Exhaustive Search Aizu

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 integers are given. In the third line q is given. Then, in the fourth line, q integers (Mi) are given.

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].

思路

设solve(i,m)为“用第i个元素后面的元素能得出m时返回true”的函数，这样一来solve(i,m)就可以分解为solve(i+1,m)和solve(i,m-A[i])这两个更小的局部问题。

函数solve(i,m)中，m==0时代表数组元素相加能够得出指定整数。相反，m>0且i>=n时表示数组元素相加得不出指定整数。

只要局部问题solve(i+1,m)和solve(i,m-A[i])之中有一个为true，原问题solve(i,m)就为true。

code

/*^....0^ .1 ^1^..     011.^     1.0^ 1  ^    ^0.11 ^        ^..^0.           ^ 0^.0            1 .^.1             ^0 .........001^.1               1. .111100....01^00             ^   11^        ^1. .1^1.^                              ^0  0^.^                                 ^0..1.1                                   1..^1 .0                                     ^  ^00.                                     ^^0.^^ 0                                     ^^110.^0   0 ^                                     ^^^10.01^^     10  1 1                                      ^^^1110.101     10  1.1                                      ^^^1111110010    01  ^^                                        ^^^1111^1.^           ^^^10  10^ 0^ 1                                            ^^111^^^0.1^       1....^11     0                                               ^^11^^^ 0..  ....1^   ^ ^1.     0^                                               ^11^^^ ^ 1 111^     ^ 0.10   00 11                                               ^^^^^   1 0           1.0^  ^0  ^0                                                ^^^^    0            0.0^  1.0  .^                                               ^^^^    1 1          .0^.^  ^^  0^                             ^1                ^^^^     0.         ^.11 ^      11                             1.                ^^^     ^ ^        ..^^..^      ^1                             ^.^               ^^^       .0       ^.00..^      ^0                              01               ^^^       ..      0..^1 ..        .1                             ^.^              ^^^       1 ^  ^0001^  1.        00                              0.             ^^^        ^.0 ^.1. 0^.        ^.^                             ^.^            ^^^         ..0.01 .^^.         .^                  1001        ^^            ^^^         . 1^. ^ ^.         11                0.    1         ^           ^^          0.0  ^.          0              ^0       1                   ^^^          0.0.^  1.          0^             0       .1                   ^^^          ...1   1.          00            .        .1                  ^^^           ..1      1.         ^.           0         .^                  ^^            ..0.     1.          .^          .         0                                  ..1     1.          01          .        .                                 ^ 0^.^     00          ^0          1.       ^                                 1 1.0      00           .            ^^^^^^                                   ..^      00           01                                                    ..1.       00           10                                                   1 ^^.1       00           ^.                                            ^^^    .1..        00            .1                                        1..01    ..1.1         00           1.                                       ..^      10^ 1^         00           ^.1                                      0 1      1.1           00            00                                       ^  1   ^.           00            ^.^                                        10^  ^^1.1           00             00                                              10^..^           1.             ^.                                               1.0 1            ^.              00                 00                            .^^            ^.              ^ 1                00   ^0000^     ^               011 0             ^.               00.0^              ^00000   1.00.1              11. 1              0               1^^0.01                      ^^^                01.^              ^                1   1^^                                       ^.^1 1                                                                              0...                                                                              1 ^1                                                                               1^ ^                                                                             .01                                                                             ^ 1..                                                          1.1            ^0.0^ 0                                                           1..01^^100000..0^1 1                                                            ^ 1 ^^1111^ ^^0 ^                                                             ^ 1      1000^.1                                                               ^.^     .   00..                                                                1.1    0.   01.                                                                  .    1.   .^1.                                                                 1    1.   ^0^ .                                                                 ^.1 00    01^.0                                                                  001.     .^*/
// Virtual_Judge —— Exhaustive Search Aizu - ALDS1_5_A.cpp created by VB_KoKing on 2019-05-04:12.
/* Procedural objectives：Variables required by the program:Procedural thinking：Functions required by the program:*/
/* My dear Max said：
"I like you,
So the first bunch of sunshine I saw in the morning is you,
The first gentle breeze that passed through my ear is you,
The first star I see is also you.
The world I see is all your shadow."FIGHTING FOR OUR FUTURE！！！
*/
#include <iostream>
using namespace std;int n,A[50];//从输入值M中减去所选元素的递归函数
int solve(int i,int m)
{if (m==0) return 1;if (i>=n) return 0;return solve(i+1,m)+solve(i+1,m-A[i]);
}int main()
{int q,M;cin>>n;for (int i = 0; i < n; i++)cin>>A[i];cin>>q;for (int i = 0; i < q; i++) {cin>>M;if (solve(0,M))cout<<"yes"<<endl;elsecout<<"no"<<endl;}return 0;
}