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:
N=int(input())
plist=list(map(int,input().split()))

sit=[[1]*N for _ in range(N)]
dist=[[min(i,j,N-1-i,N-1-j) for j in range(N)] for i in range(N)]

answer=0
for p in plist:
  i=(p-1)//N
  j=(p-1)%N
  #print(i,j)
  sit[i][j]=0
  answer+=dist[i][j]
  
  queue=[(i,j,dist[i][j])]
  d=0
  while queue:
    x,y,d=queue.pop()
    if x>0 and dist[x-1][y]>d:
      dist[x-1][y]=d
      queue.append((x-1,y,d+sit[x-1][y]))
    if x<N-1 and dist[x+1][y]>d:
      dist[x+1][y]=d
      queue.append((x+1,y,d+sit[x+1][y]))    
    if y>0 and dist[x][y-1]>d:
      dist[x][y-1]=d
      queue.append((x,y-1,d+sit[x][y-1]))
    if y<N-1 and dist[x][y+1]>d:
      dist[x][y+1]=d
      queue.append((x,y+1,d+sit[x][y+1]))
      
print(answer)

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline
n = int(input())
l = list(map(int,input().split()))
l = [((i-1)//n, (i-1) % n) for i in l]
check = [[1]*n for i in range(n)]
d =  [[min(i, n-i-1, j, n-j-1) for j in range(n)] for i in range(n)]

ans = 0
for x,y in l:
    check[x][y] = 0
    ans += d[x][y]
    q = [(x,y,d[x][y])]
    while q:
        bx,by,z = q.pop()

        if bx != 0:
            if d[bx-1][by] > z:
                d[bx-1][by] = z
                q.append((bx-1,by,z+check[bx-1][by]))
        if bx != n-1:
            if d[bx+1][by] > z:
                d[bx+1][by] = z
                q.append((bx+1,by,z+check[bx+1][by]))
        if by != 0:
            if d[bx][by-1] > z:
                d[bx][by-1] = z
                q.append((bx,by-1,z+check[bx][by-1]))
        if by != n-1:
            if d[bx][by+1] > z:
                d[bx][by+1] = z
                q.append((bx,by+1,z+check[bx][by+1]))  
print(ans)

Submission status: Accepted

Solution code:
def main():
    import sys
    input = sys.stdin.readline
    n = int(input())
    l = list(map(int,input().split()))
    l = [((i-1)//n, (i-1) % n) for i in l]
    check = [[1]*n for i in range(n)]
    d =  [[min(i, n-i-1, j, n-j-1) for j in range(n)] for i in range(n)]

    ans = 0
    for x,y in l:
        check[x][y] = 0
        ans += d[x][y]
        q = [(x,y,d[x][y])]
        while q:
            bx,by,z = q.pop()

            if bx != 0:
                if d[bx-1][by] > z:
                    d[bx-1][by] = z
                    q.append((bx-1,by,z+check[bx-1][by]))
            if bx != n-1:
                if d[bx+1][by] > z:
                    d[bx+1][by] = z
                    q.append((bx+1,by,z+check[bx+1][by]))
            if by != 0:
                if d[bx][by-1] > z:
                    d[bx][by-1] = z
                    q.append((bx,by-1,z+check[bx][by-1]))
            if by != n-1:
                if d[bx][by+1] > z:
                    d[bx][by+1] = z
                    q.append((bx,by+1,z+check[bx][by+1]))  
    print(ans)
if __name__ =="__main__":
    main()

Submission status: Accepted

Solution code:
def main():
    import sys
    input = sys.stdin.readline
    n = int(input())
    l = list(map(int,input().split()))
    l = [((i-1)//n, (i-1) % n) for i in l]
    check = [[1 for j in range(n)] for i in range(n)]
    d =  [[min(i, n-i-1, j, n-j-1) for j in range(n)] for i in range(n)]

    ans = 0
    for x,y in l:
        check[x][y] = 0
        ans += d[x][y]
        q = []
        q.append((x,y,d[x][y]))
        while q:
            bx,by,z = q.pop()

            if bx != 0:
                if d[bx-1][by] > z:
                    d[bx-1][by] = z
                    q.append((bx-1,by,z+check[bx-1][by]))
            if bx != n-1:
                if d[bx+1][by] > z:
                    d[bx+1][by] = z
                    q.append((bx+1,by,z+check[bx+1][by]))
            if by != 0:
                if d[bx][by-1] > z:
                    d[bx][by-1] = z
                    q.append((bx,by-1,z+check[bx][by-1]))
            if by != n-1:
                if d[bx][by+1] > z:
                    d[bx][by+1] = z
                    q.append((bx,by+1,z+check[bx][by+1]))  
    print(ans)
if __name__ =="__main__":
    main()

