[Practice] Maximum Subarray Sum

[lpatmo]

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

For example, if the given array is {-2, -5, 6, -2, -3, 1, 5, -6}, then the maximum subarray sum is 7 (see highlighted elements).```

[lpatmo]

//BRUTE FORCE O(N^2)
function maxSumBruteForce(arr) {
  let max = -Infinity;
  let sum = 0;
  for (let i = 0; i < arr.length; i++) {
    for (let j = i; j < arr.length; j++) {
      //0 to 0, 0 to 1, 0 to 2... etc.
      //1 to 1, 1 to 2, 1 to 3, etc. up to .length
      //2 to 2, etc.
      //if (i <= j) { //only need this if j started at 0
        sum += arr[j];
        console.log(sum+" i: " + i + " j: "+j)
     // }
      max = Math.max(sum, max)
    }
    sum = 0;
  }
  return max;
}
console.log("Answer "+maxSumBruteForce(arr))

//Alternative:
  //find midpoint
  //find max on left side
  //find max on right side
  //find max around the midpoint

/*Initialize:
    max_so_far = 0
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_ending_here < 0)
            max_ending_here = 0
  (c) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
return max_so_far*/

//Kadene's solution
function maxSumKadene(arr) {
  let maxCurrent = 0;
  let maxFinal = 0;
  for (let i = 0; i < arr.length; i++) {
    maxCurrent = maxCurrent + arr[i];
    if (maxCurrent < 0) {
      maxCurrent = 0;
    }
    if (maxFinal < maxCurrent) {
      maxFinal = maxCurrent;
    }
  }
  return maxFinal;
}
console.log("Answer "+maxSumKadene(arr))