USACO 3.3 Shopping Offers

Shopping Offers
IOI'95

In a certain shop, each kind of product has an integer price. For example, the price of a flower is 2 zorkmids (z) and the price of a vase is 5z. In order to attract more customers, the shop introduces some special offers.

A special offer consists of one or more product items together for a reduced price, also an integer. Examples:

• three flowers for 5z instead of 6z, or
• two vases together with one flower for 10z instead of 12z.

Write a program that calculates the price a customer has to pay for a purchase, making optimal use of the special offers to make the price as low as possible. You are not allowed to add items, even if that would lower the price.

For the prices and offers given above, the (lowest) price for three flowers and two vases is 14z: two vases and one flower for the reduced price of 10z and two flowers for the regular price of 4z.

PROGRAM NAME: shopping

INPUT FORMAT

The input file has a set of offers followed by a purchase.

Line 1:	s, the number of special offers, (0 <= s <= 99).
Line 2..s+1:	Each line describes an offer using several integers. The first integer is n (1 <= n <= 5), the number of products that are offered. The subsequent n pairs of integers c and k indicate that k items (1 <= k <= 5) with product code c (1 <= c <= 999) are part of the offer. The last number p on the line stands for the reduced price (1 <= p <= 9999). The reduced price of an offer is less than the sum of the regular prices.
Line s+2:	The first line contains the number b (0 <= b <= 5) of different kinds of products to be purchased.
Line s+3..s+b+2:	Each of the subsequent b lines contains three values: c, k, and p. The value c is the (unique) product code (1 <= c <= 999). The value k indicates how many items of this product are to be purchased (1 <= k <= 5). The value p is the regular price per item (1 <= p <= 999). At most 5*5=25 items can be in the basket.

SAMPLE INPUT (file shopping.in)

2
1 7 3 5
2 7 1 8 2 10
2
7 3 2
8 2 5

OUTPUT FORMAT

A single line with one integer: the lowest possible price to be paid for the purchases.

SAMPLE OUTPUT (file shopping.out)

14

————————————————————————
一开始写了暴搜，后来搜题解发现是dp……
但是我的暴搜没舍得扔，能过7个点
正解：

 /*
 ID: ivorysi
 PROG: shopping
 LANG: C++
 */
 #include <iostream>
 #include <cstdio>
 #include <cstring>
 #include <algorithm>
 #include <queue>
 #include <set>
 #include <vector>
 #include <string.h>
 #define siji(i,x,y) for(int i=(x);i<=(y);++i)
 #define gongzi(j,x,y) for(int j=(x);j>=(y);--j)
 #define xiaosiji(i,x,y) for(int i=(x);i<(y);++i)
 #define sigongzi(j,x,y) for(int j=(x);j>(y);--j)
 #define inf 0x3f3f3f3f
 #define MAXN 400005
 #define ivorysi
 #define mo 97797977
 #define ha 974711
 #define ba 47
 #define fi first
 #define se second
 #define pii pair<int,int>
 using namespace std;
 typedef long long ll;
 int id[],cnt;
 int s;
 int sale[][][][][],item[][][][][];
 int ti[];
 int reg[];
 void init() {
     scanf("%d",&s);
     int n,p,k[],c,b,t;
     memset(sale,inf,sizeof(sale));
     siji(i,,s) {
         scanf("%d",&n);
         memset(k,,sizeof(k));
         siji(j,,n) {
             scanf("%d%d",&c,&t);
             if(id[c]==) id[c]=++cnt;
             k[id[c]]=t;
         }
         scanf("%d",&p);
         sale[k[]][k[]][k[]][k[]][k[]]=min(p,sale[k[]][k[]][k[]][k[]][k[]]);
     }
     scanf("%d",&b);
     siji(i,,b) {
         scanf("%d%d%d",&c,&t,&p);
         if(id[c]==) id[c]=++cnt;
         ti[id[c]]=t;
         reg[id[c]]=p;
     }
     siji(i,,) {
         siji(j,,){
             siji(m,,) {
                 siji(o,,) {
                     siji(l,,) {
                         item[i][j][m][o][l]=i*reg[]+j*reg[]+m*reg[]+o*reg[]+l*reg[];
                     }
                 }
             }
         }
     }
 }
 int a1,a2,a3,a4,a5;
 void calc(int &x) {
     siji(i1,,a1) {
         siji(i2,,a2) {
             siji(i3,,a3){
                 siji(i4,,a4){
                     siji(i5,,a5) {
                         int temp=sale[i1][i2][i3][i4][i5]+item[a1-i1][a2-i2][a3-i3][a4-i4][a5-i5];
                         x=min(x,temp);
                     }
                 }
             }
         }
     }
 }
 void solve() {
     init();
     for(a1=;a1<=ti[];++a1) {//a1,a2等都要重新赋为0
         for(a2=;a2<=ti[];++a2) {
             for(a3=;a3<=ti[];++a3) {
                 for(a4=;a4<=ti[];++a4){
                     for(a5=;a5<=ti[];++a5) {
                         calc(item[a1][a2][a3][a4][a5]);
                     }
                 }
             }
         }
     }
     printf("%d\n",item[ti[]][ti[]][ti[]][ti[]][ti[]]);
 }
 int main(int argc, char const *argv[])
 {
 #ifdef ivorysi
     freopen("shopping.in","r",stdin);
     freopen("shopping.out","w",stdout);
 #else
     freopen("f1.in","r",stdin);
 #endif
     solve();
 }

