You are given a list of preferences for n friends, where n is always even.
For each person i, preferences[i] contains a list of friends sorted in the order of preference. In other words, a friend earlier in the list is more preferred than a friend later in the list. Friends in each list are denoted by integers from 0 to n-1.
All the friends are divided into pairs. The pairings are given in a list pairs, where pairs[i] = [xi, yi] denotes xi is paired with yi and yi is paired with xi.
However, this pairing may cause some of the friends to be unhappy. A friend x is unhappy if x is paired with y and there exists a friend u who is paired with v but:

x prefers u over y, and
u prefers x over v.

Return the number of unhappy friends.
 
Example 1:
Input: n = 4, preferences = [[1, 2, 3], [3, 2, 0], [3, 1, 0], [1, 2, 0]], pairs = [[0, 1], [2, 3]]
Output: 2
Explanation:
Friend 1 is unhappy because:
- 1 is paired with 0 but prefers 3 over 0, and
- 3 prefers 1 over 2.
Friend 3 is unhappy because:
- 3 is paired with 2 but prefers 1 over 2, and
- 1 prefers 3 over 0.
Friends 0 and 2 are happy.

Example 2:
Input: n = 2, preferences = [[1], [0]], pairs = [[1, 0]]
Output: 0
Explanation: Both friends 0 and 1 are happy.

Example 3:
Input: n = 4, preferences = [[1, 3, 2], [2, 3, 0], [1, 3, 0], [0, 2, 1]], pairs = [[1, 3], [0, 2]]
Output: 4

 
Constraints:

2 <= n <= 500
n is even.
preferences.length == n
preferences[i].length == n - 1
0 <= preferences[i][j] <= n - 1
preferences[i] does not contain i.
All values in preferences[i] are unique.
pairs.length == n/2
pairs[i].length == 2
xi != yi
0 <= xi, yi <= n - 1
Each person is contained in exactly one pair.

Difficulty: MEDIUM_HARD
Starter code: class Solution:
    def unhappyFriends(self, n: int, preferences: List[List[int]], pairs: List[List[int]]) -> int:
        

Solutions:
class Solution:

	def preferences_to_scores(self, preferences):
		scores = {}
		for (u, up) in enumerate(preferences):
			for (s, v) in enumerate(up):
				scores[u, v] = s
		return scores

	def unhappy_friends(self, scores, a, b):
		ret = set()
		for (ai, aa) in enumerate(a):
			af = a[1 - ai]
			for (bi, bb) in enumerate(b):
				bf = b[1 - bi]
				if scores[aa, bb] < scores[aa, af] and scores[bb, aa] < scores[bb, bf]:
					ret.add(aa)
					ret.add(bb)
		return ret

	def unhappyFriends(self, n: int, preferences: List[List[int]], pairs: List[List[int]]) -> int:
		scores = self.preferences_to_scores(preferences)
		ret = set()
		for (i, a) in enumerate(pairs):
			for j in range(i):
				b = pairs[j]
				ret |= self.unhappy_friends(scores, a, b)
		return len(ret)


class Solution:

	def unhappyFriends(self, n: int, preferences: List[List[int]], pairs: List[List[int]]) -> int:
		preference_list = [[0 for _ in range(n)] for _ in range(n)]
		for x in range(n):
			for (i, y) in enumerate(preferences[x]):
				preference_list[x][y] = n - i - 1
		unhappy = {}
		for i in range(n // 2):
			(x, y) = pairs[i]
			for j in range(n // 2):
				(u, v) = pairs[j]
				if i != j:
					if preference_list[x][y] < preference_list[x][u] and preference_list[u][x] > preference_list[u][v] or (preference_list[x][y] < preference_list[x][v] and preference_list[v][u] < preference_list[v][x]):
						unhappy[x] = 1
					if preference_list[y][x] < preference_list[y][u] and preference_list[u][y] > preference_list[u][v] or (preference_list[y][x] < preference_list[y][v] and preference_list[v][u] < preference_list[v][y]):
						unhappy[y] = 1
		res = len(unhappy)
		return res


class Solution:

	def unhappyFriends(self, n: int, preferences: List[List[int]], pairs: List[List[int]]) -> int:
		pref = {}
		for i in range(len(preferences)):
			pref[i] = {}
			plist = preferences[i]
			for j in range(len(plist)):
				pref[i][plist[j]] = j
		print(pref)
		unhappy = set()
		for i in range(len(pairs)):
			for j in range(len(pairs)):
				if i == j:
					continue
				for x in pairs[i]:
					y = pairs[i][1] if x == pairs[i][0] else pairs[i][0]
					for u in pairs[j]:
						v = pairs[j][1] if u == pairs[j][0] else pairs[j][0]
						if pref[x][y] > pref[x][u] and pref[u][v] > pref[u][x]:
							unhappy.add(x)
		return len(unhappy)


class Solution:

	def unhappyFriends(self, n: int, P: List[List[int]], A: List[List[int]]) -> int:
		unhappy = set()
		for i in range(n // 2):
			for j in range(i + 1, n // 2):
				(Ai0, Ai1, Aj0, Aj1) = (A[i][0], A[i][1], A[j][0], A[j][1])
				if P[Ai0].index(Ai1) > P[Ai0].index(Aj0) and P[Aj0].index(Aj1) > P[Aj0].index(Ai0):
					unhappy.add(Ai0)
					unhappy.add(Aj0)
				(Ai0, Ai1, Aj0, Aj1) = (A[i][1], A[i][0], A[j][0], A[j][1])
				if P[Ai0].index(Ai1) > P[Ai0].index(Aj0) and P[Aj0].index(Aj1) > P[Aj0].index(Ai0):
					unhappy.add(Ai0)
					unhappy.add(Aj0)
				(Ai0, Ai1, Aj0, Aj1) = (A[i][0], A[i][1], A[j][1], A[j][0])
				if P[Ai0].index(Ai1) > P[Ai0].index(Aj0) and P[Aj0].index(Aj1) > P[Aj0].index(Ai0):
					unhappy.add(Ai0)
					unhappy.add(Aj0)
				(Ai0, Ai1, Aj0, Aj1) = (A[i][1], A[i][0], A[j][1], A[j][0])
				if P[Ai0].index(Ai1) > P[Ai0].index(Aj0) and P[Aj0].index(Aj1) > P[Aj0].index(Ai0):
					unhappy.add(Ai0)
					unhappy.add(Aj0)
		return len(unhappy)


class Solution:

	def unhappyFriends(self, n: int, preferences: List[List[int]], pairs: List[List[int]]) -> int:
		unhappy = [0] * n
		for i in range(n // 2):
			(a, b) = pairs[i]
			(b_a_idx, a_b_idx) = (preferences[b].index(a), preferences[a].index(b))
			for j in range(i + 1, n // 2):
				(c, d) = pairs[j]
				c_a_idx = preferences[c].index(a)
				c_b_idx = preferences[c].index(b)
				c_d_idx = preferences[c].index(d)
				d_a_idx = preferences[d].index(a)
				d_b_idx = preferences[d].index(b)
				d_c_idx = preferences[d].index(c)
				a_c_idx = preferences[a].index(c)
				a_d_idx = preferences[a].index(d)
				b_c_idx = preferences[b].index(c)
				b_d_idx = preferences[b].index(d)
				if c_a_idx < c_d_idx and a_c_idx < a_b_idx:
					unhappy[a] = unhappy[c] = 1
				if d_a_idx < d_c_idx and a_d_idx < a_b_idx:
					unhappy[a] = unhappy[d] = 1
				if c_b_idx < c_d_idx and b_c_idx < b_a_idx:
					unhappy[b] = unhappy[c] = 1
				if d_b_idx < d_c_idx and b_d_idx < b_a_idx:
					unhappy[b] = unhappy[d] = 1
		return sum(unhappy)


class Solution:

