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number of subsequences

TimeLimit: 2000ms  MemoryLimit:32768KB

64-bit integer IO format: %I64d

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Problem Description

Definition of subsequence: For a sequence a=a[1],a[2],......a[n]. Then the non-empty sequence a'=a[p1],a[p2]......a[pm] is a subsequence of a, where 1<=p1<p2<.....<pm<= n.

For example 4,14,2,3 and 14,1,2,3 are both subsequences of 4,13,14,1,2,3.

For a given sequence a, output the number of distinct subsequences. (Since the answer is relatively large, please mod the answer to 1000000007)

 

Input

The input contains multiple sets of data. The first line of each set of data is an integer n (1<=n<=1,000,000), which represents the number of sequence elements.

The second line contains n integers a[i] (0<=a[i]<=1,000,000) representing each element in the sequence.

 

Output

Output an integer occupying one line, which is the number of different subsequences required. Since the answer is relatively large, please mod the answer by 1000000007.

 

SampleInput

4
1 2 3 2

SampleOutput

13

#include<cstdio>
#include<cstring>
#define mod 1000000007
/**
In fact, it's a matter of finding rules
Let f(n) be the substring of the string whose main string is n
greatest amount,
Available if a[n] appears in the string
f(n)=f(n-1)*2-f(flag[a[n]])
else
    f(n)=f(n-1)*2+1
**/
long long math[1000005];
long long dp[1000005];
long long flag[1000005];
int main()
{
    int n;
    while(~scanf("%d",&n))
    {
        memset(flag,0,sizeof(flag));
        memset(dp,0,sizeof(dp));
        memset(math,0,sizeof(math));
        for(int i=1; i<=n; i++)
            scanf("%lld",&math[i]);
        dp[0]=0;
        dp[1]=1;
        for(int i=1; i<=n; i++)
        {
            if(flag[math[i]]!=0)
            {
                dp[i]=(dp[i-1]*2-dp[flag[math[i]]-1]+mod)%mod;
            }
            else if(flag[math[i]]==0)
            {
                dp[i]=(dp[i-1]*2+1)%mod;
            }
            flag[math[i]]=i;
        }
        printf("%lld\n",dp[n]);
    }
    return 0;
}

View Code