HDU5800 To My Girlfrend(计数dp)
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To My Girlfriend
传送门1
传送门2
Dear Guo
I never forget the moment I met with you.You carefully asked me: “I have a very difficult problem. Can you teach me?”.I replied with a smile, “of course”.”I have n items, their weight was a[i]”,you said,”Let’s define f(i,j,k,l,m) to be the number of the subset of the weight of n items was m in total and has No.i and No.j items without No.k and No.l items.”“And then,” I asked.You said:”I want to know
Sincerely yours,
Liao
Input
The first line of input contains an integer
Each case contains 2 integers
Output
Each case print the only number — the number of her would modulo
Sample Input
2
4 4
1 2 3 4
4 4
1 2 3 4
Sample Output
8
8
题意
给定
分析
定义
显然
当然对于当前一个状态,它有四种转移状态:
1. 选中当前的, 增加权值, 增加必 选个数。
2. 选中当前的, 增加权值,不增加必 选个数。
3. 不选中当前的,不增加权值, 增加必不选个数。
4. 不选中当前的,不增加权值,不增加必不选个数。
在
参考
CODE
#include<cstdio>#include<memory.h>#define mod 1000000007#define N 1005#define FOR(i,a,b) for(int i=(a),i##_END_=(b);i<=i##_END_;i++)int dp[N][N][3][3],a[N];int main() { int T,n,s,tmp; int ans; scanf("%d",&T); while(T--) { ans=0; scanf("%d%d",&n,&s); FOR(i,1,n)scanf("%d",&a[i]); memset(dp,0,sizeof dp); dp[1][a[1]][0][0]=1; dp[1][a[1]][1][0]=1; dp[1][0][0][0]=1; dp[1][0][0][1]=1; FOR(i,2,n)FOR(j,0,s) { tmp=j+a[i]; if(tmp<=s) { //卡常大法好 dp[i][tmp][0][0]=(dp[i][tmp][0][0]+dp[i-1][j][0][0])%mod; dp[i][tmp][1][0]=(dp[i][tmp][1][0]+dp[i-1][j][0][0])%mod; dp[i][tmp][1][0]=(dp[i][tmp][1][0]+dp[i-1][j][1][0])%mod; dp[i][tmp][2][0]=(dp[i][tmp][2][0]+dp[i-1][j][1][0])%mod; dp[i][tmp][2][0]=(dp[i][tmp][2][0]+dp[i-1][j][2][0])%mod; dp[i][tmp][0][1]=(dp[i][tmp][0][1]+dp[i-1][j][0][1])%mod; dp[i][tmp][1][1]=(dp[i][tmp][1][1]+dp[i-1][j][0][1])%mod; dp[i][tmp][1][1]=(dp[i][tmp][1][1]+dp[i-1][j][1][1])%mod; dp[i][tmp][2][1]=(dp[i][tmp][2][1]+dp[i-1][j][1][1])%mod; dp[i][tmp][2][1]=(dp[i][tmp][2][1]+dp[i-1][j][2][1])%mod; dp[i][tmp][0][2]=(dp[i][tmp][0][2]+dp[i-1][j][0][2])%mod; dp[i][tmp][1][2]=(dp[i][tmp][1][2]+dp[i-1][j][0][2])%mod; dp[i][tmp][1][2]=(dp[i][tmp][1][2]+dp[i-1][j][1][2])%mod; dp[i][tmp][2][2]=(dp[i][tmp][2][2]+dp[i-1][j][1][2])%mod; dp[i][tmp][2][2]=(dp[i][tmp][2][2]+dp[i-1][j][2][2])%mod; } dp[i][j][0][0]=(dp[i][j][0][0]+dp[i-1][j][0][0])%mod; dp[i][j][0][1]=(dp[i][j][0][1]+dp[i-1][j][0][0])%mod; dp[i][j][0][1]=(dp[i][j][0][1]+dp[i-1][j][0][1])%mod; dp[i][j][0][2]=(dp[i][j][0][2]+dp[i-1][j][0][1])%mod; dp[i][j][0][2]=(dp[i][j][0][2]+dp[i-1][j][0][2])%mod; dp[i][j][1][0]=(dp[i][j][1][0]+dp[i-1][j][1][0])%mod; dp[i][j][1][1]=(dp[i][j][1][1]+dp[i-1][j][1][0])%mod; dp[i][j][1][1]=(dp[i][j][1][1]+dp[i-1][j][1][1])%mod; dp[i][j][1][2]=(dp[i][j][1][2]+dp[i-1][j][1][1])%mod; dp[i][j][1][2]=(dp[i][j][1][2]+dp[i-1][j][1][2])%mod; dp[i][j][2][0]=(dp[i][j][2][0]+dp[i-1][j][2][0])%mod; dp[i][j][2][1]=(dp[i][j][2][1]+dp[i-1][j][2][0])%mod; dp[i][j][2][1]=(dp[i][j][2][1]+dp[i-1][j][2][1])%mod; dp[i][j][2][2]=(dp[i][j][2][2]+dp[i-1][j][2][1])%mod; dp[i][j][2][2]=(dp[i][j][2][2]+dp[i-1][j][2][2])%mod; } FOR(m,1,s)ans=(ans+dp[n][m][2][2])%mod; printf("%d\n",(4LL*ans)%mod); } return 0;}
当然你不想看卡常的话可以看下面的代码
#include<cstdio>#include<memory.h>#define mod 1000000007#define N 1005#define FOR(i,a,b) for(int i=(a),i##_END_=(b);i<=i##_END_;i++)int dp[N][N][3][3],a[N];int main() { int T,n,s,tmp; int ans; scanf("%d",&T); while(T--) { ans=0; scanf("%d%d",&n,&s); FOR(i,1,n)scanf("%d",&a[i]); memset(dp,0,sizeof dp); dp[1][a[1]][0][0]=1; dp[1][a[1]][1][0]=1; dp[1][0][0][0]=1; dp[1][0][0][1]=1; FOR(i,2,n)FOR(j,0,s) { tmp=j+a[i]; if(tmp<=s)FOR(jj,0,2) { dp[i][tmp][0][jj]=(dp[i][tmp][0][jj]+dp[i-1][j][0][jj])%mod; dp[i][tmp][1][jj]=(dp[i][tmp][1][jj]+dp[i-1][j][0][jj])%mod; dp[i][tmp][1][jj]=(dp[i][tmp][1][jj]+dp[i-1][j][1][jj])%mod; dp[i][tmp][2][jj]=(dp[i][tmp][2][jj]+dp[i-1][j][1][jj])%mod; dp[i][tmp][2][jj]=(dp[i][tmp][2][jj]+dp[i-1][j][2][jj])%mod; } FOR(ii,0,2) { dp[i][j][ii][0]=(dp[i][j][ii][0]+dp[i-1][j][ii][0])%mod; dp[i][j][ii][1]=(dp[i][j][ii][1]+dp[i-1][j][ii][0])%mod; dp[i][j][ii][1]=(dp[i][j][ii][1]+dp[i-1][j][ii][1])%mod; dp[i][j][ii][2]=(dp[i][j][ii][2]+dp[i-1][j][ii][1])%mod; dp[i][j][ii][2]=(dp[i][j][ii][2]+dp[i-1][j][ii][2])%mod; } } FOR(m,1,s)ans=(ans+dp[n][m][2][2])%mod; printf("%d\n",(4LL*ans)%mod); } return 0;}
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