HDU4742----Pinball Game 3D（三维LIS、CDQ分治）

题意：三维空间内 n个小球，对应坐标（x,y,z）。输出LIS的长度以及方案数。

首先可以先按x排序，先降低一维，然后 剩下y 、z，在y上进行CDQ分治，按y的大小用前面的更新后面的。z方向离散化之后用树状数组维护就可以了。

#include <set>
#include <map>
#include <cmath>
#include <ctime>
#include <queue>
#include <stack>
#include <cstdio>
#include <string>
#include <vector>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
typedef unsigned long long ull;
typedef long long ll;
const int inf = 0x3f3f3f3f;
const double eps = 1e-8;
const int maxn = 1e5+10;
const int mod = 1 << 30;
struct Ball
{
    int x,y,z,idx;
    bool operator < (const Ball &rhs)const
    {
        return x < rhs.x || (x == rhs.x && y < rhs.y) || (x == rhs.x && y == rhs.y && z < rhs.z);
    }
} ball[maxn],tmpball[maxn];
struct DP
{
    int len,cnt;
    DP(){}
    DP(int _len,int _cnt):
        len(_len),cnt(_cnt) {}
} dp[maxn],c[maxn];
int vec[maxn],idx;
inline int lowbit (int x)
{
    return x & -x;
}
inline void update (DP &dp1, DP &dp2)
{
    if (dp1.len < dp2.len)
        dp1 = dp2;
    else if (dp1.len == dp2.len)
        dp1.cnt += dp2.cnt;
}
inline void modify(int x,DP &d)
{
    while (x <= idx)
    {
        update(c[x],d);
        x += lowbit(x);
    }
}
DP query(int x)
{
    DP ans = DP (0,0);
    while (x)
    {
        update(ans,c[x]);
        x -= lowbit(x);
    }
    return ans;
}
inline void CLR(int x)
{
    while (x <= idx)
    {
        c[x] = DP(0,0);
        x += lowbit(x);
    }
}
void CDQ (int l, int r)
{
    if (l == r)
        return ;
    int mid = (l + r) >> 1;
    CDQ (l, mid);
    for (int i = l; i <= r; i++)
    {
        tmpball[i] = ball[i];
        tmpball[i].x = 0;
    }
   sort(tmpball+l,tmpball+r+1);
    for (int i = l; i <= r; i++)
    {
        if (tmpball[i].idx <= mid)
        {
            modify(tmpball[i].z,dp[tmpball[i].idx]);
        }
        else
        {
            DP tmp = query(tmpball[i].z);
            tmp.len++;
            update(dp[tmpball[i].idx],tmp);
        }
    }
    for (int i = l; i <= r; i++)
    {
        if (tmpball[i].idx <= mid)
        {
            CLR(tmpball[i].z);
        }
    }
    CDQ (mid+1, r);
}
int main(void)
{
#ifndef ONLINE_JUDGE
    freopen("in.txt","r",stdin);
#endif
    int T, n;
    scanf ("%d",&T);
    while (T--)
    {
        scanf ("%d",&n);
        for (int i = 1; i <= n; i++)
        {
            scanf ("%d%d%d",&ball[i].x, &ball[i].y, &ball[i].z);
            vec[i-1] = ball[i].z;
        }
        sort (ball+1, ball+n+1);
        sort (vec,vec+n);
        idx = unique(vec,vec+n) - vec;
        for (int i = 1; i <= n ; i++)
        {
            ball[i].z = lower_bound(vec,vec+idx,ball[i].z) - vec + 1;
            ball[i].idx = i;
            dp[i] = DP(1,1);
        }
        CDQ(1,n);
        DP ans = DP(0,0);
        for (int i = 1; i <= n ;i++)
        {
            update(ans,dp[i]);
        }
        printf("%d %d
",ans.len, ans.cnt % mod);
    }
    return 0;
}