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2369. Check if There is a Valid Partition For The Array

Difficulty Topics

Description

You are given a 0-indexed integer array nums. You have to partition the array into one or more contiguous subarrays.

We call a partition of the array valid if each of the obtained subarrays satisfies one of the following conditions:

  1. The subarray consists of exactly 2 equal elements. For example, the subarray [2,2] is good.
  2. The subarray consists of exactly 3 equal elements. For example, the subarray [4,4,4] is good.
  3. The subarray consists of exactly 3 consecutive increasing elements, that is, the difference between adjacent elements is 1. For example, the subarray [3,4,5] is good, but the subarray [1,3,5] is not.

Return true if the array has at least one valid partition. Otherwise, return false.

 

Example 1:

Input: nums = [4,4,4,5,6]
Output: true
Explanation: The array can be partitioned into the subarrays [4,4] and [4,5,6].
This partition is valid, so we return true.

Example 2:

Input: nums = [1,1,1,2]
Output: false
Explanation: There is no valid partition for this array.

 

Constraints:

  • 2 <= nums.length <= 105
  • 1 <= nums[i] <= 106

Solution

check-if-there-is-a-valid-partition-for-the-array.py
class Solution:
    def validPartition(self, nums: List[int]) -> bool:
        N = len(nums)

        @cache
        def go(index):
            if index == N: return True

            res = False

            if index + 1 < N and nums[index] == nums[index + 1]:
                res |= go(index + 2)

            if index + 2 < N and nums[index] == nums[index + 1] == nums[index + 2]:
                res |= go(index + 3)

            if index + 2 < N and nums[index] + 1 == nums[index + 1] and nums[index + 1] + 1 == nums[index + 2]:
                res |= go(index + 3)

            return res

        return go(0)