Submission status: Accepted

Solution code:
def main():
    import sys
    input = sys.stdin.readline
    n = int(input())
    l = list(map(int,input().split()))
    check = [[1 for j in range(n)] for i in range(n)]
    d =  [[min(i, n-i-1, j, n-j-1) for j in range(n)] for i in range(n)]

    ans = 0
    for t in l:
        t -=1
        x = t//n
        y = t%n
        check[x][y] = 0
        ans += d[x][y]
        q = []
        q.append((x,y,d[x][y]))
        while q:
            bx,by,z = q.pop()

            if bx != 0:
                if d[bx-1][by] > z:
                    d[bx-1][by] = z
                    q.append((bx-1,by,z+check[bx-1][by]))
            if bx != n-1:
                if d[bx+1][by] > z:
                    d[bx+1][by] = z
                    q.append((bx+1,by,z+check[bx+1][by]))
            if by != 0:
                if d[bx][by-1] > z:
                    d[bx][by-1] = z
                    q.append((bx,by-1,z+check[bx][by-1]))
            if by != n-1:
                if d[bx][by+1] > z:
                    d[bx][by+1] = z
                    q.append((bx,by+1,z+check[bx][by+1]))  
    print(ans)
if __name__ =="__main__":
    main()

Submission status: Accepted

Solution code:
def main():
    import sys
    input = sys.stdin.readline
    n = int(input())
    l = list(map(int,input().split()))
    check = [[True]*n for i in range(n)]
    d =  [[min(i, n-i-1, j, n-j-1) for j in range(n)] for i in range(n)]

    ans = 0
    for t in l:
        t -=1
        x = t//n
        y = t%n
        check[x][y] = False
        ans += d[x][y]
        q = []
        q.append([x,y,d[x][y]])
        while q:
            bx,by,z = q.pop()

            if bx != 0:
                if d[bx-1][by] > z:
                    d[bx-1][by] = z
                    q.append([bx-1,by,z+check[bx-1][by]])
            if bx != n-1:
                if d[bx+1][by] > z:
                    d[bx+1][by] = z
                    q.append([bx+1,by,z+check[bx+1][by]])
            if by != 0:
                if d[bx][by-1] > z:
                    d[bx][by-1] = z
                    q.append([bx,by-1,z+check[bx][by-1]])
            if by != n-1:
                if d[bx][by+1] > z:
                    d[bx][by+1] = z
                    q.append([bx,by+1,z+check[bx][by+1]])  
    print(ans)
if __name__ =="__main__":
    main()

Submission status: Accepted

Solution code:
def main():
    import sys
    input = sys.stdin.readline
    n = int(input())
    l = list(map(int,input().split()))
    check = [[True]*n for i in range(n)]
    d =  [[min(i, n-i-1, j, n-j-1) for j in range(n)] for i in range(n)]

    ans = 0
    for t in l:
        t -=1
        x = t//n
        y = t%n
        check[x][y] = False
        ans += d[x][y]
        q = []
        q.append((x,y,d[x][y]))
        while q:
            bx,by,z = q.pop()

            if bx != 0:
                if d[bx-1][by] > z:
                    d[bx-1][by] = z
                    q.append((bx-1,by,z+check[bx-1][by]))
            if bx != n-1:
                if d[bx+1][by] > z:
                    d[bx+1][by] = z
                    q.append((bx+1,by,z+check[bx+1][by]))
            if by != 0:
                if d[bx][by-1] > z:
                    d[bx][by-1] = z
                    q.append((bx,by-1,z+check[bx][by-1]))
            if by != n-1:
                if d[bx][by+1] > z:
                    d[bx][by+1] = z
                    q.append((bx,by+1,z+check[bx][by+1]))  
    print(ans)
if __name__ =="__main__":
    main()

