Introduction

In this blog post, we will explore how to solve the LeetCode problem "659" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

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.

Explanation

Here's the breakdown of the approach and the Python code:

• High-Level Approach:

  • Iterate through the input array nums. Maintain two dictionaries: freq to store the frequency of each number and tails to store the number of subsequences ending with a particular number.
  • For each number num, check if it can be appended to an existing subsequence (i.e., if tails[num - 1] > 0). If so, decrement tails[num - 1] and increment tails[num].
  • If num cannot be appended to an existing subsequence, check if a new subsequence of length 3 or more can be started. This requires freq[num + 1] > 0 and freq[num + 2] > 0. If so, decrement freq[num + 1] and freq[num + 2] and increment tails[num + 2].
  • If neither of the above conditions is met, it means that num cannot be part of any valid subsequence, so return False.

• Complexity:

  • Runtime Complexity: O(n), where n is the length of the input array.
  • Storage Complexity: O(n), where n is the range of numbers in the input array which effectively translates to the number of unique elements.

Code

    from collections import defaultdict

def is_possible(nums):
    freq = defaultdict(int)
    tails = defaultdict(int)

    for num in nums:
        freq[num] += 1

    for num in nums:
        if freq[num] == 0:
            continue

        freq[num] -= 1

        if tails[num - 1] > 0:
            tails[num - 1] -= 1
            tails[num] += 1
        elif freq[num + 1] > 0 and freq[num + 2] > 0:
            freq[num + 1] -= 1
            freq[num + 2] -= 1
            tails[num + 2] += 1
        else:
            return False

    return True