDist[h - 1][w] = dist
            dfs(N, h - 1, w, minDist, isFilled)
        if w + 1 < N and minDist[h][w + 1] > dist:
            minDist[h][w + 1] = dist
            dfs(N, h, w + 1, minDist, isFilled)
        if w - 1 < N and minDist[h][w - 1] > dist:
            minDist[h][w - 1] = dist
            dfs(N, h, w - 1, minDist, isFilled)

    @cc.export('solve', 'i4(i4, i4[:])')
    def solve(N, P):
        minDist = np.ones((N, N), dtype=np.int32)
        isFilled = np.ones((N, N), dtype=np.int32)

        for h in range(N):
            for w in range(N):
                minDist[h][w] = min(h, N - h - 1, w, N - w - 1)

        ans = 0
        for p in P:
            h, w = divmod(p, N)
            ans += minDist[h][w]
            isFilled[h][w] = False
            dfs(N, h, w, minDist, isFilled)
        return ans

    cc.compile()
    exit(0)

from my_module import solve, dfs
N = int(input())
P = np.asarray(list(map(lambda a: int(a) - 1, input().split())), dtype=np.int32)

print(solve(N, P))