[Algorithm] Maximum Contiguous Subarray algorithm implementation using TypeScript / JavaScript

Posted 2021-02-02 Answer1215

The maximum subarray problem is one of the nicest examples of dynamic programming application.

In this lesson we cover an example of how this problem might be presented and what your chain of thought should be to tackle this problem efficiently.

 

 /**
  * Maximum Contiguous subarray algorithm
  * 
  * Max(i) = Max(i-1) + v(i)
  * Max(i-1) < 0 ? v(i) : Max(i-1)
  * 
  * Combining
---------
maxInc(i) = maxInc(i - 1) > 0 ? maxInc(i - 1) + val(i) : val(i)
max(i) = maxInc(i) > max(i - 1) ? maxInc(i) : max(i - 1)
  */

const numbers = [-2, 1, 3, 4, -1, 2, 1, -5, 4];
function maxSubArray (ary) {
    if (ary.length === 0) {
        return [];
    }

    let maxInc = ary[0];
    let max = ary[0];
    let maxStartInx = 0;
    let maxEndInx = 0;

    for (let i = 0; i < ary.length; i++) {
        const val = ary[i];

        maxInc = Math.max(maxInc + val, val);
        max = Math.max(max, maxInc);

        if (val === max) {
            maxStartInx = i
        }

        if (maxInc === max) {
            maxEndInx = i
        }

        return Array.slice(maxStartInx, maxEndInx + 1)
    }
}
console.log(‘maxSubArray‘, maxSubArray(numbers));