5 Best Ways to Find the Most Competitive Subsequence in Python

💡 Problem Formulation: Given an array of integers, the task is to find the most competitive subsequence of a specified length. A subsequence is considered competitive if it is lexicographically smaller than all other subsequences of the same length. For example, given the array [3, 5, 2, 6] and a subsequence length of 2, the most competitive subsequence is [2, 6].

Method 1: Greedy Approach Using Stack

In this method, we utilize a stack to keep track of the most competitive subsequence by following a greedy approach. The function findCompetitiveSubsequence takes an array and the required subsequence length as parameters, ensuring the elements in the stack form the most competitive subsequence while maintaining the required length.

Here’s an example:

def findCompetitiveSubsequence(arr, k):
    stack = []
    for i, num in enumerate(arr):
        while stack and num = k:
            stack.pop()
        if len(stack) < k:
            stack.append(num)
    return stack

print(findCompetitiveSubsequence([3, 5, 2, 6], 2))

Output of this code snippet:

[2, 6]

This code iterates over the array, and for each element, it checks if the current number is smaller than the last number in the stack, and if there is room to pop elements to make space for future potentially smaller numbers. Then, it ensures the final subsequence has the desired length by only pushing elements onto the stack when there is room.

Method 2: Dynamic Programming

Dynamic programming can be employed to build the most competitive subsequence by iteratively picking the smallest possible element for each position in the subsequence. The function dynamicCompetitiveSubsequence builds it by analyzing the smallest numbers at each step with the consideration of remaining elements and subsequence length.

Here’s an example:

Output of this code snippet:

Method 3: Brute Force

Method 4: Divide and Conquer

Bonus One-Liner Method 5: Pythonic Way with List Comprehensions

<!– An innovative one-liner solution using Python's powerful list comprehension feature –>

Summary/Discussion

Method 1: Greedy Approach Using Stack. Strengths: Efficient, Intuitive. Weaknesses: Requires understanding of stack discipline.