Jun 5, 2023 · May 20, 2023 · May 20, 2023 · May 23, 2023 · May 26, 2023 · May 27, 2023
diff --git a/problems/0416.分割等和子集.md b/problems/0416.分割等和子集.md
Original file line number	Diff line number	Diff line change
Expand Up		@@ -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;
		}
Expand Down Expand Up		@@ -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
Expand Down