added the max sum subarray problem solution

Author: namitmalasi

MaxSumSubarray.js

@@ -0,0 +1,49 @@
+
+// Brute Force approach
+function find_maximum_subarray(arr, length) {
+  /*write the code to find the maximum subarray sum
+    Both array and size of array is given */
+
+  let max_sum = arr[0];
+  for (let i = 0; i < length; i++) {
+    let curr_sum = 0;
+    for (let j = i; j < length; j++) {
+      curr_sum += arr[j];
+      if (curr_sum > max_sum) max_sum = curr_sum;
+    }
+  }
+  return max_sum;
+}
+
+console.log(find_maximum_subarray([5, 2, -4, -5, 3, -1, 2, 3, 1], 9));
+
+
+
+// Kadane's Algorithm
+
+// The idea of Kadane’s algorithm is to maintain a variable max_ending_here that stores the
+// maximum sum contiguous subarray ending at current index and a variable max_so_far stores the
+// maximum sum of contiguous subarray found so far, Everytime there is a positive-sum value
+// in max_ending_here compare it with max_so_far and update max_so_far if it is greater than
+// max_so_far.
+
+// So the main Intuition behind Kadane’s Algorithm is,
+
+// 1. The subarray with negative sum is discarded (by assigning max_ending_here = 0 in code).
+// 2. We carry subarray till it gives positive sum.
+
+
+
+function find_maximum_subarray(arr, length) {
+    
+  let max_sum = arr[0];
+  let sum = 0;
+  for (let i = 0; i < length; i++) {
+    sum = sum + arr[i];
+    if (sum > max_sum) max_sum = sum;
+    if (sum < 0) sum = 0;
+  }
+  return max_sum;
+}
+
+console.log(find_maximum_subarray([5, 2, -4, -5, 3, -1, 2, 3, 1], 9));