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:
import sys


def main():
    N = int(input())
    P = tuple(map(int, input().split()))

    Kcost = [min(row, N - 1 - row, clm, N - 1 - clm) for row in range(N) for clm in range(N)]

    Sitting = [1] * (N * N)
    Kcount = 0


    def Kcheck(qsn, cdsn):
        if Kcost[cdsn] > Kcost[qsn] + Sitting[qsn]:
            Kcost[cdsn] = Kcost[qsn] + Sitting[qsn]
            queue.append(cdsn)


    for sn in P:
        csn = sn - 1
        Kcount += Kcost[csn]
        Sitting[csn] = 0
        queue = [csn]

        while queue:
            qsn = queue.pop()
            div, mod = divmod(qsn, N)
            if mod: Kcheck(qsn, qsn - 1)
            if mod != N - 1: Kcheck(qsn, qsn + 1)
            if div: Kcheck(qsn, qsn - N)
            if div != N - 1: Kcheck(qsn, qsn + N)

    print(Kcount)

if __name__ == '__main__':
    main()

sys.exit()

Submission status: Accepted

Solution code:
import sys


def main():
    N = int(input())
    P = map(int, input().split())

    Kcost = [min(row, N - 1 - row, clm, N - 1 - clm) for row in range(N) for clm in range(N)]

    Sitting = [1] * (N * N)
    Kcount = 0


    def Kcheck(qsn, cdsn):
        if Kcost[cdsn] > Kcost[qsn] + Sitting[qsn]:
            Kcost[cdsn] = Kcost[qsn] + Sitting[qsn]
            queue.append(cdsn)


    for sn in P:
        csn = sn - 1
        Kcount += Kcost[csn]
        Sitting[csn] = 0
        queue = [csn]

        while queue:
            qsn = queue.pop()
            div, mod = divmod(qsn, N)
            if mod: Kcheck(qsn, qsn - 1)
            if mod != N - 1: Kcheck(qsn, qsn + 1)
            if div: Kcheck(qsn, qsn - N)
            if div != N - 1: Kcheck(qsn, qsn + N)

    print(Kcount)

if __name__ == '__main__':
    main()

sys.exit()

Submission status: Accepted

Solution code:
def main():
    N = int(input())
    P = map(int, input().split())

    Kcost = [min(row, N - 1 - row, clm, N - 1 - clm) for row in range(N) for clm in range(N)]

    Sitting = [1] * (N * N)
    Kcount = 0


    def Kcheck(qsn, cdsn):
        if Kcost[cdsn] > Kcost[qsn] + Sitting[qsn]:
            Kcost[cdsn] = Kcost[qsn] + Sitting[qsn]
            queue.append(cdsn)


    for sn in P:
        csn = sn - 1
        Kcount += Kcost[csn]
        Sitting[csn] = 0
        queue = [csn]

        while queue:
            qsn = queue.pop()
            div, mod = divmod(qsn, N)
            if mod: Kcheck(qsn, qsn - 1)
            if mod != N - 1: Kcheck(qsn, qsn + 1)
            if div: Kcheck(qsn, qsn - N)
            if div != N - 1: Kcheck(qsn, qsn + N)

    print(Kcount)

if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
from collections import deque
n = int(input())
Ps = list(map(lambda x: int(x)-1, input().split()))
cost = [min(i, n-1-i, j, n-1-j) for i in range(n) for j in range(n)]
exist = [1]*(n**2)


def to_idx(p):
    return divmod(p, n)


def to_v(i, j):
    return i*n+j


def bfs(init_v):
    next_v = deque([init_v])
    exist[init_v] = 0
    while next_v:
        v = next_v.popleft()
        i, j = to_idx(v)
        if 0 < i:
            v2 = v-n
            if cost[v2] > cost[v]+exist[v]:
                cost[v2] = cost[v]+exist[v]
                next_v.append(v2)

