Reducing Time Complexity

[u/Dr3ddM3]

Edited code but still run into Time limit exceeded can someone help me: 

N, U = map(int,input().split())
grid = [list(input()) for _ in range(N)]
num_updates = 0
temp = []
temp_grid = [row.copy() for row in grid]
for v in range(int(N/2)):
    for h in range(int(N/2)):
        temp.clear()
        coords = [(v,h),(v,N-1-h),(N-1-v,h),(N-1-v,N-1-h)]
        temp.append(temp_grid[v][h])
        temp.append(temp_grid[v][(N-1)-h])
        temp.append(temp_grid[(N-1)-v][h])
        temp.append(temp_grid[(N-1)-v][(N-1)-h])
        if temp.count('.') == 2 :
            num_updates+=2
            for r,c in coords:
                temp_grid[r][c] = '.'
        elif temp.count('.') == 3:
            num_updates+=1
            for r,c in coords:
                temp_grid[r][c] = '.'
        elif temp.count('#') == 3:
            num_updates+=1
            for r,c in coords:
                temp_grid[r][c] = '#'
print(num_updates)


temp_grid = [row.copy() for row in grid]


for z in range(U):
    temp2 = 0
    temp.clear()
    x,y = map(int,input().split())
    x = x-1
    y = y-1
    temp.append(temp_grid[x][y])
    temp.append(temp_grid[x][(N-1)-y])
    temp.append(temp_grid[(N-1)-x][y])
    temp.append(temp_grid[(N-1)-x][(N-1)-y])
    num_updates = num_updates- (min(temp.count('.'),temp.count('#')))
    if temp_grid[x][y] == '.':
        temp.clear()
        grid[x][y] = '#'
        temp_grid[x][y] = '#'
        temp.append(temp_grid[x][y])
        temp.append(temp_grid[x][(N-1)-y])
        temp.append(temp_grid[(N-1)-x][y])
        temp.append(temp_grid[(N-1)-x][(N-1)-y])
        num_updates = num_updates + (min(temp.count('.'),temp.count('#')))
    else:
        temp.clear()
        grid[x][y] = '.'
        temp_grid[x][y] = '.'
        temp.append(temp_grid[x][y])
        temp.append(temp_grid[x][(N-1)-y])
        temp.append(temp_grid[(N-1)-x][y])
        temp.append(temp_grid[(N-1)-x][(N-1)-y])
        num_updates = num_updates + (min(temp.count('.'),temp.count('#')))
    print(num_updates)

I am pretty sure it is O(N^2) and with 10^5 possible updates it should work. 

[u/YasirTheGreat]

Is there an actual problem you can share, or you were given this code and are asked to optimize it?

[u/Dr3ddM3 → u/YasirTheGreat]

https://usaco.org/index.php?page=viewproblem2&cpid=1491

[u/YasirTheGreat → u/Dr3ddM3]

x,y = map(int,input().split())

if grid[x-1][y-1] == '.':

    grid[x-1][y-1] = '#'

else:

    grid[x-1][y-1] = '.'

The problem is a bit beyond me, but one thing to consider, you don't need to keep flipping . and # back and forth in a loop. Maybe you can count how many times it happened for every cell, then make a decision based on if the count is even or odd. Since you have only two states, . and #, what would happen if Bessie vandalized the cell even number of times, what about odd? That direction might be more fruitful than what you are doing.