HDU 6092 17多校5 Rikka with Subset(dp+思维)

Problem Description
As we know, Rikka is poor at math. Yuta is worrying about this situation, so he gives Rikka some math tasks to practice. There is one of them:

Yuta has n positive A1−An and their sum is m. Then for each subset S of A, Yuta calculates the sum of S.

Now, Yuta has got 2n numbers between [0,m]. For each i∈[0,m], he counts the number of is he got as Bi.

Yuta shows Rikka the array Bi and he wants Rikka to restore A1−An.

It is too difficult for Rikka. Can you help her?

 
Input
The first line contains a number t(1≤t≤70), the number of the testcases.

For each testcase, the first line contains two numbers n,m(1≤n≤50,1≤m≤104).

The second line contains m+1 numbers B0−Bm(0≤Bi≤2n).

 
Output
For each testcase, print a single line with n numbers A1−An.

It is guaranteed that there exists at least one solution. And if there are different solutions, print the lexicographic minimum one.

 
Sample Input
2
2 3
1 1 1 1
3 3
1 3 3 1
 
Sample Output
1 2
1 1 1
Hint

In the first sample, $A$ is $[1,2]$. $A$ has four subsets $[],[1],[2],[1,2]$ and the sums of each subset are $0,1,2,3$. So $B=[1,1,1,1]$

 
启发博客:http://www.cnblogs.com/stepping/p/7324970.html
官方题解:

1008 Rikka with Subset

签到题,大致的思想就是反过来的背包。

如果 B​i​​ 是 B 数组中除了 B​0​​ 以外第一个值不为 0 的位置,那么显然 i 就是 A 中的最小数。

现在需要求出删掉 i 后的 B 数组,过程大概是反向的背包,即从小到大让 Bj-=B​(j−i)​​。

时间复杂度 O(nm)。

 #include<iostream>
#include<cstdio>
#include<algorithm>
#include<cstring>
#include<queue>
#include<cmath>
#include<string>
#include<map>
#include<vector>
using namespace std; int b[];//最终结果b
int bb[];//目前得出的b
int a[]; int main()
{
int T,n,m,ans;
scanf("%d",&T);
while(T--)
{
scanf("%d%d",&n,&m);
for(int i=;i<=m;i++)
scanf("%d",&b[i]);
memset(a,,sizeof(a));
memset(bb,,sizeof(bb));
bb[]=;
for(int i=;i<=m;i++)
{
a[i]=b[i]-bb[i];
for(int j=;j<=a[i];j++)//对bb进行更新
{
for(int k=m;k>=i;k--)//反着来避免已经加到结果里的数字再加一遍
bb[k]+=bb[k-i];
}
}
int flag=;
for(int i=;i<=m;i++)
for(int j=;j<=a[i];j++)
{
if(flag++) printf(" ");
printf("%d",i);
}
printf("\n");
}
return ;
}
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