Poj 3046 Ant Counting【多重背包】

Ant Counting

Time Limit: 1000MS Memory Limit: 65536KTotal Submissions: 4091 Accepted: 1591

Description

Bessie was poking around the ant hill one day watching the ants march to and fro while gathering food. She realized that many of the ants were siblings, indistinguishable from one another. She also realized the sometimes only one ant would go for food, sometimes a few, and sometimes all of them. This made for a large number of different sets of ants! 

Being a bit mathematical, Bessie started wondering. Bessie noted that the hive has T (1 <= T <= 1,000) families of ants which she labeled 1..T (A ants altogether). Each family had some number Ni (1 <= Ni <= 100) of ants. 

How many groups of sizes S, S+1, ..., B (1 <= S <= B <= A) can be formed? 

While observing one group, the set of three ant families was seen as {1, 1, 2, 2, 3}, though rarely in that order. The possible sets of marching ants were: 

3 sets with 1 ant: {1} {2} {3} 
5 sets with 2 ants: {1,1} {1,2} {1,3} {2,2} {2,3} 
5 sets with 3 ants: {1,1,2} {1,1,3} {1,2,2} {1,2,3} {2,2,3} 
3 sets with 4 ants: {1,2,2,3} {1,1,2,2} {1,1,2,3} 
1 set with 5 ants: {1,1,2,2,3} 

Your job is to count the number of possible sets of ants given the data above. 

Input

* Line 1: 4 space-separated integers: T, A, S, and B 

* Lines 2..A+1: Each line contains a single integer that is an ant type present in the hive

Output

* Line 1: The number of sets of size S..B (inclusive) that can be created. A set like {1,2} is the same as the set {2,1} and should not be double-counted. Print only the LAST SIX DIGITS of this number, with no leading zeroes or spaces.

Sample Input

3 5 2 312213

Sample Output

10

Hint

INPUT DETAILS: 

Three types of ants (1..3); 5 ants altogether. How many sets of size 2 or size 3 can be made? 


OUTPUT DETAILS: 

5 sets of ants with two members; 5 more sets of ants with three members

Source

USACO 2005 November Silver

题意：

给出每个数字的个数，问选出s-b 个元素的不同的组合形式有多少种

题解：

确实不会做多重背包问题，看的大神的博客，慢慢理解吧

点击膜拜大神

#include<cstdio>#include<cstring>#include<algorithm>using namespace std;const int mod=1e6,maxn=mod+5;int dp[2][maxn],num[maxn];int sum[maxn],up[maxn];int main(){int T,S,A,B;scanf("%d%d%d%d",&T,&A,&S,&B);for(int i=1;i<=A;++i){int tp;scanf("%d",&tp);++num[tp];}for(int i=1;i<=T;++i){up[i]=up[i-1]+num[i];} dp[0][0]=1;int *pre=dp[0],*nxt=dp[1];for(int i=1;i<=T;++i){sum[0]=pre[0];for(int j=1;j<=up[i];++j){sum[j]=(sum[j-1]+pre[j])%mod;}for(int j=0;j<=up[i];++j){int tmp=max(0,j-num[i]);nxt[j]=(tmp==0?sum[j]:(sum[j]-sum[tmp-1]+mod))%mod;}swap(nxt,pre);}int ans=0;for(int i=S;i<=B;++i){ans=(ans+pre[i])%mod;}printf("%d\n",ans);return 0;}