Submission status: Accepted

Solution code:
def main():
    import sys
    input = sys.stdin.readline
    n = int(input())
    l = list(map(int,input().split()))
    check = [[1]*n for i in range(n)]
    d =  [[min(i, n-i-1, j, n-j-1) for j in range(n)] for i in range(n)]

    ans = 0
    for t in l:
        t -=1
        x = t//n
        y = t%n
        check[x][y] = 0
        ans += d[x][y]
        q = []
        q.append((x,y,d[x][y]))
        while q:
            bx,by,z = q.pop()

            if bx != 0:
                if d[bx-1][by] > z:
                    d[bx-1][by] = z
                    q.append((bx-1,by,z+check[bx-1][by]))
            if bx != n-1:
                if d[bx+1][by] > z:
                    d[bx+1][by] = z
                    q.append((bx+1,by,z+check[bx+1][by]))
            if by != 0:
                if d[bx][by-1] > z:
                    d[bx][by-1] = z
                    q.append((bx,by-1,z+check[bx][by-1]))
            if by != n-1:
                if d[bx][by+1] > z:
                    d[bx][by+1] = z
                    q.append((bx,by+1,z+check[bx][by+1]))  
    print(ans)
if __name__ =="__main__":
    main()

Submission status: Accepted

Solution code:
def main():
    from collections import deque
    import sys
    input = sys.stdin.readline
    n = int(input())
    l = list(map(int,input().split()))
    check = [[1]*n for i in range(n)]
    d =  [[min(i, n-i-1, j, n-j-1) for j in range(n)] for i in range(n)]
    
    ans = 0
    for t in l:
        t -=1
        x = t//n
        y = t%n
        check[x][y] = 0
        ans += d[x][y]
        q = deque([])
        q.append((x,y,d[x][y]))
        while q:
            bx,by,z = q.popleft()

            if bx != 0:
                if d[bx-1][by] > z:
                    d[bx-1][by] = z
                    q.append((bx-1,by,z+check[bx-1][by]))
            if bx != n-1:
                if d[bx+1][by] > z:
                    d[bx+1][by] = z
                    q.append((bx+1,by,z+check[bx+1][by]))
            if by != 0:
                if d[bx][by-1] > z:
                    d[bx][by-1] = z
                    q.append((bx,by-1,z+check[bx][by-1]))
            if by != n-1:
                if d[bx][by+1] > z:
                    d[bx][by+1] = z
                    q.append((bx,by+1,z+check[bx][by+1]))  
    print(ans)
if __name__ =="__main__":
    main()

Submission status: Accepted

Solution code:
def main():
    from collections import deque
    import sys
    input = sys.stdin.readline
    n = int(input())
    l = list(map(int,input().split()))
    check = [[1]*n for i in range(n)]
    d = [[float("INF")]*n for i in range(n)]

    for i in range((n+1)//2):
        for j in range(i,n-i):
            d[i][j] = i
            d[-1-i][j] = i
        for j in range(i,n-i):
            d[j][i] = i
            d[j][-1-i] = i
    def solve(l):
        ans = 0
        for t in l:
            t -=1
            x = t//n
            y = t%n
            check[x][y] = 0
            ans += d[x][y]
            q = deque([])
            q.append((x,y,d[x][y]))
            while q:
                bx,by,z = q.popleft()

                if bx != 0:
                    if d[bx-1][by] > z:
                        d[bx-1][by] = z
                        q.append((bx-1,by,z+check[bx-1][by]))
                if bx != n-1:
                    if d[bx+1][by] > z:
                        d[bx+1][by] = z
                        q.append((bx+1,by,z+check[bx+1][by]))
                if by != 0:
                    if d[bx][by-1] > z:
                        d[bx][by-1] = z
                        q.append((bx,by-1,z+check[bx][by-1]))
                if by != n-1:
                    if d[bx][by+1] > z:
                        d[bx][by+1] = z
                        q.append((bx,by+1,z+check[bx][by+1]))  
        return ans

    
    print(solve(l))

if __name__ =="__main__":
    main()