	def unhappyFriends(self, n: int, preferences: List[List[int]], pairs: List[List[int]]) -> int:
		idx_table = collections.defaultdict(lambda : collections.defaultdict(int))
		for i in range(n):
			for (idx, person) in enumerate(preferences[i]):
				idx_table[i][person] = idx
		unhappy = [0] * n
		for i in range(n // 2):
			(a, b) = pairs[i]
			(b_a_idx, a_b_idx) = (idx_table[b][a], idx_table[a][b])
			for j in range(i + 1, n // 2):
				(c, d) = pairs[j]
				c_a_idx = idx_table[c][a]
				c_b_idx = idx_table[c][b]
				c_d_idx = idx_table[c][d]
				d_a_idx = idx_table[d][a]
				d_b_idx = idx_table[d][b]
				d_c_idx = idx_table[d][c]
				a_c_idx = idx_table[a][c]
				a_d_idx = idx_table[a][d]
				b_c_idx = idx_table[b][c]
				b_d_idx = idx_table[b][d]
				if c_a_idx < c_d_idx and a_c_idx < a_b_idx:
					unhappy[a] = unhappy[c] = 1
				if d_a_idx < d_c_idx and a_d_idx < a_b_idx:
					unhappy[a] = unhappy[d] = 1
				if c_b_idx < c_d_idx and b_c_idx < b_a_idx:
					unhappy[b] = unhappy[c] = 1
				if d_b_idx < d_c_idx and b_d_idx < b_a_idx:
					unhappy[b] = unhappy[d] = 1
		return sum(unhappy)


class Solution:

	def unhappyFriends(self, n: int, preferences: List[List[int]], pairs: List[List[int]]) -> int:
		res = set()
		mem = [[0 for _ in range(n)] for _ in range(n)]
		for i in range(n):
			for j in range(n - 1):
				mem[i][preferences[i][j]] = j + 1
		for i in range(n // 2):
			x = pairs[i][0]
			y = pairs[i][1]
			for j in range(i + 1, n // 2):
				u = pairs[j][0]
				v = pairs[j][1]
				if mem[x][u] < mem[x][y] and mem[u][x] < mem[u][v]:
					res.add(x)
					res.add(u)
				if mem[x][v] < mem[x][y] and mem[v][x] < mem[v][u]:
					res.add(x)
					res.add(v)
				if mem[y][u] < mem[y][x] and mem[u][y] < mem[u][v]:
					res.add(y)
					res.add(u)
				if mem[y][v] < mem[y][x] and mem[v][y] < mem[v][u]:
					res.add(y)
					res.add(v)
		return len(res)


import numpy as np

class Solution:

	def check_happy(self, x, y, u, v, fmatrix, unhappy):
		if fmatrix[x][u] > fmatrix[x][y] and fmatrix[u][x] > fmatrix[u][v]:
			unhappy.add(x)
			unhappy.add(u)

	def unhappyFriends(self, n, preferences, pairs) -> int:
		if n == 2:
			return 0
		unhappy = set()
		fmatrix = np.zeros((n, n), dtype=int)
		for (i, friendpref) in enumerate(preferences):
			for (j, pref_ind) in enumerate(friendpref):
				fmatrix[i][pref_ind] = n - 1 - j
		for i in range(n // 2 - 1):
			for j in range(i + 1, n // 2):
				(x, y, u, v) = (pairs[i][0], pairs[i][1], pairs[j][0], pairs[j][1])
				self.check_happy(x, y, u, v, fmatrix, unhappy)
				self.check_happy(x, y, v, u, fmatrix, unhappy)
				self.check_happy(y, x, u, v, fmatrix, unhappy)
				self.check_happy(y, x, v, u, fmatrix, unhappy)
		return len(unhappy)


class Solution:

	def get_pair(self, i):
		for j in self.pairs:
			if i in j:
				for k in j:
					if k != i:
						return k

	def t_happy(self, t, i):
		pair = self.get_pair(t)
		for j in self.prefer[t]:
			if j == pair:
				return True
			if j == i:
				return False

	def happy(self, i, p):
		prefer = self.prefer[i]
		if prefer[0] == p:
			return True
		for j in range(1, len(prefer)):
			if not self.t_happy(prefer[j - 1], i):
				return False
			if prefer[j] == p:
				return True

	def unhappyFriends(self, n: int, preferences: List[List[int]], pairs: List[List[int]]) -> int:
		self.prefer = preferences
		self.pairs = pairs
		count = 0
		for i in range(n):
			p = self.get_pair(i)
			if not self.happy(i, p):
				count += 1
		return count