From a4dcbe67217574e6fd197ad0c9598177faec79e9 Mon Sep 17 00:00:00 2001
From: Lozakaka <102352821+Lozakaka@users.noreply.github.com>
Date: Fri, 26 May 2023 18:05:09 -0400
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1. 新增java二維"整數"數組的解法，原本是用boolean數組，有一點繞，故附上二維"整數"數組。

2. 優化一維數組的解法(剪枝)，在每一次內層循環完後，立刻檢查dp[target] == target。實測時間複雜度: 26ms -> 20ms
---
 problems/0416.分割等和子集.md | 61 ++++++++++++++++++++++++++++-
 1 file changed, 60 insertions(+), 1 deletion(-)

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