BZOJ 3236 AHOI 2013 作业 莫队算法

题目大意：给出一些数，问在一个区间中不同的数值有多少种，和在一个区间中不同的数值有多少个。

思路：因为没有改动，所以就想到了莫队算法。然后我写了5K+的曼哈顿距离最小生成树，然后果断T了。(100s的时限啊,刷status都要刷疯了..,结果最后加了手写读入也没能A)。

后来果断放弃，写了分块版的莫队算法。

84sAC。。。这题卡的。。貌似莫队并非正解。

其有用分块来写莫队就非常easy了。仅仅须要将全部询问的区间排序。左端点所在块作为第一键值，右端点作为第二季键值排序，之后就能够转移了。理论上来时还是曼哈顿距离最小生成树比較快。可是常数实在是太大。随处可见的pair。sort。。

还不太好写。

。

唉。

。

时代的眼泪。。。

CODE(84816AC)：

#include <cmath>
#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#define MAX 1100010
using namespace std;

struct Ask{
	int x,y,_id;
	int block;
	int a,b;

	bool operator <(const Ask &a)const {
		if(block == a.block)	return y < a.y;
		return block < a.block;
	}
	void Read(int p) {
		scanf("%d%d%d%d",&x,&y,&a,&b);
		_id = p;
	}
}ask[MAX];

int cnt,asks;
pair<int,int *> xx[MAX << 1];
int src[MAX];

int t;
int fenwick[MAX << 1],_fenwick[MAX];
int num[MAX];
pair<int,int> ans[MAX];

inline int GetSum(int fenwick[],int x)
{
	int re = 0;
	for(; x; x -= x&-x)
		re += fenwick[x];
	return re;
}

inline void Fix(int fenwick[],int x,int c)
{
	for(; x <= t; x += x&-x)
		fenwick[x] += c;
}

int main()
{
	cin >> cnt >> asks;
	int temp = 0;
	for(int i = 1; i <= cnt; ++i)
		scanf("%d",&xx[++temp].first),xx[temp].second = &src[i];
	for(int i = 1; i <= asks; ++i) {
		ask[i].Read(i);
		xx[++temp] = make_pair(ask[i].a,&ask[i].a);
		xx[++temp] = make_pair(ask[i].b,&ask[i].b);
	}
	sort(xx + 1,xx + temp + 1);
	for(int i = 1; i <= temp; ++i) {
		if(!t || xx[i].first != xx[i - 1].first)
			++t;
		*xx[i].second = t;
	}
	int block = static_cast<int>(sqrt(cnt));
	for(int i = 1; i <= asks; ++i)
		ask[i].block = ask[i].x / block;
	sort(ask + 1,ask + asks + 1);
	int l = 1,r = 0;
	for(int x = 1; x <= asks; ++x) {
		while(r < ask[x].y) {
			++num[src[++r]];
			Fix(fenwick,src[r],1);
			if(num[src[r]] == 1)	Fix(_fenwick,src[r],1);
		}
		while(l > ask[x].x) {
			++num[src[--l]];
			Fix(fenwick,src[l],1);
			if(num[src[l]] == 1)	Fix(_fenwick,src[l],1);
		}
		while(r > ask[x].y) {
			--num[src[r]];
			Fix(fenwick,src[r],-1);
			if(!num[src[r]])	Fix(_fenwick,src[r],-1);
			--r;
		}
		while(l < ask[x].x) {
			--num[src[l]];
			Fix(fenwick,src[l],-1);
			if(!num[src[l]])	Fix(_fenwick,src[l],-1);
			++l;
		}
		int p = ask[x]._id;
		ans[p].first = GetSum(fenwick,ask[x].b) - GetSum(fenwick,ask[x].a - 1);
		ans[p].second = GetSum(_fenwick,ask[x].b) - GetSum(_fenwick,ask[x].a - 1);
	}
	for(int i = 1; i <= asks; ++i)
		printf("%d %d\n",ans[i].first,ans[i].second);
	return 0;
}

CODE(TLE)：

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#define MAX 1100010
#define INF 0x3f3f3f3f
using namespace std;

inline int GetInt()
{
    int res=0;
    char t=getchar();
    for (;t>'9'||t<'0';t=getchar());
    for (;t>='0'&&t<='9';t=getchar()) res=res*10+t-'0';
    return res;
}

struct Ask{
    int x,y,_id;
    int a,b;

    bool operator <(const Ask &a)const {
        if(x == a.x)    return y < a.y;
        return x < a.x;
    }
    void Read() {
        x = GetInt();
        y = GetInt();
        a = GetInt();
        b = GetInt();
    }
}ask[MAX];

struct Edge{
    int x,y,length;

