Codeforces 189A：Cut Ribbon（完全背包，DP）
time limit per test : 1 second
memory limit per test : 256 megabytes
input : standard input
output : standard output
Polycarpus has a ribbon, its length is n n n. He wants to cut the ribbon in a way that fulfils the following two conditions:
- After the cutting each ribbon piece should have length a a a, b b b or c c c.
- After the cutting the number of ribbon pieces should be maximum.
Help Polycarpus and find the number of ribbon pieces after the required cutting.
Input
The first line contains four space-separated integers n n n, a a a, b b b and c c c ( 1 ≤ n , a , b , c ≤ 4000 ) (1 ≤ n, a,b, c≤ 4000) (1 ≤ n, a,b, c≤ 4000) — the length of the original ribbon and the acceptable lengths of the ribbon pieces after the cutting, correspondingly. The numbers a a a, b b b and c c c can coincide.
Output
Print a single number — the maximum possible number of ribbon pieces. It is guaranteed that at least one correct ribbon cutting exists.
Examples
input
5 5 3 2
output
2
input
7 5 5 2
output
2
Note
In the first example Polycarpus can cut the ribbon in such way: the first piece has length 2 2 2, the second piece has length 3 3 3.
In the second example Polycarpus can cut the ribbon in such way: the first piece has length 5 5 5, the second piece has length 2 2 2.
Solve
完全背包，看成给出三种商品，恰好能够装满背包的情况
注意初始化的问题，如果把 d p dp dp数组全部初始化为 − 1 -1 −1的话，需要注意 d p [ j ] = − 1 & & d p [ j − a [ i ] ] = − 1 dp[j]=-1\&\&dp[j-a[i]]=-1 dp[j]=−1&&dp[j−a[i]]=−1的情况。或者就全部初始值给成小于 − 1 -1 −1的数
Code
/*************************************************************************
> Author: WZY
> School: HPU
> Created Time: 2019-04-01 18:30:38
************************************************************************/
#include
#define bug cerr<<"-------------"<
#define debug(...) cerr<<"["<<#__VA_ARGS__":"<<(__VA_ARGS__)<<"]"<<"\n"
#define LEN(A) strlen(A)
const double E=exp(1);
const double eps=1e-9;
const double pi=acos(-1.0);
const int mod=1e9+7;
const int maxn=1e6+10;
const int maxm=1e3+10;
const int moha=19260817;
const int inf=1<<30;
const ll INF=1LL<<60;
using namespace std;
inline void Debug(){cerr<<'\n';}
inline void MIN(int &x,int y) {if(y<x) x=y;}
inline void MAX(int &x,int y) {if(y>x) x=y;}
inline void MIN(ll &x,ll y) {if(y<x) x=y;}
inline void MAX(ll &x,ll y) {if(y>x) x=y;}
template<class FIRST, class... REST>void Debug(FIRST arg, REST... rest){
cerr<<arg<<"";Debug(rest...);}
int dp[maxn];
int main(int argc, char const *argv[])
{
ios::sync_with_stdio(false);cin.tie(0);
cout.precision(20);
#ifndef ONLINE_JUDGE
freopen("in.txt", "r", stdin);
freopen("out.txt", "w", stdout);
srand((unsigned int)time(NULL));
#endif
int n;
int a[4];
cin>>n>>a[0]>>a[1]>>a[2];
ms(dp,-1);
dp[0]=0;
for(int i=0;i<3;i++)
for(int j=a[i];j<=n;j++)
if(dp[j-a[i]]!=-1)
MAX(dp[j],dp[j-a[i]]+1);
cout<<dp[n]<<endl;
#ifndef ONLINE_JUDGE
cerr<<"Time elapsed: "<<1.0*clock()/CLOCKS_PER_SEC<<" s.\n";
#endif
return 0;
}