feat: solve maximum subarray

maximum-subarray/GangBean.java

@@ -0,0 +1,28 @@
+class Solution {
+    public int maxSubArray(int[] nums) {
+        /**
+        1. understanding
+        - integer array nums
+        - find largest subarray sum
+        2. starategy
+        - calculate cumulative sum
+        - mem[i+1] = num[i+1] + mem[i] if (num[i+1] + mem[i] >= 0) else num[i+1]
+        3. complexity
+        - time: O(N)
+        - space: O(1)
+        */
+        int prev = 0;
+        int curr = 0;
+        int max = Integer.MIN_VALUE;
+        for (int i = 0 ; i < nums.length; i++) {
+            curr = nums[i];
+            if (prev >= 0) {
+                curr += prev;
+            }
+            max = Math.max(max, curr);
+            prev = curr;
+        }
+        return max;
+    }
+}
+