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Merge pull request #2100 from Lozakaka/patch-16

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新增java二維"整數"數組的解法、優化一維數組的解法(剪枝)
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程序员Carl
2023-06-05 08:53:29 +08:00
committed by GitHub
parent 741d5c9fdf a4dcbe6721
commit dd061da22e
1 changed files with 60 additions and 1 deletions
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problems/0416.分割等和子集.md
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@ -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