friends-of-appropriate-ages.py

# Time:  O(a^2 + n), a is the number of ages,
#                    n is the number of people
# Space: O(a)

# Some people will make friend requests.
# The list of their ages is given and ages[i] is the age of the ith person.
#
# Person A will NOT friend request person B (B != A)
# if any of the following conditions are true:
#
# age[B] <= 0.5 * age[A] + 7
# age[B] > age[A]
# age[B] > 100 && age[A] < 100
# Otherwise, A will friend request B.
#
# Note that if A requests B, B does not necessarily request A.
# Also, people will not friend request themselves.
#
# How many total friend requests are made?
#
# Example 1:
#
# Input: [16,16]
# Output: 2
# Explanation: 2 people friend request each other.
# Example 2:
#
# Input: [16,17,18]
# Output: 2
# Explanation: Friend requests are made 17 -> 16, 18 -> 17.
# Example 3:
#
# Input: [20,30,100,110,120]
# Output:
# Explanation: Friend requests are made 110 -> 100, 120 -> 110, 120 -> 100.
#
# Notes:
# - 1 <= ages.length <= 20000.
# - 1 <= ages[i] <= 120.

try:
    xrange          # Python 2
except NameError:
    xrange = range  # Python 3

import collections


class Solution(object):
    def numFriendRequests(self, ages):
        """
        :type ages: List[int]
        :rtype: int
        """
        def request(a, b):
            return 0.5*a+7 < b <= a

        c = collections.Counter(ages)
        return sum(int(request(a, b)) * c[a]*(c[b]-int(a == b))
                   for a in c
                   for b in c)