        if i < n-1:
            v2 = v+n
            if cost[v2] > cost[v]+exist[v]:
                cost[v2] = cost[v]+exist[v]
                next_v.append(v2)

        if 0 < j:
            v2 = v-1
            if cost[v2] > cost[v]+exist[v]:
                cost[v2] = cost[v]+exist[v]
                next_v.append(v2)

        if j < n-1:
            v2 = v+1
            if cost[v2] > cost[v]+exist[v]:
                cost[v2] = cost[v]+exist[v]
                next_v.append(v2)

ans = 0
for p in Ps:
    ans += cost[p]
    bfs(p)
print(ans)

Submission status: Accepted

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

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

distance = [[min(i, j, n - i - 1, n - j - 1) for i in range(n)] for j in range(n)]
check = [[1] * n for i in range(n)]
p = [((i - 1) // n, (i - 1) % n) for i in p]

def move(x,y,nx,ny):
    if distance[nx][ny] > distance[x][y] + check[x][y]:
        distance[nx][ny] = distance[x][y] + check[x][y]
        d.append((nx,ny))

ans = 0
for i, j in p:
    ans += distance[j][i]
    d=[]
    d.append((j,i))
    check[j][i] = 0
    while len(d):
        x, y = d.pop()
        if x!=0:
            move(x,y,x-1,y)
        if x!=n-1:
            move(x,y,x+1,y)
        if y!=0:
            move(x,y,x,y-1)
        if y!=n-1:
            move(x,y,x,y+1)

print(ans)

Submission status: Accepted

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

N=int(input())
P=list(map(int,input().split()))

DP=[[0]*N for i in range(N)]
for i in range(N):
    for j in range(N):
        DP[i][j]=min(i,j,N-1-i,N-1-j)

USED=[[1]*N for i in range(N)]
ANS=0

def update(z,w):
    if 0<=z<N and 0<=w<N:
        if DP[z][w]>DP[x][y]+USED[z][w]:
            DP[z][w]=DP[x][y]+USED[z][w]
            Q.append((z,w))
    

for p in P:
    q,r=divmod(p-1,N)
    ANS+=DP[q][r]
    DP[q][r]-=1
    USED[q][r]=0

    Q=[(q,r)]

    while Q:
        x,y=Q.pop()

        update(x+1,y)
        update(x-1,y)
        update(x,y+1)
        update(x,y-1)

print(ANS)

Submission status: Accepted

Solution code:
# coding: utf-8
import sys

# from operator import itemgetter
sysread = sys.stdin.readline
read = sys.stdin.buffer.read
from heapq import heappop, heappush
from collections import defaultdict

sys.setrecursionlimit(10 ** 7)
# import math
# from itertools import product, accumulate, combinations, product
# import bisect# lower_bound etc
import numpy as np
# from copy import deepcopy
#from collections import deque
import numba

N = int(input())
P = np.array(list(map(int, sysread().split())))
#@numba.njit("void(i8,i8[:])")
@numba.njit
def run():
    seats = np.zeros((N,N), dtype=np.int16)
    seen = np.zeros((N,N), dtype=np.int8)  # there is a person : 1
    up, down = 0, N - 1
    dist = 0
    while True:
        seats[up, up:down+1] = dist
        seats[down, up:down+1] = dist
        seats[up:down+1, up] = dist
        seats[up:down+1, down] = dist
        up += 1
        down -= 1
        dist += 1
        if up > down:
            break

    ret = 0
    ###
    for i in range(N ** 2):
        # print(seats)
        cur_i, cur_j = (P[i] - 1) // N, (P[i] - 1) % N
        ret += seats[cur_i,cur_j]
        seen[cur_i,cur_j] = 1
        stack = [(cur_i, cur_j)]
        while stack:
            cur_i, cur_j = stack.pop()
            for i, j in ((1, 0), (0, 1), (-1, 0), (0, -1)):
                n_i = cur_i + i
                n_j = cur_j + j
                del_val = seats[cur_i, cur_j]
                if 0 <= n_i <= N - 1 and 0 <= n_j <= N - 1:
                    if seen[cur_i, cur_j] and del_val < seats[n_i, n_j]:
                        seats[n_i, n_j] = del_val
                        stack.append((n_i, n_j))
                    else:
                        if del_val + 1 < seats[n_i, n_j]:
                            seats[n_i, n_j] = del_val + 1
                            stack.append((n_i, n_j))

    print(ret)


if __name__ == "__main__":
    run()

