USACO 3.4 Raucous Rockers
You just inherited the rights to N (1 <= N <= 20) previously unreleased songs recorded by the popular group Raucous Rockers. You plan to release a set of M (1 <= M <= 20) compact disks with a selection of these songs. Each disk can hold a maximum of T (1 <= T <= 20) minutes of music, and a song can not overlap from one disk to another.
Since you are a classical music fan and have no way to judge the artistic merits of these songs, you decide on the following criteria for making the selection:
- The songs on the set of disks must appear in the order of the dates that they were written.
- The total number of songs included will be maximized.
PROGRAM NAME: rockers
INPUT FORMAT
| Line 1: | Three integers: N, T, and M. |
| Line 2: | N integers that are the lengths of the songs ordered by the date they were written. |
SAMPLE INPUT (file rockers.in)
4 5 2 4 3 4 2
OUTPUT FORMAT
A single line with an integer that is the number of songs that will fit on M disks.
SAMPLE OUTPUT (file rockers.out)
3
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一道连我这种蒟蒻都能做出来的dp
dp(i,j)=dp(i-1,k)+packbag(v=t,k+1--j)
【i表示选了几个背包，j表示从前到后选了几首歌】
【然后做一个背包，关于容量为t然后从k+1到j之间选歌】
【背包预处理应该会更快，然而在线处理复杂度够了而且绰绰有余】
1 /* 2 ID: ivorysi 3 PROG: rockers 4 LANG: C++ 5 */ 6 #include <iostream> 7 #include <cstdio> 8 #include <cstring> 9 #include <algorithm> 10 #include <queue> 11 #include <set> 12 #include <vector> 13 #include <string.h> 14 #define siji(i,x,y) for(int i=(x);i<=(y);++i) 15 #define gongzi(j,x,y) for(int j=(x);j>=(y);--j) 16 #define xiaosiji(i,x,y) for(int i=(x);i<(y);++i) 17 #define sigongzi(j,x,y) for(int j=(x);j>(y);--j) 18 #define inf 0x3f3f3f3f 19 #define MAXN 400005 20 #define ivorysi 21 #define mo 97797977 22 #define ha 974711 23 #define ba 47 24 #define fi first 25 #define se second 26 #define pii pair<int,int> 27 using namespace std; 28 typedef long long ll; 29 int n,m,t; 30 int song[25]; 31 int getso[25][25]; 32 int f[25]; 33 inline int max(int a,int b){return a>b?a:b;} 34 int check(int b,int e) { 35 if(e<b) return 0; 36 memset(f,0,sizeof(f)); 37 siji(i,b,e) { 38 gongzi(j,t,song[i]) { 39 f[j]=max(f[j],f[j-song[i]]+1); 40 } 41 } 42 return f[t]; 43 } 44 void solve() { 45 scanf("%d%d%d",&n,&t,&m); 46 siji(i,1,n) scanf("%d",&song[i]); 47 siji(i,1,m) { 48 siji(j,1,n) { 49 xiaosiji(k,0,j) { 50 getso[i][j]=max(getso[i][j],getso[i-1][k]+check(k+1,j)); 51 } 52 } 53 } 54 printf("%d\n",getso[m][n]); 55 } 56 int main(int argc, char const *argv[]) 57 { 58 #ifdef ivorysi 59 freopen("rockers.in","r",stdin); 60 freopen("rockers.out","w",stdout); 61 #else 62 freopen("f1.in","r",stdin); 63 #endif 64 solve(); 65 }
