max-chunks-to-make-sorted-ii.py

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

# This question is the same as "Max Chunks to Make Sorted"
# except the integers of the given array are not necessarily distinct,
# the input array could be up to length 2000, and the elements could be up to 10**8.
#
# Given an array arr of integers (not necessarily distinct),
# we split the array into some number of "chunks" (partitions),
# and individually sort each chunk.
# After concatenating them, the result equals the sorted array.
#
# What is the most number of chunks we could have made?
#
# Example 1:
#
# Input: arr = [5,4,3,2,1]
# Output: 1
# Explanation:
# Splitting into two or more chunks will not return the required result.
# For example, splitting into [5, 4], [3, 2, 1] will result in [4, 5, 1, 2, 3], which isn't sorted.
# Example 2:
#
# Input: arr = [2,1,3,4,4]
# Output: 4
# Explanation:
# We can split into two chunks, such as [2, 1], [3, 4, 4].
# However, splitting into [2, 1], [3], [4], [4] is the highest number of chunks possible.
#
# Note:
# - arr will have length in range [1, 2000].
# - arr[i] will be an integer in range [0, 10**8].

class Solution(object):
    def maxChunksToSorted(self, arr):
        """
        :type arr: List[int]
        :rtype: int
        """
        def compare(i1, i2):
            return arr[i1]-arr[i2] if arr[i1] != arr[i2] else i1-i2
        
        idxs = [i for i in xrange(len(arr))]
        result, max_i = 0, 0
        for i, v in enumerate(sorted(idxs, cmp=compare)):
            max_i = max(max_i, v)
            if max_i == i:
                result += 1
        return result