Submission status: Accepted

Solution code:
# coding: utf-8
import sys

# from operator import itemgetter
sysread = sys.stdin.readline
read = sys.stdin.buffer.read
from heapq import heappop, heappush
from collections import defaultdict

sys.setrecursionlimit(10 ** 7)
# import math
# from itertools import product, accumulate, combinations, product
# import bisect# lower_bound etc
import numpy as np
# from copy import deepcopy
from collections import deque
import numba

N = int(input())
P = np.array(list(map(int, sysread().split())))
#@numba.njit("void(i8,i8[:])")
@numba.njit
def run():
    seats = np.zeros((N,N), dtype=np.int16)
    seen = np.zeros((N,N), dtype=np.int8)  # there is a person : 1
    up, down = 0, N - 1
    dist = 0
    while True:
        seats[up, up:down+1] = dist
        seats[down, up:down+1] = dist
        seats[up:down+1, up] = dist
        seats[up:down+1, down] = dist
        up += 1
        down -= 1
        dist += 1
        if up > down:
            break

    ret = 0
    ###
    for i in range(N ** 2):
        # print(seats)
        cur_i, cur_j = (P[i] - 1) // N, (P[i] - 1) % N
        ret += seats[cur_i,cur_j]
        seen[cur_i,cur_j] = 1
        stack = [(cur_i, cur_j)]
        while stack:
            cur_i, cur_j = stack.pop()
            for i, j in ((1, 0), (0, 1), (-1, 0), (0, -1)):
                n_i = cur_i + i
                n_j = cur_j + j
                del_val = seats[cur_i, cur_j]
                if 0 <= n_i <= N - 1 and 0 <= n_j <= N - 1:
                    if seen[cur_i, cur_j]:
                        if del_val < seats[n_i, n_j]:
                            seats[n_i, n_j] = del_val
                            stack.append((n_i, n_j))
                    else:
                        if del_val + 1 < seats[n_i, n_j]:
                            seats[n_i, n_j] = del_val + 1
                            stack.append((n_i, n_j))

    print(ret)


if __name__ == "__main__":
    run()

Submission status: Accepted

Solution code:
from numba import njit
import numpy as np


def cc_export():
    @njit('(i8, i8, i8[:], i8[:], i8[:], i8)')
    def update(n, w, que, there, cost, pos):
        que[0] = pos
        i, l = 0, 1
        while i < l:
            pos = que[i]
            i += 1
            c = cost[pos]
            t = there[pos]
            k = c + t
            for df in (-w, w, -1, 1):
                pp = pos + df
                if cost[pp] > k:
                    cost[pp] = k
                    que[l] = pp
                    l += 1

    @njit('(i8, i8[:])')
    def main(n, p):
        w = n + 2
        que = np.zeros(4 * w * w, dtype=np.int64)
        there = np.ones(w * w, dtype=np.int64)
        # there = np.array([
        #     1 if 1 <= i and i <= n and 1 <= j and j <= n else 0
        #     for j in range(w) for i in range(w)
        # ],
        #                  dtype=np.int64)
        cost = np.array([
            -1 if i == 0 or i == n + 1 or j == 0 or j == n + 1 else min(
                i - 1, n - i, j - 1, n - j) for j in range(w) for i in range(w)
        ],
                        dtype=np.int64)