Submission status: Accepted

Solution code:
# coding: utf-8
import sys
from collections import deque

sr = lambda: sys.stdin.readline().rstrip()
ir = lambda: int(sr())
lr = lambda: list(map(int, sr().split()))

def main():
    N = ir()
    P = lr()
    P = [((p-1)//N, (p-1)%N) for p in P]
    dp = [[min(i, N-1-i, j, N-1-j) for j in range(N)] for i in range(N)]
    people = [[True] * N for i in range(N)]

    answer = 0
    for i, j in P:
        answer += dp[i][j]
        people[i][j] = False
        que = deque([(i, j, dp[i][j])])
        popleft = que.popleft; append = que.append
        while que:
            y, x, cur = popleft()
            cur += people[y][x]
            if x > 0:
                if dp[y][x-1] > cur:
                    dp[y][x-1] = cur
                    append((y, x-1, cur))
            if x < N-1:
                if dp[y][x+1] > cur:
                    dp[y][x+1] = cur
                    append((y, x+1, cur))
            if y > 0:
                if dp[y-1][x] > cur:
                    dp[y-1][x] = cur
                    append((y-1, x, cur))
            if y < N-1:
                if dp[y+1][x] > cur:
                    dp[y+1][x] = cur
                    append((y+1, x, cur))

    print(answer)
    
if __name__ == "__main__":
    main()

Submission status: Accepted

Solution code:
from collections import deque
n = int(input())
Ps = list(map(int, input().split()))
Ps = [p-1 for p in Ps]
fs = [0] * (n**2)

## フロアフィールドを作る
for x in range(n**2):
    i,j = divmod(x,n)
    x = min(i,n-1-i)
    y = min(j,n-1-j)
    fs[i*n+j] = min(x,y)

ans = 0
mvs = [1, -1, n, -n]
occupied = [1] * (n**2)
for p in Ps:
    ans += fs[p]
    occupied[p] = 0
    q = deque([])
    q.append(p)
    while len(q) > 0: #pを起点にBFS
        p_ = q.popleft()
        dist = fs[p_]
        for mv in mvs:
            if 0 <= p_+mv < n**2:
                p_next = p_ + mv
                # ある位置h,wが
                # occupiedなら、隣接マス+1で到達
                # vacantなら、隣接マス+0で到達
                if dist+occupied[p_] < fs[p_next]:
                    q.append(p_next)
                    fs[p_next] = dist + occupied[p_]

print(ans)

Submission status: Accepted

Solution code:
def main():
    n=int(input())
    Num=[0]*(n**2+1)
    Exited=[0]*(n**2+1)
    X=tuple(map(int,input().split()))
    for i in range(n**2):
        q,r=divmod(i,n)
        Num[i+1]=min(q,n-q-1,r,n-r-1)
    ans=0
    for x in X:
        ans+=Num[x]
        Exited[x]=1
        Stack=[x]
        while Stack:
            v=Stack.pop()
            if v>n and (Num[v]<Num[v-n] and (Exited[v] or Num[v-n]-Num[v]>1)):
                Num[v-n]-=1
                Stack.append(v-n)
            if v<=n**2-n and (Num[v]<Num[v+n] and (Exited[v] or Num[v+n]-Num[v]>1)):
                Num[v+n]-=1
                Stack.append(v+n)
            if v%n!=0 and (Num[v]<Num[v+1] and (Exited[v] or Num[v+1]-Num[v]>1)):
                Num[v+1]-=1
                Stack.append(v+1)
            if v%n!=1 and (Num[v]<Num[v-1] and (Exited[v] or Num[v-1]-Num[v]>1)):
                Num[v-1]-=1
                Stack.append(v-1)
    print(ans)

if __name__=='__main__':
    main()

Submission status: Accepted

Solution code:
# -*- coding: utf-8 -*-
import sys
buff_readline = sys.stdin.buffer.readline


def read_int():
    return int(buff_readline())


def read_int_n():
    return list(map(int, buff_readline().split()))


def slv(N, P):
    M = N+2
    cost = [0] * M**2
    occupy = [1] * M**2
    for i in range(N):
        im = i*M + M + 1
        for j in range(N):
            cost[im+j] = min(i, j, N-i-1, N-j-1)

    ds = [-1, 1, -M, M]
    ans = 0
    for p in P:
        p -= 1
        x = p // N
        y = p % N
        p = x * M + y + M + 1
        ans += cost[p]
        occupy[p] = 0
        s = []
        s.append(p)
        while s:
            pi = s.pop()
            for d in ds:
                ni = pi + d
                nc = cost[pi] + occupy[pi]
                if nc < cost[ni]:
                    cost[ni] = nc
                    s.append(ni)
    return ans


def main():
    N = read_int()
    P = read_int_n()
    print(slv(N, P))


if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
import sys
input = lambda : sys.stdin.readline().rstrip()
sys.setrecursionlimit(max(1000, 10**9))
write = lambda x: sys.stdout.write(x+"\n")


