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659. Split Array into Consecutive Subsequences

Difficulty Topics

Description

You are given an integer array nums that is sorted in non-decreasing order.

Determine if it is possible to split nums into one or more subsequences such that both of the following conditions are true:

  • Each subsequence is a consecutive increasing sequence (i.e. each integer is exactly one more than the previous integer).
  • All subsequences have a length of 3 or more.

Return true if you can split nums according to the above conditions, or false otherwise.

A subsequence of an array is a new array that is formed from the original array by deleting some (can be none) of the elements without disturbing the relative positions of the remaining elements. (i.e., [1,3,5] is a subsequence of [1,2,3,4,5] while [1,3,2] is not).

 

Example 1:

Input: nums = [1,2,3,3,4,5]
Output: true
Explanation: nums can be split into the following subsequences:
[1,2,3,3,4,5] --> 1, 2, 3
[1,2,3,3,4,5] --> 3, 4, 5

Example 2:

Input: nums = [1,2,3,3,4,4,5,5]
Output: true
Explanation: nums can be split into the following subsequences:
[1,2,3,3,4,4,5,5] --> 1, 2, 3, 4, 5
[1,2,3,3,4,4,5,5] --> 3, 4, 5

Example 3:

Input: nums = [1,2,3,4,4,5]
Output: false
Explanation: It is impossible to split nums into consecutive increasing subsequences of length 3 or more.

 

Constraints:

  • 1 <= nums.length <= 104
  • -1000 <= nums[i] <= 1000
  • nums is sorted in non-decreasing order.

Solution

split-array-into-consecutive-subsequences.py
class Solution:
    def isPossible(self, nums: List[int]) -> bool:
        once = defaultdict(int)
        twice = defaultdict(int)
        complete = defaultdict(int)

        for num in nums:
            if once[num - 1]:
                once[num - 1] -= 1
                twice[num] += 1
            elif twice[num - 1]:
                twice[num - 1] -= 1
                complete[num] += 1
            elif complete[num - 1]:
                complete[num - 1] -= 1
                complete[num] += 1
            else:
                once[num] += 1

        return sum(once.values()) + sum(twice.values()) == 0