        ans = 0
        for pos in p:
            # v = list(map(lambda x: ' ' if x == 0 else '*', list(there)))
            # for i in range(w):
            #     print(' '.join(v[i * w:(i + 1) * w]))
            # print(cost.reshape((w, w)))
            # print("add", cost[pos], "for", divmod(pos, w))
            ans += cost[pos]
            there[pos] = 0
            update(n, w, que, there, cost, pos)
        return ans

    from numba.pycc import CC
    cc = CC('solution')
    cc.export('update', '(i8, i8, i8[:], i8[:], i8[:], i8)')(update)
    cc.export('main', '(i8, i8[:])')(main)
    cc.compile()


if __name__ == '__main__':
    import sys
    if sys.argv[-1] == 'ONLINE_JUDGE':
        cc_export()
        sys.exit(0)

    def transform(t):
        y, x = divmod(int(t) - 1, n)
        return (y + 1) * (n + 2) + (x + 1)

    from solution import update, main
    n = int(input())
    p = np.array(list(map(transform, input().split())), dtype=np.int64)
    print(main(n, p))

Submission status: Accepted

Solution code:
# coding: utf-8
import sys
#from operator import itemgetter
sysread = sys.stdin.readline
read = sys.stdin.buffer.read
#from heapq import heappop, heappush
#from collections import defaultdict
sys.setrecursionlimit(10**7)
#import math
#from itertools import product, accumulate, combinations, product
#import bisect# lower_bound etc
import numpy as np
#from copy import deepcopy
#from collections import deque
import numba

def run():
    N = int(input())
    P = np.array((list(map(int, sysread().split()))))
    P -= 1

    @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)


if __name__ == "__main__":
    run()

Submission status: Accepted

Solution code:
from numba import njit
import numpy as np

@njit
def main(N, P):
    lista = [1, -1, N, -N]
    d = np.zeros((N, N), dtype=np.int32)
    d = d.ravel()
    sit = np.ones_like(d)
    stack = np.empty_like(d)
    count = 0
    for i in range(N*N):
        d[i] = min(i % N, (N-1-i) % N, i//N, N-1-i//N)
    for player in P:
        sit[player-1] = 0
        count += d[player-1]
        stack[0] = player
        num = 0
        while num >= 0:
            p = stack[num]
            num -= 1
            a = d[p-1]+sit[p-1]
            for i in lista:
                if p+i < 1 or p + i > N*N:
                    continue
                if d[p+i-1] > a:
                    d[p+i-1] = a
                    num += 1
                    stack[num] = p+i
    print(count)

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

main(N, P)

Submission status: Accepted

Solution code:
import sys

def input(): return sys.stdin.readline().strip()
def list2d(a, b, c): return [[c] * b for i in range(a)]
def list3d(a, b, c, d): return [[[d] * c for j in range(b)] for i in range(a)]
def list4d(a, b, c, d, e): return [[[[e] * d for j in range(c)] for j in range(b)] for i in range(a)]
def ceil(x, y=1): return int(-(-x // y))
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(N=None): return list(MAP()) if N is None else [INT() for i in range(N)]
def Yes(): print('Yes')
def No(): print('No')
def YES(): print('YES')
def NO(): print('NO')
sys.setrecursionlimit(10 ** 9)
INF = 10 ** 19
MOD = 10 ** 9 + 7

def bfs(src):
    from collections import deque

    que = deque()
    h, w = src
    que.append((dist[h][w], h, w))
    while que:
        cost, h, w = que.popleft()
        if h > 1:
            if dist[h-1][w] > cost:
                dist[h-1][w] = cost
                que.append((cost+seated[h-1][w], h-1, w))
        if h < N-1:
            if dist[h+1][w] > cost:
                dist[h+1][w] = cost
                que.append((cost+seated[h+1][w], h+1, w))
        if w > 1:
            if dist[h][w-1] > cost:
                dist[h][w-1] = cost
                que.append((cost+seated[h][w-1], h, w-1))
        if w < N-1:
            if dist[h][w+1] > cost:
                dist[h][w+1] = cost
                que.append((cost+seated[h][w+1], h, w+1))

