diff --git a/problems/0416.分割等和子集.md b/problems/0416.分割等和子集.md
index 8115e18e..54d90612 100644
--- a/problems/0416.分割等和子集.md
+++ b/problems/0416.分割等和子集.md
@@ -218,8 +218,12 @@ class Solution {
         for(int i = 0; i < n; i++) {
             for(int j = target; j >= nums[i]; j--) {
                 //物品 i 的重量是 nums[i]，其价值也是 nums[i]
-                dp[j] = Math.max(dp[j], dp[j-nums[i]] + nums[i]);
+                dp[j] = Math.max(dp[j], dp[j - nums[i]] + nums[i]);
             }
+           
+            //剪枝一下，每一次完成內層的for-loop，立即檢查是否dp[target] == target，優化時間複雜度（26ms -> 20ms）
+            if(dp[target] == target)
+                return true;
         }
         return dp[target] == target;
     }
@@ -294,6 +298,61 @@ false true false false false true true false false false false false
 false true false false false true true false false false false true 
 false true false false false true true false false false true true 
 ```
+二維數組整數版本
+```Java
+class Solution {
+    public boolean canPartition(int[] nums) {
+        //using 2-D DP array.
+        int len = nums.length;
+        //check edge cases;
+        if(len == 0)
+            return false;
+
+        int sum = 0;
+        for (int num : nums)
+            sum += num;
+        //we only deal with even numbers. If sum is odd, return false;
+        if(sum % 2 == 1)
+            return false;
+        
+        int target = sum / 2;
+        int[][] dp = new int[nums.length][target + 1];
+
+        // for(int j = 0; j <= target; j++){
+        //     if(j < nums[0])
+        //         dp[0][j] = 0;
+        //     else
+        //         dp[0][j] = nums[0];
+        // }
+
+        //initialize dp array
+        for(int j = nums[0]; j <= target; j++){
+            dp[0][j] = nums[0];
+        }
+
+        for(int i = 1; i < len; i++){
+            for(int j = 0; j <= target; j++){
+                if (j < nums[i]) 
+                    dp[i][j] = dp[i - 1][j];
+                else 
+                    dp[i][j] = Math.max(dp[i - 1][j], dp[i - 1][j - nums[i]] + nums[i]);
+            }
+        }
+
+        //print out DP array
+        // for(int x : dp){
+        //     System.out.print(x + ",");
+        // }
+        // System.out.print("    "+i+" row"+"\n");
+        return dp[len - 1][target] == target;
+    }
+}
+//dp数组的打印结果 for test case 1.
+0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
+0, 1, 1, 1, 1, 5, 6, 6, 6, 6, 6, 6, 
+0, 1, 1, 1, 1, 5, 6, 6, 6, 6, 6, 11, 
+0, 1, 1, 1, 1, 5, 6, 6, 6, 6, 10, 11, 
+```
 
 ### Python：
 ```python