Check if There is a Valid Partition For The Array

Problem 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.

Key Insights

• The problem requires checking for valid partitions based on specific conditions.
• Dynamic programming can be used to keep track of valid partitions up to each index.
• The potential partitioning can be checked in constant time for each index.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(n)

Solution

The approach uses dynamic programming to determine if a valid partition exists for the array. We maintain a boolean array dp where dp[i] indicates whether the subarray nums[0:i] can be partitioned into valid segments. The algorithm iterates through the array and checks the last one or two elements to see if they can form valid segments.

• Data Structures Used: An array dp for storing boolean values indicating valid partitions.
• Algorithm: Dynamic programming to build up the solution by checking the conditions for each partition.

Code Solutions