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

設(shè)solve(i,m)為“用第i個(gè)元素后面的元素能得出m時(shí)返回true”的函數(shù)，這樣一來solve(i,m)就可以分解為solve(i+1,m)和solve(i,m-A[i])這兩個(gè)更小的局部問題。

函數(shù)solve(i,m)中，m==0時(shí)代表數(shù)組元素相加能夠得出指定整數(shù)。相反，m>0且i>=n時(shí)表示數(shù)組元素相加得不出指定整數(shù)。

只要局部問題solve(i+1,m)和solve(i,m-A[i])之中有一個(gè)為true，原問題solve(i,m)就為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];//從輸入值M中減去所選元素的遞歸函數(shù) 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; }

總結(jié)

以上是生活随笔為你收集整理的Exhaustive Search Aizu - ALDS1_5_A的全部?jī)?nèi)容，希望文章能夠幫你解決所遇到的問題。

如果覺得生活随笔網(wǎng)站內(nèi)容還不錯(cuò)，歡迎將生活随笔推薦給好友。