N = INT()
P = [p-1 for p in LIST()]

dist = list2d(N, N, 0)
for i in range(N):
    for j in range(N):
        dist[i][j] = min(i, N-i-1, j, N-j-1)

ans = 0
seated = list2d(N, N, 1)
for p in P:
    h, w = divmod(p, N)
    ans += dist[h][w]
    bfs((h, w))
    seated[h][w] = 0
print(ans)

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline
N = int(input())
P = list(map(lambda x:int(x)-1,input().split()))

costs = [0]*(N*N)
for i in range(N):
    for j in range(N):
        costs[i*N+j] = min(i,j,N-1-i,N-1-j)
exist = [1]*(N*N)

from collections import deque
ans = 0
for p in P:
    ans += costs[p]
    exist[p] = 0
    q = deque([p])
    while q:
        p = q.popleft()
        y,x = divmod(p,N)
        if x < N-1:
            np = p + 1
            if costs[np] > costs[p] + exist[p]:
                costs[np] = costs[p] + exist[p]
                q.append(np)
        if x > 0:
            np = p - 1
            if costs[np] > costs[p] + exist[p]:
                costs[np] = costs[p] + exist[p]
                q.append(np)
        if y < N-1:
            np = p + N
            if costs[np] > costs[p] + exist[p]:
                costs[np] = costs[p] + exist[p]
                q.append(np)
        if y > 0:
            np = p - N
            if costs[np] > costs[p] + exist[p]:
                costs[np] = costs[p] + exist[p]
                q.append(np)
print(ans)

Submission status: Accepted

Solution code:
# -*- coding: utf-8 -*-
import sys
sys.setrecursionlimit(10**9)
INF=10**18
MOD=10**9+7
input=lambda: sys.stdin.readline().rstrip()
YesNo=lambda b: bool([print('Yes')] if b else print('No'))
YESNO=lambda b: bool([print('YES')] if b else print('NO'))
int1=lambda x:int(x)-1


def main():
    d=[0]*M
    for i in range(N):
        for j in range(N):
            d[i*N+j]=min(min(i,N-1-i),min(j,N-1-j))
    used=[1]*M
    ans=0
    que=[]
    for p in P:
        ans+=d[p]
        used[p]=0
        que.append(p)
        while que:
            x=que.pop()
            for ddx in (-1,1,-N,N):
                nx=x+ddx
                if 0<=nx<M:
                    if used[x]==0 and d[nx]-d[x]>=1:
                        d[nx]-=1
                        que.append(nx)
                    elif used[x]==1 and d[nx]-d[x]>=2:
                        d[nx]-=1
                        que.append(nx)
    print(ans)

if __name__ == '__main__':
    N=int(input())
    M=N**2
    P=tuple(map(int1,input().split()))
    main()

Submission status: Accepted

Solution code:
# -*- coding: utf-8 -*-
import sys
from collections import deque
sys.setrecursionlimit(10**9)
INF=10**18
MOD=10**9+7
input=lambda: sys.stdin.readline().rstrip()
YesNo=lambda b: bool([print('Yes')] if b else print('No'))
YESNO=lambda b: bool([print('YES')] if b else print('NO'))
int1=lambda x:int(x)-1

N=int(input())
M=N**2
P=tuple(map(int1,input().split()))
d=[0]*M
for i in range(N):
    for j in range(N):
        d[i*N+j]=min(min(i,N-1-i),min(j,N-1-j))
used=[1]*M
ans=0
que=deque()
for p in P:
    ans+=d[p]
    used[p]=0
    que.append(p)
    while que:
        x=que.pop()
        for ddx in (-1,1,-N,N):
            nx=x+ddx
            if 0<=nx<M:
                if used[x]==0 and d[nx]-d[x]>=1:
                    d[nx]-=1
                    que.append(nx)
                elif used[x]==1 and d[nx]-d[x]>=2:
                    d[nx]-=1
                    que.append(nx)
print(ans)

