maximum-length-of-pair-chain.py

# Time:  O(nlogn)
# Space: O(1)

# You are given n pairs of numbers.
# In every pair, the first number is always smaller than the second number.
#
# Now, we define a pair (c, d) can follow another pair (a, b)
# if and only if b < c. Chain of pairs can be formed in this fashion.
#
# Given a set of pairs, find the length longest chain which can be formed.
# You needn't use up all the given pairs. You can select pairs in any order.
#
# Example 1:
# Input: [[1,2], [2,3], [3,4]]
# Output: 2
# Explanation: The longest chain is [1,2] -> [3,4]
# Note:
# The number of given pairs will be in the range [1, 1000].

class Solution(object):
    def findLongestChain(self, pairs):
        """
        :type pairs: List[List[int]]
        :rtype: int
        """
        pairs.sort(key=lambda x: x[1])
        cnt, i = 0, 0
        for j in xrange(len(pairs)):
            if j == 0 or pairs[i][1] < pairs[j][0]:
                cnt += 1
                i = j
        return cnt