leetcode-53-maximum-subarray.swift

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https://leetcode.com/problems/maximum-subarray/


Given an integer array nums, find the contiguous subarray (containing at least one number) which has the largest sum and return its sum.

Example:

Input: [-2,1,-3,4,-1,2,1,-5,4],
Output: 6
Explanation: [4,-1,2,1] has the largest sum = 6.
Follow up:

If you have figured out the O(n) solution, try coding another solution using the divide and conquer approach, which is more subtle.

*/

/**
Big O Annotation
Time complexity O(n) where n is the amount of elements in nums.
Space complexity O(1) as we're at most storing 2 variables at the same time.
*/
func maxSubArray(_ nums: [Int]) -> Int {
	
    /**
    If we have nothing in the array, 
    there's nothing to return.
    */
    guard nums.count > 0 else {
        return 0
    }

    /**
    We need a reference to the current
    maximum number and the largest maximum 
    number generally, as we're looking for 
    "contiguous subarray"

    Intialized with nums first element.
    */ 
    var maximumLocal: Int = nums[0] 
    var maximumGlobal: Int = nums[0] 

    // Iterate through the array from 1
    for index in 1..<nums.count {
        
        /**
        First we want to check if current maximum
        is larger than the one before.

        In the first iteration that of an example array of:
        [-2,1,-3,4,-1,2,1,-5,4], we'd be checking max(1, -2 + 1).

        In this example 1 or just nums[index] is the larger subarray
        as [-2, 1] is combined -1.
        */
        maximumLocal = max(nums[index], maximumLocal + nums[index])
    
        /**
        Then we need to check, if our new maximumLocal
        is larger than our formerly stored maximumGlobal.

        In above's example of [1], we've had [-2] as our
        maximumGlobal so now we need to update maximumGlobal to 1.
        */
        if maximumLocal > maximumGlobal {
            maximumGlobal = maximumLocal
        }
    }

    return maximumGlobal
}