2018. The Debut Album
Time limit: 2.0 second
Memory limit: 64 MB
Memory limit: 64 MB
Pop-group “Pink elephant” entered on recording their debut album. In fact they have only two songs: “My love” and “I miss you”, but each of them has a large number of remixes.
The producer of the group said that the album should consist of
n remixes. On second thoughts the musicians decided that the album will be of interest only if there are no more than
a remixes on “My love” in a row and no more than
b remixes on “I miss you” in a row. Otherwise, there is a risk that even the most devoted fans won’t listen to the disk up to the end.
How many different variants to record the album of interest from
n remixes exist? A variant is a sequence of integers 1 and 2, where ones denote remixes on “My love” and twos denote remixes on “I miss you”. Two variants are considered different if for some
i in one variant at
i-th place stands one and in another variant at the same place stands two.
Input
The only line contains integers
n,
a,
b (1 ≤
a,
b ≤ 300;
max(
a,
b) + 1 ≤
n ≤ 50 000).
Output
Output the number of different record variants modulo 10
9+7.
Sample
input | output |
---|---|
3 2 1 | 4 |
Hint
In the example there are the following record variants: 112, 121, 211, 212.
Problem Author: Olga Soboleva (prepared by Alex Samsonov)
Problem Source: NEERC 2014, Eastern subregional contest
Problem Source: NEERC 2014, Eastern subregional contest
构造一个仅有1和2组成的长度为n的串,要求连续1的个数不能超过a,连续2的个数不能超过b,求一共有多少种符合情况的串。
参考:点击打开链接
//0.562 210 KB
#include<stdio.h>
#include<string.h>
#include<algorithm>
#define M 1000000007
#define ll long long
using namespace std;
ll dp[2][2][307];
int main()
{
int n,a,b,now,pre;
while(scanf("%d%d%d",&n,&a,&b)!=EOF)
{
memset(dp,0,sizeof(dp));
dp[0][0][0]=1;dp[0][1][0]=1;
for(int i=1;i<=n;i++)
{
now=i&1,pre=(i-1)&1;
memset(dp[now],0,sizeof(dp[now]));
for(int j=1;j<=a;j++)
{
dp[now][0][j]+=dp[pre][0][j-1];
if(dp[now][0][j]>M)dp[now][0][j]%=M;
dp[now][1][1]+=dp[pre][0][j];
if(dp[now][1][1]>M)dp[now][1][1]%=M;
}
for(int j=1;j<=b;j++)
{
dp[now][1][j]+=dp[pre][1][j-1];
if(dp[now][1][j]>M)dp[now][1][j]%=M;
dp[now][0][1]+=dp[pre][1][j];
if(dp[now][0][1]>M)dp[now][0][1]%=M;
}
}
ll ans=0;
for(int i=1;i<=a;i++)
{
ans+=dp[n&1][0][i];
if(ans>M)ans%=M;
}
for(int i=1;i<=b;i++)
{
ans+=dp[n&1][1][i];
if(ans>M)ans%=M;
}
printf("%lld\n",ans);
}
return 0;
}