Description
Give you three sequences of numbers A, B, C, then we give you a number X. Now you need to calculate if you can find the three numbers Ai, Bj, Ck, which satisfy the formula Ai+Bj+Ck = X.
Input
There are many cases. Every data case is described as followed: In the first line there are three integers L, N, M, in the second line there are L integers represent the sequence A, in the third line there are N integers represent the sequences B, in the forth line there are M integers represent the sequence C. In the fifth line there is an integer S represents there are S integers X to be calculated. 1<=L, N, M<=500, 1<=S<=1000. all the integers are 32-integers.
Output
For each case, firstly you have to print the case number as the form "Case d:", then for the S queries, you calculate if the formula can be satisfied or not. If satisfied, you print "YES", otherwise print "NO".
Sample Input
3 3 3
1 2 3
1 2 3
1 2 3
3
1
4
10
Sample Output
Case 1:
NO
YES
NO
解题思路：
首先我们考虑这个问题：给定两个序列A，B，和确定的数x，问是否存在i，j使满足A［i］＋B［j］＝x的？最快的方法是枚举A，然后在B中二分查找
x－A。现在回到这个问题，这道题给了三组序列A，B，C如何查找呢？我们不妨将A，C两数组合并成新数组LN，LN中每个元素都是Ai+Bj的和。然后枚举B，在LN中二分查找x－B。
＊这里有个细节：由于x为32位整数，当A+B>INT32_MAX时，可以不用加入LN.
代码如下：
1 #include <iostream>
2 #include <cstdio>
3 #include <algorithm>
4 #include <time.h>
5 using namespace std;
6 #define clock__ printf("%f\n",double(clock())/CLOCKS_PER_SEC);
7 #define maxn 500
8 #define INT_32_MAX ((1<<31)-1)
9 typedef long long LL;
10 int A[maxn+3],B[maxn+3],C[maxn+3];
11 int L,M,N,S;
12 int LN[maxn*maxn+5];
13 int h;
14
15 bool search_LN(int a,int b,int x){
16 int len=b-a;
17 int mid=a+len/2;
18 if(len==1){
19 if(LN[a]==x) return true;
20 else return false;
21 }
22 if(LN[mid]==x) return true;
23 else if(LN[mid]>x) return search_LN(a, mid, x);
24 else return search_LN(mid, b, x);
25 }
26
27 int main() {
28
29 int T=0;
30 while(scanf("%d%d%d",&L,&M,&N)==3){
31 printf("Case %d:\n",++T);
32 for(int i=0;i<L;i++)
33 scanf("%d",&A[i]);
34 for(int i=0;i<M;i++)
35 scanf("%d",&B[i]);
36 for(int i=0;i<N;i++)
37 scanf("%d",&C[i]);
38 h=0;
39 for(int i=0;i<L;i++)
40 for(int j=0;j<N;j++){
41 if(LL(A[i])+C[j]<=INT_32_MAX)
42 LN[h++]=A[i]+C[j];
43 }
44 sort(LN, LN+h);
45 scanf("%d",&S);
46 for(int i=1;i<=S;i++){
47 int x;
48 scanf("%d",&x);
49 bool ok=0;
50 for(int j=0;!ok&&j<M;j++){
51 if(search_LN(0,h, x-B[j]))
52 ok=1;
53 }
54 if(ok)printf("YES\n");
55 else printf("NO\n");
56 }
57 }
58 //clock__
59 return 0;
60 }