Kadane's algorithm explained

Question

Could someone take me through what is happening here in Kadane's algorithm? Wanted to check my understanding. here's how I see it.

you are looping through the array, and each time you set the ans variable to the largest value seen, until that value becomes negative, then ans becomes zero.

At the same time, the sum variable is overwritten each time through the loop, to the max between previously seen sums or the largest 'ans' so far. Once the loop is finished executing you will have the largest sum or answer seen so far!

var sumArray = function(array) {
      var ans = 0;
      var sum = 0;
      //loop through the array.


      for (var i = 0; i < array.length; i++) {
        //this is to make sure that the sum is not negative. 
        ans = Math.max(0, ans + array[i]);

        //set the sum to be overwritten if something greater appears.
        sum = Math.max(sum, ans)
      }

      return sum;

    };

Answer 1

Consider tracing the values:

var maximumSubArray = function(array) {
    var ans = 0;
    var sum = 0;

    console.log(ans, sum);
    for (var i = 0; i < array.length; i++) {

        ans = Math.max(0, ans + array[i]);
        sum = Math.max(sum, ans);
        console.log(ans, sum, array[i]);
    }
    console.log(ans, sum);
    return sum;

};

maximumSubArray([-2, 1, -3, 4, -1, 2, 1, -5, 4]);

Prints:

0 0
0 0 -2
1 1 1
0 1 -3
4 4 4
3 4 -1
5 5 2
6 6 1
1 6 -5
5 6 4
5 6

The first column is ans, which is the sum of the current subarray. The second is sum, representing the sum of the greatest seen so far. The third is the element that was just visited. You can see that the contiguous subarray with the largest sum is 4, −1, 2, 1, with sum 6.

The example is from Wikipedia.

The following is a translation of the code given in Wikipedia under the paragraph: "A variation of the problem that does not allow zero-length subarrays to be returned, in the case that the entire array consists of negative numbers, can be solved with the following code:" [EDIT: Small bug fixed in the code below]

var maximumSubArray = function(array) {
    var ans = array[0];
    var sum = array[0];

    console.log(ans, sum);
    for (var i = 1; i < array.length; i++) {

        ans = Math.max(array[i], ans + array[i]);
        sum = Math.max(sum, ans);
        console.log(ans, sum, array[i]);
    }
    console.log(ans, sum);
    return sum;

};

See that:

> maximumSubArray([-10, -11, -12])
-10 -10
-10 -10 -11
-10 -10 -12
-10 -10
-10

The last number is the expected result. The others are as in the previous example.