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[pull] master from youngyangyang04:master #279

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pull merged 8 commits into AlgorithmAndLeetCode:master from youngyangyang04:master
Jun 5, 2023
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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) 
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
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Lozakaka authored May 26, 2023
commit a4dcbe67217574e6fd197ad0c9598177faec79e9
61 changes: 60 additions & 1 deletion problems/0416.分割等和子集.md
View file Open in desktop
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

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