    Edge(int _,int __,int ___):x(_),y(__),length(___) {}
    Edge() {}
    bool operator <(const Edge &a)const {
        return length < a.length;
    }
}edge[MAX << 3];

int cnt,asks;
int src[MAX];

int y_x[MAX],t,gt,edges;
pair<int,int *> xx[MAX << 1];
int fenwick[MAX << 1],_fenwick[MAX];

int father[MAX];

int head[MAX],total;
int next[MAX << 1],aim[MAX << 1];

int num[MAX];
pair<int,int> ans[MAX];

inline int CalcM(const Ask &a,const Ask &b)
{
    return abs(a.x - b.x) + abs(a.y - b.y);
}

inline int GetPos(int x)
{
    int re = 0;
    for(; x <= t; x += x&-x)
        if(ask[fenwick[x]].x + ask[fenwick[x]].y < ask[re].x + ask[re].y)
            re = fenwick[x];
    return re;
}

inline void Fix(int x,int pos)
{
    for(; x; x -= x&-x)
        if(ask[fenwick[x]].x + ask[fenwick[x]].y > ask[pos].x + ask[pos].y)
            fenwick[x] = pos;
}

void MakeGraph()
{
    for(int dir = 1; dir <= 4; ++dir) {
        if(dir == 2 || dir == 4)
            for(int i = 1; i <= asks; ++i)
                swap(ask[i].x,ask[i].y);
        if(dir == 3)
            for(int i = 1; i <= asks; ++i)
                ask[i].y *= -1;
        sort(ask + 1,ask + asks + 1);
        for(int i = 1; i <= asks; ++i)
            xx[i] = make_pair(ask[i].y - ask[i].x,&y_x[i]);
        sort(xx + 1,xx + asks + 1);
        t = 0;
        for(int i = 1; i <= asks; ++i) {
            if(!t || xx[i].first != xx[i - 1].first)
                ++t;
            *xx[i].second = t;
        }
        memset(fenwick,0,sizeof(fenwick));
        for(int i = asks; i; --i) {
            int temp = GetPos(y_x[i]);
            if(temp)
                edge[++edges] = Edge(ask[temp]._id,ask[i]._id,CalcM(ask[temp],ask[i]));
            Fix(y_x[i],i);
        }
    }
    for(int i = 1; i <= asks; ++i)
        ask[i].x *= -1;
}

int Find(int x)
{
    if(father[x] == x)  return x;
    return father[x] = Find(father[x]);
}

inline void Add(int x,int y)
{
    next[++total] = head[x];
    aim[total] = y;
    head[x] = total;
}

void MST()
{
    sort(edge + 1,edge + edges + 1);
    for(int i = 1; i <= edges; ++i) {
        int fx = Find(edge[i].x);
        int fy = Find(edge[i].y);
        if(fx != fy) {
            father[fx] = fy;
            Add(fx,fy),Add(fy,fx);
        }
    }
}

inline int GetSum(int fenwick[],int x)
{
    int re = 0;
    for(; x; x -= x&-x)
        re += fenwick[x];
    return re;
}

inline void Fix(int fenwick[],int x,int c)
{
    for(; x <= gt; x += x&-x)
        fenwick[x] += c;
}

void DFS(int x,int last)
{
    static int l = 1,r = 0;

    while(r < ask[x].y) {
        ++num[src[++r]];
        Fix(fenwick,src[r],1);
        if(num[src[r]] == 1)    Fix(_fenwick,src[r],1);
    }
    while(l > ask[x].x) {
        ++num[src[--l]];
        Fix(fenwick,src[l],1);
        if(num[src[l]] == 1)    Fix(_fenwick,src[l],1);
    }
    while(r > ask[x].y) {
        --num[src[r]];
        Fix(fenwick,src[r],-1);
        if(!num[src[r]])    Fix(_fenwick,src[r],-1);
        --r;
    }
    while(l < ask[x].x) {
        --num[src[l]];
        Fix(fenwick,src[l],-1);
        if(!num[src[l]])    Fix(_fenwick,src[l],-1);
        ++l;
    }

    int p = ask[x]._id;
    ans[p].first = GetSum(fenwick,ask[x].b) - GetSum(fenwick,ask[x].a - 1);
    ans[p].second = GetSum(_fenwick,ask[x].b) - GetSum(_fenwick,ask[x].a - 1);

    for(int i = head[x]; i; i = next[i]) {
        if(aim[i] == last)  continue;
        DFS(aim[i],x);

        while(r < ask[x].y) {
            ++num[src[++r]];
            Fix(fenwick,src[r],1);
            if(num[src[r]] == 1)    Fix(_fenwick,src[r],1);
        }
        while(l > ask[x].x) {
            ++num[src[--l]];
            Fix(fenwick,src[l],1);
            if(num[src[l]] == 1)    Fix(_fenwick,src[l],1);
        }
        while(r > ask[x].y) {
            --num[src[r]];
            Fix(fenwick,src[r],-1);
            if(!num[src[r]])    Fix(_fenwick,src[r],-1);
            --r;
        }
        while(l < ask[x].x) {
            --num[src[l]];
            Fix(fenwick,src[l],-1);
            if(!num[src[l]])    Fix(_fenwick,src[l],-1);
            ++l;
        }
    }
}

int main()
{
    ask[0].x = ask[0].y = INF;
    cnt = GetInt();
    asks = GetInt();
    int temp = 0;
    for(int i = 1; i <= cnt; ++i) {
        xx[++temp].first = GetInt();
        xx[temp].second = &src[i];
    }
    for(int i = 1; i <= asks; ++i) {
        ask[i].Read();
        xx[++temp] = make_pair(ask[i].a,&ask[i].a);
        xx[++temp] = make_pair(ask[i].b,&ask[i].b);
        ask[i]._id = i;
        father[i] = i;
    }
    sort(xx + 1,xx + temp + 1);
    for(int i = 1; i <= temp; ++i) {
        if(!gt || xx[i].first != xx[i - 1].first)
            ++gt;
        *xx[i].second = gt;
    }
    MakeGraph();
    MST();
    memset(fenwick,0,sizeof(fenwick));
    DFS(1,0);
    for(int i = 1; i <= asks; ++i)
        printf("%d %d\n",ans[i].first,ans[i].second);
    return 0;
}