DP big combat-combination backpack and dp big combat backpack

DP big combat-combination backpack and dp big combat backpack
Description

Combination backpack: Some items can be taken only once (01 backpack), some items can be taken unlimited times (full backpack), and some items can be taken up to a maximum of times (multiple backpacks ).

DD Daniel's pseudocode for I = 1 to N if item I belongs to 01 backpack ZeroOnePack (F, Ci, Wi) else if item I belongs to complete backpack CompletePack (F, ci, Wi) else if the I-th item belongs to MultiplePack (F, Ci, Wi, Ni)

Input

The first number is the number of data groups n 1 <= n <= 10

The next n groups of test data, each of which consists of two parts.

First behavior: backpack capacity V, number of item types N. 1 <= V <= 200, 1 <= N <=

In the next N rows, each row contains three values: item value v, item weight w, and item quantity M. M = 233 indicates that the item is infinite.

1 <= v, w <= 200, 1 <= M <= 25

Output

For each group of data, output a row, the maximum value of the items that the backpack can accommodate

Input example

110 32 2 2333 2 14 3 3

Output example

13
Source of http://biancheng.love/contest/10/problem/F/index
Solution:
Combination backpack: 0-1 backpack, full backpack, multiple backpacks.
Therefore, we need to combine the solution of the above three backpack problems to solve the backpack.
0-1 backpack code:

1 void Zeronepack(int w,int v)2 {3     for(int i=V; i>=w; i--)4         if(dp[i]<dp[i-w]+v)5             dp[i]=dp[i-w]+v;6 }

Full backpack code:

1 void Compack(int w,int v)2 {3     for(int i=w; i<=V; i++)4         if(dp[i]<dp[i-w]+v)5             dp[i]=dp[i-w]+v;6 }

Code for multiple backpacks:

 1 void Multipack(int w,int v,int num) 2 { 3     int k; 4     if(w*num>=V) 5     { 6         Compack(w,v); 7         return; 8     } 9     for(k=1; k<num; k<<1)10     {11         Zeronepack(k*w,k*v);12         num-=k;13     }14     Zeronepack(num*w,num*v);15 }

Code for combining this question with a backpack:

 

 1 #include <bits/stdc++.h> 2 int dp[30005]; 3 int V,N; 4  5 void Compack(int w,int v) 6 { 7     for(int i=w; i<=V; i++) 8         if(dp[i]<dp[i-w]+v) 9             dp[i]=dp[i-w]+v;10 }11 12 void Zeronepack(int w,int v)13 {14     for(int i=V; i>=w; i--)15         if(dp[i]<dp[i-w]+v)16             dp[i]=dp[i-w]+v;17 }18 19 void Multipack(int w,int v,int num)20 {21     int k;22     if(w*num>=V)23     {24         Compack(w,v);25         return;26     }27     for(k=1; k<num; k<<1)28     {29         Zeronepack(k*w,k*v);30         num-=k;31     }32     Zeronepack(num*w,num*v);33 }34 35 int main()36 {37     int kase,v,w,m;38     scanf("%d",&kase);39     while(kase--)40     {41         memset(dp,0,sizeof(dp));42         scanf("%d%d",&V,&N);43         for(int i=1;i<=N;i++)44         {45             scanf("%d%d%d",&v,&w,&m);46             if(m==1)47                 Zeronepack(w,v);48             else if(m==233)49                 Compack(w,v);50             else51                 Multipack(w,v,m);52         }53         printf("%d\n",dp[V]);54     }55     return 0;56 }