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

d = [None] * (n**2)
for i in range(n):
    for j in range(n):
        d[i*n+j] = min(i, n-1-i, j, n-1-j)
vacant = [False] * (n**2)

ans = 0
for pos in p:
    pos -= 1
    ans += d[pos]
    vacant[pos] = True
    q = [pos]
    while q:
        pos = q.pop()
        tmp = not vacant[pos]
#         for diff in (-1, 1, -n, n):
#             ppos = diff+pos
#             if ppos<0 or ppos>=n*n:
#                 continue
#             if d[ppos]>d[pos]+tmp:
#                 d[ppos] = d[pos] + tmp
#                 q.append(ppos)
        if pos+n<n*n:
            ppos = pos + n
            if d[ppos]>d[pos]+tmp:
                d[ppos] = d[pos] + tmp
                q.append(ppos)
        if pos-n>=0:
            ppos = pos - n
            if d[ppos]>d[pos]+tmp:
                d[ppos] = d[pos] + tmp
                q.append(ppos)
        if pos+1<n*n:
            ppos = pos + 1
            if d[ppos]>d[pos]+tmp:
                d[ppos] = d[pos] + tmp
                q.append(ppos)
        if pos-1>=0:
            ppos = pos - 1
            if d[ppos]>d[pos]+tmp:
                d[ppos] = d[pos] + tmp
                q.append(ppos)
print(ans)

Submission status: Accepted

Solution code:
n = int(input())
p = [int(x) for x in input().split()]

ans = 0
seat = [[min(i, j, n-i-1, n-j-1) for j in range(n)] for i in range(n)]
reserved = [[True for j in range(n)] for i in range(n)]

vec = [(-1, 0), (1, 0), (0, -1), (0, 1)]

for i in range(n**2):
    v = p[i]-1
    x, y = v//n, v % n
    reserved[x][y] = False
    ans += seat[x][y]
    q = [(x, y)]
    while q:
        x, y = q.pop()
        if 0 <= x+1 < n and 0 <= y < n and seat[x+1][y] > seat[x][y] + reserved[x][y]:
            seat[x+1][y] = seat[x][y] + reserved[x][y]
            q.append((x+1, y))
        if 0 <= x-1 < n and 0 <= y < n and seat[x-1][y] > seat[x][y] + reserved[x][y]:
            seat[x-1][y] = seat[x][y] + reserved[x][y]
            q.append((x-1, y))
        if 0 <= x < n and 0 <= y+1 < n and seat[x][y+1] > seat[x][y] + reserved[x][y]:
            seat[x][y+1] = seat[x][y] + reserved[x][y]
            q.append((x, y+1))
        if 0 <= x < n and 0 <= y-1 < n and seat[x][y-1] > seat[x][y] + reserved[x][y]:
            seat[x][y-1] = seat[x][y] + reserved[x][y]
            q.append((x, y-1))


print(ans)

Submission status: Accepted

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


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

cost = [0] * (n * n)
for i in range(n):
    for j in range(n):
        cost[i * n + j] = min(i, j, n - i - 1, n - j - 1)

occ = [True] * (n * n)
ans = 0
for start in p:
    start -= 1
    q = deque([start])
    ans += cost[start]
    occ[start] = False
    while q:
        ij = q.popleft()
        i, j = divmod(ij, n)

        nxt_ij = (i + 1) * n + j
        if not(0 <= i + 1 < n and 0 <= j < n):
             pass
        elif not occ[ij] and cost[nxt_ij] > cost[ij]:
            cost[nxt_ij] = cost[ij]
            q.append(nxt_ij)
        elif cost[nxt_ij] > cost[ij] + 1:
            cost[nxt_ij] = cost[ij] + 1
            q.append(nxt_ij)
              
        nxt_ij = (i - 1) * n + j
        if not(0 <= i - 1 < n and 0 <= j < n):
            pass
        elif not occ[ij] and cost[nxt_ij] > cost[ij]:
            cost[nxt_ij] = cost[ij]
            q.append(nxt_ij)
        elif cost[nxt_ij] > cost[ij] + 1:
            cost[nxt_ij] = cost[ij] + 1
            q.append(nxt_ij)