Submission status: Accepted

Solution code:
# -*- coding: utf-8 -*-
import sys
sys.setrecursionlimit(10**9)
INF=10**18
MOD=10**9+7
input=lambda: sys.stdin.readline().rstrip()
YesNo=lambda b: bool([print('Yes')] if b else print('No'))
YESNO=lambda b: bool([print('YES')] if b else print('NO'))
int1=lambda x:int(x)-1

N=int(input())
M=N**2
P=tuple(map(int1,input().split()))
d=[0]*M
for i in range(N):
    for j in range(N):
        d[i*N+j]=min(min(i,N-1-i),min(j,N-1-j))
used=[1]*M
ans=0
que=[]
for p in P:
    ans+=d[p]
    used[p]=0
    que.append(p)
    while que:
        x=que.pop()
        for ddx in (-1,1,-N,N):
            nx=x+ddx
            if 0<=nx<M:
                if used[x]==0 and d[nx]-d[x]>=1:
                    d[nx]-=1
                    que.append(nx)
                elif used[x]==1 and d[nx]-d[x]>=2:
                    d[nx]-=1
                    que.append(nx)
print(ans)

Submission status: Accepted

Solution code:
# -*- coding: utf-8 -*-
import sys
from collections import deque
sys.setrecursionlimit(10**9)
INF=10**18
MOD=10**9+7
input=lambda: sys.stdin.readline().rstrip()
YesNo=lambda b: bool([print('Yes')] if b else print('No'))
YESNO=lambda b: bool([print('YES')] if b else print('NO'))
int1=lambda x:int(x)-1

N=int(input())
M=N**2
P=tuple(map(int1,input().split()))
d=[0]*M
for i in range(N):
    for j in range(N):
        d[i*N+j]=min(min(i,N-1-i),min(j,N-1-j))
used=[1]*M
ans=0
que=[]
for p in P:
    ans+=d[p]
    used[p]=0
    que.append(p)
    while que:
        x=que.pop()
        for ddx in (-1,1,-N,N):
            nx=x+ddx
            if 0<=nx<M:
                if used[x]==0 and d[nx]-d[x]>=1:
                    d[nx]-=1
                    que.append(nx)
                elif used[x]==1 and d[nx]-d[x]>=2:
                    d[nx]-=1
                    que.append(nx)
print(ans)

Submission status: Accepted

Solution code:
import sys

input_methods=['clipboard','file','key']
using_method=0
input_method=input_methods[using_method]

#+++++

def main():
	n = int(input())
	nn = [[min(i,j,n-i-1,n-j-1) for j in range(n)] for i in range(n)]
	is_sit = [[True] * n for _ in range(n)]
	cc = [[0]*n for _ in range(n)]
	
	#b , c = tin()
	pl = list(map(int, input().split()))
	ans = 0
	for p in pl:
		x, y = (p-1) // n, (p-1) % n
		ans += nn[x][y]
		is_sit[x][y] = False
		q = [(x, y, nn[x][y])]
		while q:
			(x, y, v) = q.pop()
			if x >= 0 and nn[x-1][y]>v:
				nn[x-1][y] = v
				q.append((x-1, y, v+is_sit[x-1][y]))
			if x < n-1 and nn[x+1][y]>v:
				nn[x+1][y] = v
				q.append((x+1, y, v+is_sit[x+1][y]))		
			if y >= 0 and nn[x][y-1]>v:
				nn[x][y-1] = v
				q.append((x, y-1, v+is_sit[x][y-1]))
			if y < n-1 and nn[x][y+1]>v:
				nn[x][y+1] = v
				q.append((x, y+1, v+is_sit[x][y+1]))	
		
	print(ans)
	#s = input()	
	
