ALDS1_5_A Exhaustive Search 窮竭搜尋
Write a program which reads a sequence A of n elements and an integer M, and outputs "yes" if you can make M by adding elements in A, otherwise "no". You can use an element only once.
You are given the sequence A and q questions where each question contains Mi.
Input
In the first line n is given. In the second line, n
Output
For each question Mi, print yes or no.
Constraints
- n ≤ 20
- q ≤ 200
- 1 ≤ elements in A ≤ 2000
- 1 ≤ Mi ≤ 2000
Sample Input 1
5 1 5 7 10 21 8 2 4 17 8 22 21 100 35
Sample Output 1
no no yes yes yes yes no no
Notes
You can solve this problem by a Burte Force approach. Suppose solve(p, t) is a function which checkes whether you can make t by selecting elements after p-th element (inclusive). Then you can recursively call the following functions:
solve(0, M)
solve(1, M-{sum created from elements before 1st element})
solve(2, M-{sum created from elements before 2nd element})
...
The recursive function has two choices: you selected p-th element and not. So, you can check solve(p+1, t-A[p]) and solve(p+1, t) in solve(p, t) to check the all combinations.
For example, the following figure shows that 8 can be made by A[0] + A[2].
程式碼如下:
#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
const int maxn=25;
int n,q;
int a[maxn];
int flag;
int x;
void cho (int loc,int sum)
{
if(sum==x)
{
flag=1;
return;
}
if(loc>n)
return;
cho (loc+1,sum);
cho (loc+1,sum+a[loc]);
}
void input ()
{
scanf("%d",&n);
for (int i=1;i<=n;i++)
scanf("%d",&a[i]);
scanf("%d",&q);
while (q--)
{
scanf("%d",&x);
flag=0;
cho (1,0);
if(flag)
printf("yes\n");
else
printf("no\n");
}
}
int main()
{
input();
return 0;
}