        nxt_ij = i * n + (j + 1)
        if not(0 <= i + 0 < n and 0 <= j + 1 < n):
            pass
        elif not occ[ij] and cost[nxt_ij] > cost[ij]:
            cost[nxt_ij] = cost[ij]
            q.append(nxt_ij)
        elif cost[nxt_ij] > cost[ij] + 1:
            cost[nxt_ij] = cost[ij] + 1
            q.append(nxt_ij)

        nxt_ij = i * n + (j - 1)
        if not(0 <= i < n and 0 <= j - 1 < n):
            pass
        elif not occ[ij] and cost[nxt_ij] > cost[ij]:
            cost[nxt_ij] = cost[ij]
            q.append(nxt_ij)
        elif cost[nxt_ij] > cost[ij] + 1:
            cost[nxt_ij] = cost[ij] + 1
            q.append(nxt_ij)
print(ans)

Submission status: Accepted

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

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

def nears(n):
    ret = []
    if n%N != 0:
        ret.append(n-1)
    if n%N != N-1:
        ret.append(n+1)
    if n//N != 0:
        ret.append(n-N)
    if n//N != N-1:
        ret.append(n+N)
    return ret

NeedS = []
for p in range(N**2):
    NeedS.append(min([p%N, p//N, N-1-p%N, N-1-p//N]))

isChecked = [False]*(N**2)
ans = 0
for p in P:
    p -= 1
    ans += NeedS[p]
    isChecked[p] = True
    q = deque()
    q.append(p)
    while q:
        p = q.popleft()
        d = NeedS[p]
        if not isChecked[p]: d += 1
        for np in nears(p):
            if d < NeedS[np]:
                NeedS[np] = d
                q.append(np)
print(ans)

Submission status: Accepted

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


def input(): return sys.stdin.readline().rstrip()


@njit
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(input())
P = np.array(input().split(), np.int32)

print(solve(N, P))

Submission status: Accepted

Solution code:
import sys
import numpy as np

from numba import njit


@njit
def solve(n, ppp):
    n2 = n + 2
    nsq = n2 * n2
    seats = np.zeros(nsq, dtype=np.int16)
    is_seated = np.zeros(nsq, dtype=np.int8)
    for i in range(n):
        ud = min(i, n - 1 - i)
        ri = (i + 1) * n2
        for j in range(n):
            ij = ri + j + 1
            seats[ij] = min(ud, j, n - 1 - j)
            is_seated[ij] = 1

    MOVES = np.array([-n2, -1, 1, n2], dtype=np.int32)

    ans = 0

    for pi in range(n * n):
        i, j = divmod(ppp[pi], n)
        i = (i + 1) * n2 + j + 1
        res = seats[i]
        ans += res
        is_seated[i] = 0

        q = []
        for mi in range(4):
            ni = i + MOVES[mi]
            if seats[ni] > res:
                seats[ni] = res
                q.append(ni)

        while q:
            j = q.pop()
            # print(val, j, seats[j], l, r)
            val = seats[j]

            if is_seated[j]:
                val += 1
            for mi in range(4):
                nj = j + MOVES[mi]
                if seats[nj] > val:
                    seats[nj] = val
                    q.append(nj)

        # print(ppp[pi] + 1, i, ans)
        # print(seats.reshape((n2, n2)))
        # print(is_seated.reshape((n2, n2)))

    return ans


n = int(sys.stdin.buffer.readline())
ppp = np.array(list(map(int, sys.stdin.buffer.read().split())), dtype=np.int32) - 1

# n = 20
# np.random.seed(seed=32)
# ppp = np.random.permutation(n * n).astype(np.int32)
# print(ppp)

print(solve(n, ppp))

Submission status: Accepted

Solution code:
import sys
import numpy as np

from numba import njit


@njit('i4(i4,i4[:])', cache=True)
def solve(n, ppp):
    n2 = n + 2
    nsq = n2 * n2
    seats = np.zeros(nsq, dtype=np.int16)
    is_seated = np.zeros(nsq, dtype=np.int8)
    for i in range(n):
        ud = min(i, n - 1 - i)
        ri = (i + 1) * n2
        for j in range(n):
            ij = ri + j + 1
            seats[ij] = min(ud, j, n - 1 - j)
            is_seated[ij] = 1