	
#+++++
isTest=False

def pa(v):
	if isTest:
		print(v)
		
def input_clipboard():
	import clipboard
	input_text=clipboard.get()
	input_l=input_text.splitlines()
	for l in input_l:
		yield l

if __name__ == "__main__":
	if sys.platform =='ios':
		if input_method==input_methods[0]:
			ic=input_clipboard()
			input = lambda : ic.__next__()
		elif input_method==input_methods[1]:
			sys.stdin=open('inputFile.txt')
		else:
			pass
		isTest=True
	else:
		input = sys.stdin.readline
			
	ret = main()
	if ret is not None:
		print(ret)

Submission status: Accepted

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

def solve():
  n=int(input())
  arr=list(map(int,input().split()))
  cost=[[30000]*n for _ in range(n)]
  for i in range(n):
    for j in range(n):
      cost[i][j]=min(i,n-(i+1),j,n-(j+1))
  board=[[1]*n for _ in range(n)]
  ans=0
  for val in arr:
    x=(val-1)%n
    y=(val-1)//n
    ans+=cost[y][x]
    board[y][x]=0
    q=collections.deque()
    q.append((x,y))
    while len(q)!=0:
      x,y=q.popleft()
      c=cost[y][x]+board[y][x]
      if x>0 and c<cost[y][x-1]:
        cost[y][x-1]=c
        q.append((x-1,y))    
      if x<n-1 and c<cost[y][x+1]:
        cost[y][x+1]=c
        q.append((x+1,y))    
      if y>0 and c<cost[y-1][x]:
        cost[y-1][x]=c
        q.append((x,y-1))    
      if y<n-1 and c<cost[y+1][x]:
        cost[y+1][x]=c
        q.append((x,y+1))
  print(ans)
solve()

Submission status: Accepted

Solution code:
# https://atcoder.jp/contests/agc044/submissions/13571248

def main():
    from collections import deque

    N = int(input())
    *p, = (int(x) - 1 for x in input().split())

    H = [min(r, N - 1 - r, c, N - 1 - c) for r in range(N) for c in range(N)]  # 離席コスト
    S = [1] * N * N  # 着席

    ans = 0
    for pi in p:
        hpi = H[pi]  # piの離席コスト
        ans += hpi  # piの離席コストを加算
        S[pi] = 0  # piを空席にする

        # BFSで離席コストを更新
        dq = deque()
        dq.append((pi, hpi))
        while dq:
            x, h = dq.popleft()
            r, c = divmod(x, N)

            nx = x - N
            if r != 0 and H[nx] > h:
                H[nx] = h
                dq.append((nx, h + S[nx]))

            nx = x + N
            if r != N - 1 and H[nx] > h:
                H[nx] = h
                dq.append((nx, h + S[nx]))

            nx = x - 1
            if c != 0 and H[nx] > h:
                H[nx] = h
                dq.append((nx, h + S[nx]))

            nx = x + 1
            if c != N - 1 and H[nx] > h:
                H[nx] = h
                dq.append((nx, h + S[nx]))

    print(ans)


if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
def build_cost_table(n):
    ret = [-1] * (n ** 2)
    for r in range(n):
        dr = min(r, n - 1 - r)
        for c in range(n):
            dc = min(c, n - 1 - c)
            ret[r * n + c] = min(dr, dc)
    return ret


def main():
    from collections import deque

    N = int(input())
    *p, = (int(x) - 1 for x in input().split())

    H = build_cost_table(N)  # 離席コスト
    S = [1] * (N ** 2)  # 着席

    ans = 0
    for pi in p:
        hpi = H[pi]  # piの離席コスト
        ans += hpi  # piの離席コストを加算
        S[pi] = 0  # piを空席にする

