# Task
 Pac-Man got lucky today! Due to minor performance issue all his enemies have frozen. Too bad Pac-Man is not brave enough to face them right now, so he doesn't want any enemy to see him. 
 
 Given a gamefield of size `N` x `N`, Pac-Man's position(`PM`) and his enemies' positions(`enemies`), your task is to count the number of coins he can collect without being seen.

 An enemy can see a Pac-Man if they are standing on the same row or column. 
 
 It is guaranteed that no enemy can see Pac-Man on the starting position. There is a coin on each empty square (i.e. where there is no Pac-Man or enemy).

# Example

 For `N = 4, PM = [3, 0], enemies = [[1, 2]]`, the result should be `3`.
```
Let O represent coins, P - Pac-Man and E - enemy.
OOOO
OOEO
OOOO
POOO```
Pac-Man cannot cross row 1 and column 2. 

 He can only collect coins from points `(2, 0), (2, 1) and (3, 1)`, like this:
 ```
x is the points that Pac-Man can collect the coins.
OOOO
OOEO
xxOO
PxOO
 ```

# Input/Output


 - `[input]` integer `N`

  The field size.


 - `[input]` integer array `PM`

  Pac-Man's position (pair of integers)


 - `[input]` 2D integer array `enemies`

  Enemies' positions (array of pairs)


 - `[output]` an integer

  Number of coins Pac-Man can collect.
  
  
# More PacMan Katas

 - [Play PacMan: Devour all](https://www.codewars.com/kata/575c29d5fcee86cb8b000136)

 - [Play PacMan 2: The way home](https://www.codewars.com/kata/575ed46e23891f67d90000d8)

Difficulty: EASY
Starter code: def pac_man(N, PM, enemies):
	

Solutions:
def pac_man(size, pacman, enemies):
	(px, py) = pacman
	(mx, my, Mx, My) = (-1, -1, size, size)
	for (x, y) in enemies:
		if x < px and x > mx:
			mx = x
		if y < py and y > my:
			my = y
		if x > px and x < Mx:
			Mx = x
		if y > py and y < My:
			My = y
	return (Mx - mx - 1) * (My - my - 1) - 1


def pac_man(N, PM, enemies):
	dims = [[0, N], [0, N]]
	for pos in enemies:
		for (i, x) in enumerate(pos):
			if PM[i] > x:
				dims[i][0] = max(dims[i][0], x + 1)
			else:
				dims[i][1] = min(dims[i][1], x)
	return (dims[0][1] - dims[0][0]) * (dims[1][1] - dims[1][0]) - 1


def pac_man(n, pm, enemies):
	row = lambda c='O': [c] * n
	grid = [row() for _ in range(n)]
	grid[pm[0]][pm[1]] = 'P'
	for (er, ec) in enemies:
		grid[er] = row('#')
		grid = [['#' if c == ec else v for (c, v) in enumerate(r)] for r in grid]
	for (er, ec) in enemies:
		grid[er][ec] = 'E'
	edges = [pm]
	count = 0
	while edges:
		new_edges = []
		for (er, ec) in edges:
			for (dr, dc) in [(0, 1), (0, -1), (1, 0), (-1, 0)]:
				(r, c) = (er + dr, ec + dc)
				if 0 <= r < n and 0 <= c < n:
					if grid[r][c] == 'O':
						count += 1
						grid[r][c] = '.'
						new_edges.append((r, c))
		edges = new_edges
	return count


def pac_man(N, PM, enemies):
	borders = [[-1, 0], [0, -1], [-1, N - 1], [N - 1, -1], [N, 0], [N, N - 1], [0, N], [N - 1, N]]
	for n in range(1, N - 1):
		borders.append([-1, n])
		borders.append([n, -1])
		borders.append([n, N])
		borders.append([N, n])
	ghosts = []
	for i in enemies:
		x = i[0]
		y = i[1]
		for n in range(N):
			ghosts.append([x, n])
			ghosts.append([n, y])
	possibilities = []
	moved = [PM]
	while moved != []:
		moved2 = moved
		moved = []
		for i in moved2:
			x = i[0]
			y = i[1]
			mon = [[x, y + 1], [x, y - 1], [x + 1, y], [x - 1, y]]
			for m in mon:
				if m not in borders and m not in ghosts:
					if m not in possibilities and m not in moved and (m != PM):
						possibilities.append(m)
						moved.append(m)
	return len(possibilities)


import numpy as np

def count(gamefield, PM, N):
	gamefield[PM[0], PM[1]] = -1
	case1 = 0
	case2 = 0
	case3 = 0
	case4 = 0
