14 Provincial---Multiple parts and problems (multiple packs + binary optimization)

1210:f. Multiple parts and issues time limit: 1 Sec memory limit: up to MB
Submitted: Solution: Title Description

There are n different sizes of numbers, each of each. Determine whether some of these numbers can be selected to make their and exactly K.

Input

The first is a positive integer T (1<=t<=100)
Next is the T-group data
The first row of each set of data is a positive integer n (1<=n<=100), indicating that there are n different size numbers
The second line is n different-sized positive integer AI (1<=ai<=100000)
The third line is n positive integer mi (1<=mi<=100000), which indicates that each number has a MI
Line four is a positive integer K (1<=k<=100000)

Output

For each set of data, if you can select some of these numbers to make them and exactly k, then output "Yes", otherwise output "No", each output is a separate row

Sample input233 583 2 2 -21 21 14Sample outputYesNoOne-dimensional multi-backpack binary optimization thinking: First look at this problem, 100=1+2+4+8+16+32+37, observation can be concluded that any number within 100 can be obtained from the above 7 number selection combination, so the number of items is not from 0 to 100 times, but 0,1,2,4,5, 16,32,37 traversal, time is greatly optimized.

1#include <cstdio>2#include <iostream>3#include <cstring>4#include <algorithm>5#include <cmath>6 using namespacestd;7 intMain ()8 {9     intT,n,k,count;Ten     inta[101],b[101]; One     intf[100001]; A     inti,j,m,p,g; -Cin>>T; -      while(t--) the     { -Memset (F,0,sizeof(f)); -Cin>>N; -          for(i=1; i<=n;i++) +Cin>>A[i]; -          for(i=1; i<=n;i++) +Cin>>B[i]; ACin>>K; at          for(i=1; i<=n;i++) -         {    -p=0; -g=0; -              while(b[i]>g) -             { in                  for(j=k;j>=a[i]*g;j--) -                 { toF[j]=max (f[j],f[j-a[i]*g]+a[i]*g); +                 } -b[i]-=G; theG=pow (2, p); *p++; $             }Panax Notoginseng              for(j=k;j>=a[i]*b[i];--j) -             { theF[j]=max (f[j],f[j-a[i]*b[i]]+a[i]*b[i]); +             } A         } the         if(f[k]==k) +cout<<"Yes"<<Endl; -         Else $cout<<"No"<<Endl; $     } -}

Timeout code (not optimized)

1#include <cstdio>2#include <iostream>3#include <cstring>4#include <algorithm>5#include <cmath>6 using namespacestd;7 intMain ()8 {9     intT,n,k,count;Ten     inta[101],b[101]; One     intf[100001]; A     inti,j,m; -     intMax; -Cin>>T; the      while(t--) -     { -Memset (F,0,sizeof(f)); -Cin>>N; +          for(i=1; i<=n;i++) -Cin>>A[i]; +          for(i=1; i<=n;i++) ACin>>B[i]; atCin>>K; -          for(i=1; i<=n;i++) -         { -              for(j=0; j<=b[i];j++) -             { -                  for(m=k;m>=a[i]*j;m--) in                 { -                     if(f[m]< (f[m-j*a[i]]+j*A[i])) tof[m]=f[m-j*a[i]]+j*A[i]; +                 } -             } the         } *cout<<f[k]<<Endl; $         if(f[k]==k)Panax Notoginsengcout<<"Yes"<<Endl; -         Else thecout<<"No"<<Endl; +     } A}

14 Provincial---Multiple parts and problems (multiple packs + binary optimization)