Counting Sequences HDU - 3450（多元上升组 树状数组）

For a set of sequences of integers｛a1，a2，a3，…an｝, we define a sequence｛ai1,ai2,ai3…aik｝in which 1<=i1<i2<i3<…<ik<=n, as the sub-sequence of ｛a1，a2，a3，…an｝. It is quite obvious that a sequence with the length n has 2^n sub-sequences. And for a sub-sequence｛ai1,ai2,ai3…aik｝，if it matches the following qualities: k >= 2, and the neighboring 2 elements have the difference not larger than d, it will be defined as a Perfect Sub-sequence. Now given an integer sequence, calculate the number of its perfect sub-sequence.
Input
Multiple test cases The first line will contain 2 integers n, d（2<=n<=100000，1<=d=<=10000000） The second line n integers, representing the suquence
Output
The number of Perfect Sub-sequences mod 9901
Sample Input
4 2
1 3 7 5
Sample Output
4

题意：
求所有长度至少为2的子序列，满足子序列相邻两个元素的差值不大于d
思路：
与Crazy Thairs POJ - 3378 这道题很像，这道题求的是5元上升组的个数。本题中加了一个相邻元素不大于d的限制，而且求的是大于1元上升组的和。

那道题维护了5个树状数组，分别表示5元上升序列的长度。
本题只需要维护2个就可以了，一个是一元，一个是大于一元。
转移的条件就是abs(a[i] - a[j]) ≤ d。再用二分找出j的最大值和最小值。

#include <cstdio>
#include <cstring>
#include <algorithm>

using namespace std;

const int maxn = 1e5 + 7;
const int mod = 9901;

int a[maxn],b[maxn],c[3][maxn];
int n,d;

struct Node
{
    int id,v;
    bool operator < (const Node &rhs)const
    {
        return v < rhs.v;
    }
}nodes[maxn];

int bin_l(int x)
{
    int l = 1,r = n,val = b[x];
    int ans = 0;
    while(l <= r)
    {
        int mid = (l + r) >> 1;
        if(val - nodes[mid].v <= d)
        {
            ans = mid;
            r = mid - 1;
        }
        else
        {
            l = mid + 1;
        }
    }
    return a[nodes[ans].id];
}

int bin_r(int x)
{
    int l = 1,r = n,val = b[x];
    int ans = 0;
    while(l <= r)
    {
        int mid = (l + r) >> 1;
        if(nodes[mid].v - val <= d)
        {
            ans = mid;
            l = mid + 1;
        }
        else
        {
            r = mid - 1;
        }
    }
    return a[nodes[ans].id];
}

void add(int num,int x,int v)
{
    while(x <= n)
    {
        c[num][x] += v;
        c[num][x] %= mod;
        x += x & (-x);
    }
}

int query(int num,int x)
{
    int res = 0;
    while(x)
    {
        res += c[num][x];
        res %= mod;
        x -= x & (-x);
    }
    return res;
}

int main()
{
    while(~scanf("%d%d",&n,&d))
    {
        for(int i = 1;i <= n;i++)
        {
            scanf("%d",&b[i]);
            nodes[i].id = i;nodes[i].v = b[i];
        }
        sort(nodes + 1,nodes + 1 + n);
        int cnt = 0;
        a[nodes[1].id] = ++cnt;
        for(int i = 2;i <= n;i++)
        {
            if(nodes[i].v == nodes[i - 1].v)a[nodes[i].id] = cnt;
            else a[nodes[i].id] = ++cnt;
        }
        memset(c,0,sizeof(c));
        for(int i = 1;i <= n;i++)
        {
            int l = bin_l(i);
            int r = bin_r(i);
            
            int tmp = query(1,r) - query(1,l - 1) + query(2,r) - query(2,l - 1);
            tmp = (tmp + mod) % mod;
            add(1,a[i],1);add(2,a[i],tmp);
        }
        int ans = query(2,n);
        printf("%d\n",ans);
    }
    return 0;
}