        # BFSで離席コストを更新
        dq = deque()
        dq.append((pi, hpi))
        while dq:
            x, h = dq.popleft()
            r, c = divmod(x, N)

            nx = x - N
            if r != 0 and H[nx] > h:
                H[nx] = h
                dq.append((nx, h + S[nx]))

            nx = x + N
            if r != N - 1 and H[nx] > h:
                H[nx] = h
                dq.append((nx, h + S[nx]))

            nx = x - 1
            if c != 0 and H[nx] > h:
                H[nx] = h
                dq.append((nx, h + S[nx]))

            nx = x + 1
            if c != N - 1 and H[nx] > h:
                H[nx] = h
                dq.append((nx, h + S[nx]))

    print(ans)


if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline
from collections import deque
def main():
    N = int(input())
    P = list(map(int, input().split()))
    costs = [-1 for _ in range(N**2)]
    sit = [1 for _ in range(N**2)]
    for i in range(N**2):
        q, mod = divmod(i, N)
        up, down, left, right = q, N-q-1, mod, N-mod-1
        costs[i] = min(up, down, left, right)
    ans = 0
    for p in P:
        ans += costs[p-1]
        sit[p-1] = 0
        que = deque([])
        que.append((p-1, costs[p-1]))
        while len(que) != 0:
            v, d = que.popleft()
            if v > N and costs[v-N] > d:
                costs[v-N] = d
                que.append((v-N, d+sit[v-N]))
            if v < N**2-N-1 and costs[v+N] > d:
                costs[v+N] = d
                que.append((v+N, d+sit[v+N]))
            if v % N != 0 and costs[v-1] > d:
                costs[v-1] = d
                que.append((v-1, d+sit[v-1]))
            if (v+1) % N != 0 and costs[v+1] > d:
                costs[v+1] = d
                que.append((v+1, d+sit[v+1]))
    print(ans)
if __name__ == "__main__":
    main()

Submission status: Accepted

Solution code:
import sys
n,*p = map(int,sys.stdin.read().split())
dist = [min(a,n-1-a,b,n-1-b) for a in range(n) for b in range(n)]

def update(v,nv):
    if dist[nv] > dist[v] + iru[v]:
        q.append(nv)
        dist[nv] = dist[v] + iru[v]

ans = 0
iru = [1]*n*n
for pi in p:
    pi -= 1
    ans += dist[pi]
    iru[pi] = 0
    q = [pi]
    while q:
        v = q.pop()
        if v%n != n-1: update(v,v+1)
        if v%n: update(v,v-1)
        if v >= n: update(v,v-n)
        if v+n < n*n: update(v,v+n)
print(ans)

Submission status: Accepted

Solution code:
import sys
from collections import deque
readline = sys.stdin.readline

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

geta = N+2
G = [0]*(geta*geta)

for v in range(-1-(-N//2), -1, -1):
    l = v+1
    r = N-v
    for i in range(geta):
        G[i*geta+l] = v
        G[i*geta+r] = v
        G[l*geta+i] = v
        G[r*geta+i] = v

for i in range(geta):
    G[i*geta] = -1
    G[i*geta + geta-1] = -1
    G[i] = -1
    G[geta*(geta-1)+i] = -1

Pn = []

for p in P:
    a, b = divmod(p-1, N)
    Pn.append((1+a)*geta+1+b)

DIREC = (1, -1, geta, -geta)
ans = 0
used = [False]*(geta*geta)
for p in Pn:
    ans += G[p]
    res = G[p]
    for d in DIREC:
        res = min(res, G[p+d])
    if G[p] != res:
        G[p] = res
        Q = [p]
        while Q:
            vn = Q.pop()
            for d in DIREC:
                vf = vn + d
                if not used[vf]:
                    if G[vf] > G[vn] + 1:
                        G[vf] = G[vn] + 1
                        Q.append(vf)
                else:
                    if G[vf] > G[vn]:
                        G[vf] = G[vn]
                        Q.append(vf)
                    
    used[p] = True
print(ans)