feat-kadane's algo

[AtharvaPatange]

• Purpose: Implements Kadane’s algorithm to find the maximum-sum contiguous subarray in a numeric vector.

• Time / Space: O(n) time, O(1) extra space (excluding output subarray).

• Main function: kadane(arr) — returns a list: max_sum, start (1-based), end (1-based), and subarray.

• Edge-case handling: correct behavior for empty arrays (returns -Inf and NA indices) and all-negative arrays (returns the largest element).

• Initialization: starts with the first element so single-element and negative-only inputs are handled naturally.

• Tie behavior: returns the first-occurring maximum subarray (current code favors earlier segments).

• Helper utilities: print_kadane_result() for nicely formatted output of results.

• Tests included: mixed signs, all-positive, all-negative, single-element, empty array, and large random array (with timing).

• Variant provided: kadane_circular() — computes max subarray sum for circular/wrap-around arrays (uses total sum − min-subarray trick); indices for wrap-around are not computed in that variant by default.

• Extensibility: easy to adapt to return all maximum subarrays, or to compute wrap-around start/end indices, or to track multiple occurrences.

[Copilot]

Pull Request Overview

This PR implements Kadane's algorithm for finding the maximum-sum contiguous subarray in O(n) time and O(1) space. The implementation includes comprehensive edge-case handling and a circular variant.

Key Changes:

• Core kadane() function with proper handling of empty, single-element, and all-negative arrays
• Circular array variant kadane_circular() for wrap-around maximum subarray detection
• Comprehensive test suite covering edge cases and performance validation

[Copilot]

Pull Request Overview

Copilot reviewed 1 out of 1 changed files in this pull request and generated 3 comments.

[siriak]

Looks good, thanks!