求有序数列的排列数

如{1,2,3,4,5}的排序数目

{1}，{2}，{3}，{4}，{5}，{1,2}，{1,3}，{1,4}......

代码：

#include <iostream>
#include <stdio.h>
#include <memory.h>
#include <algorithm>
using namespace std;

struct node
{
    int val, id;
}a[100005];

bool cmp(node a, node b)
{
    return a.val < b.val;
}

int b[100005], c[100005], s[100005], n;

int lowbit(int i)
{
    return i&(-i);
}

void update(int i, int x)
{
    while(i <= n)
    {
        s[i] += x;
        if(s[i] >= 1000000007)
            s[i] %= 1000000007;
        i += lowbit(i);
    }
}

int sum(int i)
{
    int sum = 0;
    while(i > 0)
    {
        sum += s[i];
        if(sum >= 1000000007)
            sum %= 1000000007;
        i -= lowbit(i);
    }
    return sum;
}

int main()
{
    int i, res;
    while(scanf("%d", &n) != EOF)
    {
        memset(b, 0, sizeof(b));
        memset(s, 0, sizeof(s));
        for(i = 1; i <= n; i++)
        {
            scanf("%d", &a[i].val);
            a[i].id = i;
        }
        sort(a+1, a+n+1, cmp);
        b[a[1].id] = 1;
        for(i = 2; i <= n; i++)
        {
            if(a[i].val != a[i-1].val)
                b[a[i].id] = i;
            else b[a[i].id] = b[a[i-1].id];
        }
        res = 0;
        for(i = 1; i <= n; i++)
        {
            c[i] = sum(b[i]);
            update(b[i], c[i]+1);
        }
        printf("%d\n", sum(n));
    }
    return 0;
}