[POJ 2528] Mayor's posters Splay樹

http://poj.org/problem?id=2528

題意：有一面空白的牆，然後在上面貼廣告，新的廣告會覆蓋以前貼的廣告。問最後牆上有多少能看到的廣告。

思路：區間問題可以用Splay樹，線段樹等算法，由於廣告的長度最大能到 10000000 但是廣告的數量最多隻有 10000 所以現對數據離散化，離散化的時候要在間隔大於 1 的兩個點之間插入一個數，避免覆蓋兩端後中間的的也沒了，例如數據：
1
3
2 4
1 2
4 5
如果離散化的時候不再 2 和 4 中間插入一個 3 的話，最後的結果就會變成 2。

線段樹（94ms）：

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

using namespace std;

const int maxn = 40005;

struct Tree{
    int l, r;
    int val, lazy;
    inline void SetTree(int l, int r, int val, int lazy){
        this->l = l;
        this->r = r;
        this->val = val;
        this->lazy = lazy;
    }
};

struct Node{
    int l, r;
};

int n, m;
Tree tr[maxn << 2];
Node node[maxn >> 1];

int ary[maxn];
int ary1[maxn];

int Find(int *ary, int l, int r, int val)
{
    int mid = (l + r) >> 1;
    if(ary[mid] == val){
        return mid;
    }else if(ary[mid] > val){
        return Find(ary, l, mid, val);
    }else{
        return Find(ary, mid + 1, r, val);
    }
}

void PushDown(int rt)
{
    if(!tr[rt].lazy || tr[rt].l == tr[rt].r)
        return ;
    tr[rt << 1].val = tr[rt].lazy;
    tr[rt << 1 | 1].val = tr[rt].lazy;
    tr[rt << 1].lazy = tr[rt].lazy;
    tr[rt << 1 | 1].lazy = tr[rt].lazy;
    tr[rt].lazy = 0;
}

void BuildTree(int rt, int l, int r)
{
    tr[rt].SetTree(l, r, 0, 0);
    if(l == r)
        return ;
    int mid = (l + r) >> 1;
    BuildTree(rt << 1, l, mid);
    BuildTree(rt << 1 | 1, mid  + 1, r);
}

void Updata(int rt, int l, int r, int  val)
{
    PushDown(rt);
    if(tr[rt].l > r || tr[rt].r < l)
        return ;
    if(tr[rt].l >= l && tr[rt].r <= r){
        tr[rt].val = val;
        tr[rt].lazy = val;
        return ;
    }
    Updata(rt << 1, l, r, val);
    Updata(rt << 1 | 1, l, r, val);
    return ;
}

bool res[maxn];

void Query(int rt)
{
    PushDown(rt);
    if(tr[rt].l == tr[rt].r){
        res[tr[rt].val] = true;
    }else{
        Query(rt << 1);
        Query(rt << 1 | 1);
    }
}


int main()
{
    int Test;
    scanf("%d", &Test);
    while(Test--){
        scanf("%d", &m);
        for(int i = 0; i < m; i++){
            scanf("%d%d", &node[i].l, &node[i].r);
            ary[i << 1] = node[i].l;
            ary[i << 1 | 1] = node[i].r;
        }
        int len = (m << 1);
        sort(ary, ary + len);
        int temp = 0;
        ary1[temp++] = ary[0];
        for(int i = 1; i < len; i++){
            if(ary[i] > ary[i - 1] + 1)  //在間隔大於 1 的位置插入一個數
                ary1[temp++] = ary[i - 1] + 1;
            ary1[temp++] = ary[i];
        }
        len = temp;
        temp = 0;
        for(int i = 1; i < len; i++){   //離散化
            if(ary1[i] == ary[temp])
                continue;
            ary[++temp] = ary1[i];
        }
        len = temp + 1;
        BuildTree(1, 1, len);
        memset(res, false, sizeof(res));
        for(int i = 0; i < m; i++){
            node[i].l = Find(ary, 0, len - 1, node[i].l) + 1;
            node[i].r = Find(ary, 0, len - 1, node[i].r) + 1;
            Updata(1, node[i].l, node[i].r, i + 1);
        }
        Query(1);
        int ans = 0;
        for(int i = 1; i <= m; i++){
            ans += (res[i] == true);
        }
        printf("%d\n", ans);
    }
    return 0;
}

