update 53 java

Author: yennanliu

README.md

@@ -1031,7 +1031,7 @@
 
 |  #  | Title           |  Solution       |  Time           | Space           | Difficulty    | Tag          | Status| 
 |-----|---------------- | --------------- | --------------- | --------------- | ------------- |--------------|-----|
-053| [Maximum Subarray](https://leetcode.com/problems/maximum-subarray/)| [Python](./leetcode_python/Dynamic_Programming/maximum-subarray.py), [Java](./leetcode_java/src/main/java/LeetCodeJava/Greedy/MaximumSubarray.java)  | _O(n)_     | _O(1)_    | Medium  |Curated Top 75, brute force, divied & conquer, `DP`,`dp basic`,`amazon`,`fb`| AGAIN************* (7)
+053| [Maximum Subarray](https://leetcode.com/problems/maximum-subarray/)| [Python](./leetcode_python/Dynamic_Programming/maximum-subarray.py), [Java](./leetcode_java/src/main/java/LeetCodeJava/Greedy/MaximumSubarray.java)  | _O(n)_     | _O(1)_    | Medium  |Curated Top 75, brute force, pre-sum array,`dp basic`,`amazon`,`fb`| AGAIN************* (7)
 062| [Unique Paths](https://leetcode.com/problems/unique-paths/)| [Python](./leetcode_python/Dynamic_Programming/unique-paths.py), [Java](./leetcode_java/src/main/java/LeetCodeJava/DynamicProgramming/UniquePaths.java)  | _O(m * n)_| _O(m + n)_   | Medium|Curated Top 75, `dp`, `basic`, fb, google, apple, amazon, m$| AGAIN**** (2)
 063| [Unique Paths II](https://leetcode.com/problems/unique-paths-ii/) | [Python](./leetcode_python/Dynamic_Programming/unique-paths-ii.py)  |  _O(m * n)_ | _O(m + n)_   | Medium |`trick`, check `#062 Unique Paths`, `amazon`|  AGAIN* 
 064| [Minimum Path Sum](https://leetcode.com/problems/minimum-path-sum/)|  [Python](./leetcode_python/Dynamic_Programming/minimum-path-sum.py) | _O(m * n)_ | _O(m + n)_  | Medium |`DP`, `amazon`| AGAIN* 

leetcode_java/src/main/java/LeetCodeJava/Greedy/MaximumSubarray.java

@@ -86,6 +86,34 @@ public int maxSubArray(int[] nums) {
         return maxSum;
     }
 
+    // V0'-1
+    // IDEA : PRE-SUM ARRAY (fixed by gpt)
+    public int maxSubArray_0_1_1(int[] nums) {
+        if (nums == null || nums.length == 0) {
+            throw new IllegalArgumentException("Input array cannot be null or empty");
+        }
+
+        int n = nums.length;
+        int[] prefixSum = new int[n + 1];
+
+        // Build the prefix sum array
+        for (int i = 0; i < n; i++) {
+            prefixSum[i + 1] = prefixSum[i] + nums[i];
+        }
+
+        int maxSum = Integer.MIN_VALUE;
+        int minPrefixSum = 0;
+
+        // Calculate max subarray sum using prefix sums
+        for (int i = 1; i <= n; i++) {
+            maxSum = Math.max(maxSum, prefixSum[i] - minPrefixSum);
+            minPrefixSum = Math.min(minPrefixSum, prefixSum[i]);
+        }
+
+        return maxSum;
+    }
+
+
     // V0'
     // IDEA : BRUTE FORCE
     // https://www.bilibili.com/video/BV1aY4y1Z7ya/?share_source=copy_web&vd_source=49348a1975630e1327042905e52f488a