暴搜：

 /*
 ID: ivorysi
 PROG: shopping
 LANG: C++
 */
 #include <iostream>
 #include <cstdio>
 #include <cstring>
 #include <algorithm>
 #include <queue>
 #include <set>
 #include <vector>
 #include <string.h>
 #define siji(i,x,y) for(int i=(x);i<=(y);++i)
 #define gongzi(j,x,y) for(int j=(x);j>=(y);--j)
 #define xiaosiji(i,x,y) for(int i=(x);i<(y);++i)
 #define sigongzi(j,x,y) for(int j=(x);j>(y);--j)
 #define inf 0x7fffffff
 #define MAXN 400005
 #define ivorysi
 #define mo 97797977
 #define ha 974711
 #define ba 47
 #define fi first
 #define se second
 #define pii pair<int,int>
 using namespace std;
 typedef long long ll;
 int s;
 struct state {
     int val,item[];
     int& operator[](int x) {return item[x];}
     bool operator < (const state& rhs)const {
         bool flag=;
         siji(i,,) {
             if(item[i]>rhs.item[i]) {flag=;break;}
         }
         return flag;
     }
     bool operator ==(const state& rhs)const{
         return !memcmp(rhs.item,item,sizeof(item));
     }
     bool operator <=(const state& rhs)const{
         return (*this<rhs)||(*this==rhs);
     }
     state operator -(const state& rhs)const {
         state res;
         siji(i,,) {
             res[i]=item[i]-rhs.item[i];
         }
         return res;
     }
 }qwq,sale[];
 int re[];
 int ans;
 void init() {
     scanf("%d",&s);
     int n,p,k,c,b;
     siji(i,,s) {
         scanf("%d",&n);
         siji(j,,n) {
             scanf("%d%d",&c,&k);
             sale[i][c]=k;
         }
         scanf("%d",&p);
         sale[i].val=p;
     }
     scanf("%d",&b);
     siji(i,,b) {
         scanf("%d%d%d",&c,&k,&p);
         qwq[c]=k;qwq.val+=k*p;
         re[c]=p;
     }
     siji(i,,s) {
         int z=;
         siji(j,,) {
             z+=sale[i][j]*re[j];
         }
         sale[i].val-=z;
     }
     ans=qwq.val;
 }
 void dfs(state x) {
     if(x.val<ans) ans=x.val;

     siji(i,,s) {
         state nw=x;
         while(sale[i]<=x) {
             nw=nw-sale[i];
             nw.val+=sale[i].val;
             dfs(nw);
         }
     }
 }
 void solve() {
     init();
     dfs(qwq);
     printf("%d\n",ans);
 }
 int main(int argc, char const *argv[])
 {
 #ifdef ivorysi
     freopen("shopping.in","r",stdin);
     freopen("shopping.out","w",stdout);
 #else
     freopen("f1.in","r",stdin);
 #endif
     solve();
 }