	if PM[0] + 1 < N and gamefield[PM[0] + 1, PM[1]] != -1:
		case1 = 1 + count(gamefield, [PM[0] + 1, PM[1]], N)
	if PM[0] - 1 > -1 and gamefield[PM[0] - 1, PM[1]] != -1:
		case2 = 1 + count(gamefield, [PM[0] - 1, PM[1]], N)
	if PM[1] + 1 < N and gamefield[PM[0], PM[1] + 1] != -1:
		case3 = 1 + count(gamefield, [PM[0], PM[1] + 1], N)
	if PM[1] - 1 > -1 and gamefield[PM[0], PM[1] - 1] != -1:
		case4 = 1 + count(gamefield, [PM[0], PM[1] - 1], N)
	return case1 + case2 + case3 + case4

def pac_man(N, PM, enemies):
	if N == 1:
		return 0
	if len(enemies) == 0:
		return N ** 2 - 1
	gamefield = np.ones((N, N))
	gamefield[PM[0], PM[1]] = 7
	for e in enemies:
		gamefield[:, e[1]] = -1
		gamefield[e[0], :] = -1
	print(gamefield)
	return count(gamefield, PM, N)


from bisect import bisect

def pac_man(n, p, es):
	if not es:
		return n * n - 1
	l = len(es)
	(y, x) = list(map(sorted, list(zip(*es))))
	i = bisect(y, p[0])
	hy = y[i] if i < l else n
	ly = y[i - 1] if i > 0 else -1
	i = bisect(x, p[1])
	hx = x[i] if i < l else n
	lx = x[i - 1] if i > 0 else -1
	return (hy - ly - 1) * (hx - lx - 1) - 1


def pac_man(n, pm, enemies):
	(left, right, top, floor) = (-1, n, -1, n)
	for (y, x) in enemies:
		if top < y < pm[0]:
			top = y
		if pm[0] < y < floor:
			floor = y
		if left < x < pm[1]:
			left = x
		if pm[1] < x < right:
			right = x
	return (right - left - 1) * (floor - top - 1) - 1


def pac_man(N, PM, enemies):
	if not enemies:
		return N ** 2 - 1
	rows = []
	columns = []
	for (i, c) in enumerate(enemies):
		rows.append(c[0])
		columns.append(c[1])
	rows = sorted(rows)
	columns = sorted(columns)
	PM = list(map(lambda x: x + 1, PM))
	rows = list(map(lambda x: x + 1, rows))
	columns = list(map(lambda x: x + 1, columns))
	rows_less = list(filter(lambda a: a < PM[0], rows))
	rows_more = list(filter(lambda a: a > PM[0], rows))
	columns_less = list(filter(lambda a: a < PM[1], columns))
	columns_more = list(filter(lambda a: a > PM[1], columns))
	list(rows_more)
	if not rows_more:
		rows_more.append(N + 1)
	if not rows_less:
		rows_less.append(0)
	if not columns_more:
		columns_more.append(N + 1)
	if not columns_less:
		columns_less.append(0)
	y = min(rows_more) - max(rows_less) - 1
	x = min(columns_more) - max(columns_less) - 1
	return x * y - 1


from collections import deque

def pac_man(N, PM, enemies):
	grid = [[2] * N for i in range(N)]
	for enemy in enemies:
		for i in range(N):
			grid[enemy[0]][i] = 'E'
		for j in range(N):
			grid[j][enemy[1]] = 'E'
	directions = [[0, 1], [0, -1], [1, 0], [-1, 0]]
	(queue, ans) = (deque([tuple(PM)]), 0)
	visited = set()
	while queue:
		node = queue.popleft()
		for dirc in directions:
			new_pos = (node[0] + dirc[0], node[1] + dirc[1])
			if 0 <= new_pos[0] < N and 0 <= new_pos[1] < N:
				if grid[new_pos[0]][new_pos[1]] == 2:
					if new_pos not in visited:
						ans += 1
						visited.add(new_pos)
						queue.append(tuple(new_pos))
	return ans - 1 if ans > 0 else 0


def pac_man(N, PM, enemies):
	print(N)
	print(PM)
	print(enemies)
	board = []
	row = []
	column = []
	if enemies == []:
		return N ** 2 - 1
	for i in enemies:
		row.append(PM[1] - i[1])
		column.append(PM[0] - i[0])
	rowMinus = [(PM[1] - N) * -1]
	rowPlus = [PM[1] + 1]
	columnMinus = [(PM[0] - N) * -1]
	columnPlus = [PM[0] + 1]
	for i in row:
		if i < 0:
			rowMinus.append(i * -1)
		else:
			rowPlus.append(i)
	for i in column:
		if i < 0:
			columnMinus.append(i * -1)
		else:
			columnPlus.append(i)
	ColumnD = min(rowPlus) + min(rowMinus) - 1
	RowD = min(columnPlus) + min(columnMinus) - 1
	print('x')
	(print(RowD), print(columnPlus), print(columnMinus))
	print(ColumnD)
	return ColumnD * RowD - 1