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:
2, equal elements. For example, the subarray [2,2] is good.3, equal elements. For example, the subarray [4,4,4] is good.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 <= 1051 <= nums[i] <= 106The dynamic programming approach uses a dp array where dp[i] is true if there is a valid partition for the subarray nums[0..i]. We initialize dp[0] as false because there cannot be a valid partition for a single element. Then, for each i, we check for all valid configurations of subarrays ending at i, i.e., [i-1,i], [i-2,i], and [i-2,i-1,i], updating the dp array accordingly.
This code uses a dynamic programming approach to iterate through the list, checking and updating the validity of partitions.
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Time Complexity: O(n), where n is the length of the array since we iterate through the array once.
Space Complexity: O(n) for the dp array.
The greedy approach attempts to form valid subarrays by traversing the array and greedily picking the largest valid partition at each position. While processing the elements, if a valid subarray is found, the elements involved are ignored in subsequent iterations. Note, this provides a simple but possibly non-optimal solution for certain edge cases.
This solution greedily attempts to find and skip valid subarrays during a single pass through the array, which can be efficient but is less robust than dynamic programming.
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Time Complexity: O(n)
Space Complexity: O(1)
| Approach | Complexity |
|---|---|
| Dynamic Programming Approach | Time Complexity: O(n), where n is the length of the array since we iterate through the array once. |
| Greedy Approach | Time Complexity: O(n) |
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