Splay（94ms）：

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

using namespace std;

const int maxn = 40005;

struct Tree{
    int pre, chd[2];
    int val, lazy, Size;
    inline void SetTree(int pre, int chd0, int chd1, int val, int lazy, int Size){
        this->pre = pre;
        this->chd[0] = chd0;
        this->chd[1] = chd1;
        this->val = val;
        this->lazy = lazy;
        this->Size = Size;
    }
};

struct Node{
    int l, r;
};

int n, m;
Tree tr[maxn];
Node node[maxn >> 1];

int ary[maxn];
int ary1[maxn];

bool res[maxn];

void PushUp(int rt)
{
    tr[tr[rt].chd[0]].pre = rt;
    tr[tr[rt].chd[1]].pre = rt;
    tr[rt].Size = tr[tr[rt].chd[0]].Size + tr[tr[rt].chd[1]].Size + 1;
}

void PushDown(int rt)
{
    if(!tr[rt].lazy)
        return ;
    if(tr[rt].chd[0]){
        tr[tr[rt].chd[0]].val = tr[rt].lazy;
        tr[tr[rt].chd[0]].lazy = tr[rt].lazy;
    }
    if(tr[rt].chd[1]){
        tr[tr[rt].chd[1]].val = tr[rt].lazy;
        tr[tr[rt].chd[1]].lazy = tr[rt].lazy;
    }
    tr[rt].lazy = 0;
}

int F(int rt){
    return tr[tr[rt].pre].chd[1] == rt;
}

void Rotate(int rt)
{
    int chd = F(rt);
    int pre = tr[rt].pre;
    tr[rt].pre = tr[pre].pre;
    tr[tr[pre].pre].chd[F(pre)] = rt;
    tr[pre].chd[chd] = tr[rt].chd[!chd];
    tr[rt].chd[!chd] = pre;
    PushUp(pre);
    PushUp(rt);
}


int Splay(int rt, int rw)
{
    while(tr[rw].pre != rt){
        int pre = tr[rw].pre;
        if(F(rw) != F(pre) || tr[pre].pre == rt){
            Rotate(rw);
        }else{
            Rotate(pre);
            Rotate(rw);
        }
    }
    if(rt)
        PushUp(rt);
    return rw;
}

int Serch(int rt, int pos)
{
    int ret = rt;
    PushDown(rt);
    if(tr[tr[rt].chd[0]].Size == pos - 1){
        ret = rt;
    }else if(tr[tr[rt].chd[0]].Size >= pos){
        ret = Serch(tr[rt].chd[0], pos);
    }else{
        ret = Serch(tr[rt].chd[1], pos - tr[tr[rt].chd[0]].Size - 1);
    }
    return ret;
}

void Query(int rt)
{
    if(!rt)
        return ;
    PushDown(rt);
    res[tr[rt].val] = true;
    Query(tr[rt].chd[0]);
    Query(tr[rt].chd[1]);
}

int BuildTree(int Size)
{
    for(int i = 1; i < Size; i++){
        tr[i].SetTree(i - 1, 0, i + 1, 0, 0, Size - i + 1);
    }
    tr[0].SetTree(0, 0, 0, 0, 0, 0);
    tr[Size].SetTree(Size - 1, 0, 0, 0, 0, 1);
    return 1;
}

int Find(int *ary, int l, int r, int val)
{
    int mid = (l + r) >> 1;
    if(ary[mid] == val){
        return mid;
    }else if(ary[mid] > val){
        return Find(ary, l, mid, val);
    }else{
        return Find(ary, mid + 1, r, val);
    }
}


int main()
{
    int Test;
    scanf("%d", &Test);
    while(Test--){
        scanf("%d", &m);
        for(int i = 0; i < m; i++){
            scanf("%d%d", &node[i].l, &node[i].r);
            ary[i << 1] = node[i].l;
            ary[i << 1 | 1] = node[i].r;
        }
        int len = (m << 1);
        sort(ary, ary + len);
        int temp = 0;
        ary1[temp++] = ary[0];
        for(int i = 1; i < len; i++){
            if(ary[i] > ary[i - 1] + 1)
                ary1[temp++] = ary[i - 1] + 1;
            ary1[temp++] = ary[i];
        }
        len = temp;
        temp = 0;
        for(int i = 1; i < len; i++){
            if(ary1[i] == ary[temp])
                continue;
            ary[++temp] = ary1[i];
        }
        len = temp + 1;
        int rt = BuildTree(len + 2);
        rt = Splay(0, len + 2);
        memset(res, false, sizeof(res));
        for(int i = 0; i < m; i++){
            node[i].l = Find(ary, 0, len - 1, node[i].l) + 1;
            node[i].r = Find(ary, 0, len - 1, node[i].r) + 1;
            rt = Splay(0, Serch(rt, node[i].l));
            Splay(rt, Serch(rt, node[i].r + 2));
            tr[tr[tr[rt].chd[1]].chd[0]].val = i + 1;
            tr[tr[tr[rt].chd[1]].chd[0]].lazy = i + 1;
        }
        Query(rt);
        int ans = 0;
        for(int i = 1; i <= m; i++){
            ans += (res[i] == true);
        }
        printf("%d\n", ans);
    }
    return 0;
}