    MOVES = np.array([-n2, -1, 1, n2], dtype=np.int32)

    ans = 0

    for pi in range(n * n):
        i, j = divmod(ppp[pi], n)
        i = (i + 1) * n2 + j + 1
        res = seats[i]
        ans += res
        is_seated[i] = 0

        q = []
        for mi in range(4):
            ni = i + MOVES[mi]
            if seats[ni] > res:
                seats[ni] = res
                q.append(ni)

        while q:
            j = q.pop()
            # print(val, j, seats[j], l, r)
            val = seats[j]

            if is_seated[j]:
                val += 1
            for mi in range(4):
                nj = j + MOVES[mi]
                if seats[nj] > val:
                    seats[nj] = val
                    q.append(nj)

        # print(ppp[pi] + 1, i, ans)
        # print(seats.reshape((n2, n2)))
        # print(is_seated.reshape((n2, n2)))

    return ans


n = int(sys.stdin.buffer.readline())
ppp = np.array(list(map(int, sys.stdin.buffer.read().split())), dtype=np.int32) - 1

# n = 20
# np.random.seed(seed=32)
# ppp = np.random.permutation(n * n).astype(np.int32)
# print(ppp)

print(solve(n, ppp))

Submission status: Accepted

Solution code:
N, = map(int, input().split())
R = [0] * (N**2+1)
V = [0] * (N**2+1)
X = list(map(int, input().split()))
for ai in range(N**2):
    i, j = divmod(ai, N)
    R[ai+1] = min([i, N-i-1, j, N-j-1])
r = 0
for a in X:
    r += R[a]
    V[a] = 1
    stack=[a]
    while stack:
        v = stack.pop()
        if v>N and (R[v]<R[v-N] and (V[v] or R[v]+1<R[v-N])):
            R[v-N] -= 1
            stack.append(v-N)
        if v<N**2+1-N and (R[v]<R[v+N] and (V[v] or R[v]+1<R[v+N])):
            R[v+N] -= 1
            stack.append(v+N)
        if v%N and (R[v]<R[v+1] and (V[v] or R[v]+1<R[v+1])):
            R[v+1] -= 1
            stack.append(v+1)
        if v%N-1 and (R[v]<R[v-1] and (V[v] or R[v]+1<R[v-1])):
            R[v-1] -= 1
            stack.append(v-1)
print(r)

Submission status: Accepted

Solution code:
N, = map(int, input().split())
R = [0] * (N**2+1)
V = [0] * (N**2+1)
X = list(map(int, input().split()))
for ai in range(N**2):
    i, j = divmod(ai, N)
    R[ai+1] = min([i, N-i-1, j, N-j-1])

r = 0
for a in X:
    r += R[a]
    V[a] = 1
    stack=[a]
    while stack:
        v = stack.pop()
        if v>N:
            if not(R[v]>=R[v-N] or ((1-V[v]) and R[v]+1 >= R[v-N])):
                R[v-N] -= 1
                stack.append(v-N)
        if v<N**2+1-N:
            if not(R[v]>=R[v+N] or ((1-V[v]) and R[v]+1 >= R[v+N])):
                R[v+N] -= 1
                stack.append(v+N)
        if v%N:
            if not(R[v]>=R[v+1] or ((1-V[v]) and R[v]+1 >= R[v+1])):
                R[v+1] -= 1
                stack.append(v+1)
        if v%N!=1:
            if not(R[v]>=R[v-1] or ((1-V[v]) and R[v]+1 >= R[v-1])):
                R[v-1] -= 1
                stack.append(v-1)
print(r)

Submission status: Accepted

Solution code:
N, = map(int, input().split())
R = [0] * (N**2+1)
V = [0] * (N**2+1)
X = list(map(int, input().split()))
for ai in range(N**2):
    i, j = divmod(ai, N)
    R[ai+1] = min([i, N-i-1, j, N-j-1])

r = 0
for a in X:
    r += R[a]
    V[a] = 1
    stack=[a]
    while stack:
        v = stack.pop()
        ccs = []
        if v>N:
            ccs.append(v-N)
        if v<N**2+1-N:
            ccs.append(v+N)
        if v%N:
            ccs.append(v+1)
        if v%N!=1:
            ccs.append(v-1)
        for u in ccs:
            if R[v]>=R[u] or ((1-V[v]) and R[v]+1 >= R[u]):
                continue
            R[u] -= 1
            stack.append(u)
print(r)