[Multi] Transport Ship backpack

【source】

　　2018 Jiaozuo network game

Reference [blog]

　　https://blog.csdn.net/baymax520/article/details/82719454 

[Title] Italy

　　There are N kinds of boats, cargo capacity of each vessel is v [i], each vessel has 2 ^ c [i] -1 species, there are times query q, each asked how many ways to fill the cargo capacity s .

[Thinking]

　　If 01 backpack bare, then the time complexity is O (N * 2 ^ c [i] * 10000), clearly timeout, but we can put each vessel were combined, such as a vessel that 2 ^ x-1 boat (s) then it is split into 2 ^ 0 + 2 ^ 1 + 2 ^ 2 + ... + 2 ^ (x-1), any of a number of 1 ~ 2 ^ x-1 are split may be formed out of several compositions, the result of all combined for a 01 backpack can be.

 

 1 #include<cstdio>
 2 #include<cstring>
 3 #include<algorithm>
 4 using namespace std;
 5 typedef long long ll;
 6 const int M = 1e4+5;
 7 const int mod = 1e9+7;
 8 ll dp[M],v[25],c[25],V;
 9 int main()
10 {
11     int t,n,Q,s;
12     scanf("%d",&t);
13     while(t--){
14         scanf("%d%d",&n,&Q);
15         for(int i=1;i<=n;i++)
16             scanf("%d%d",&v[i],&c[i]);
17 
18         memset(dp,0,sizeof dp );
19         dp[0] = 1 ;
20         for(int i=1;i<=n;i++){
21             for(int k=0;k<c[i];k++){
22                 V = 1ll* v[i] << k ;
23                 for(int j=M-1;j>=V;j--){
24                     dp[j] += dp[j-V];
25                     dp[j] %= mod ;
26                 }
27             }
28         }
29         for(int i=1;i<=Q;i++){
30             scanf("%d",&s);
31             printf("%lld\n",dp[s]);
32         }
33     }
34     return 0;
35 }

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