【BZOJ 3223】 文艺平衡树

【题目链接】

点击打开链接

【算法】

本题是splay区间操作的模板题

我们每个点的权值设为”当前在序列中的排名“，根据二叉排序树的性质，这棵树的中序遍历就是当前序列

如果我们要获得一段区间[l,r]，那么我们将l-1splay到根节点，将r+1splay到根节点的右子树的根，我们发现，根节点

的右节点的左子树就是区间[l,r]

对于翻转操作，我们其实只需将“根节点的右节点的左子树”这棵树不断地进行左右子树交换就可以了，但是，为了避免

交换次数太多，我们可以像线段树那样，每个点都存一个懒惰标记

【代码】

#include<bits/stdc++.h>
using namespace std;
#define MAXN 100000

int i,N,M,l,r;

template <typename T> inline void read(T &x) {
        int f = ; x = ;
        char c = getchar();
        for (; !isdigit(c); c = getchar()) { if (c == '-') f = -f; }
        for (; isdigit(c); c = getchar()) x = (x << ) + (x << ) + c - '';
        x *= f;
}

template <typename T> inline void write(T x) {
    if (x < ) { putchar('-'); x = -x; }
    if (x > ) write(x/);
    putchar(x%+'');
}

template <typename T> inline void writeln(T x) {
    write(x);
    puts("");
}

struct Splay {
        int root,total;
        struct Node {
                int size,val,son[],fa;
                bool rev;
        } Tree[MAXN+];
        inline bool get(int x) {
                return Tree[Tree[x].fa].son[] == x;
        }
        inline void update(int index) {
                Tree[index].size = Tree[Tree[index].son[]].size + Tree[Tree[index].son[]].size + ;
        }
        inline void build(int index,int l,int r) {
                int mid = (l + r) >> ;
                Tree[index].rev = false;
                Tree[index].val = mid;
                Tree[index].size = ;
                if (l == r) return;
                if (l <= mid - ) {
                        ++total;
                        Tree[index].son[] = total;
                        Tree[total].fa = index;
                        build(total,l,mid-);
                        Tree[index].size += Tree[Tree[index].son[]].size;
                }
                if (mid +  <= r) {
                        ++total;
                        Tree[index].son[] = total;
                        Tree[total].fa = index;
                        build(total,mid+,r);
                        Tree[index].size += Tree[Tree[index].son[]].size;
                }
        }
        inline void rotate(int x) {
                int f = Tree[x].fa,g = Tree[f].fa,
                tmpx = get(x),tmpf = get(f);
                if (Tree[f].rev) pushdown(f);
                if (Tree[x].rev) pushdown(x);
                if (!f) return;
                Tree[f].son[tmpx] = Tree[x].son[tmpx^];
                if (Tree[x].son[tmpx^]) Tree[Tree[x].son[tmpx^]].fa = f;
                Tree[x].son[tmpx^] = f;
                Tree[f].fa = x;
                Tree[x].fa = g;
                if (g) Tree[g].son[tmpf] = x;
                update(f);
                update(x);
        }
        inline void splay(int x) {
                int f;
                for (f = Tree[x].fa; (f = Tree[x].fa); rotate(x))
                        if (Tree[f].fa) rotate(get(x) == get(f) ? f : x);
                root = x;
        }
        inline void splayII(int x) {
                int f;
                for (f = Tree[x].fa; (f = Tree[x].fa) != root; rotate(x)) {
                        if (Tree[f].fa != root) rotate(get(x) == get(f) ? f : x);
                }
        }
        inline void pushdown(int index) {
                swap(Tree[index].son[],Tree[index].son[]);
                Tree[Tree[index].son[]].rev ^= ;
                Tree[Tree[index].son[]].rev ^= ;
                Tree[index].rev = ;
        }
        inline int query_pos(int x) {
                int index = root;
                while (true) {
                        if (Tree[index].rev) pushdown(index);
                        if (x <= Tree[Tree[index].son[]].size) index = Tree[index].son[];
                        else {
                                x -= Tree[Tree[index].son[]].size;
                                if (x == ) return index;
                                --x;
                                index = Tree[index].son[];
                        }
                }
        }
        inline int query_val(int x) {
                int pos = query_pos(x);
                return Tree[pos].val;
        }
        inline void reverse(int l,int r) {
                int x = query_pos(l-),
                        y = query_pos(r+);
                splay(x); splayII(y);
                Tree[Tree[Tree[root].son[]].son[]].rev ^= ;
        }
} T;

int main() {

        read(N); read(M);

        T.total = ;
        T.root = ;
        T.build(,,N+);

        while (M--) {
                read(l); read(r);
                T.reverse(l+,r+);
        }

        for (i = ; i <= N + ; i++) {
                if (i == ) write(T.query_val(i)-);
                else { putchar(' '); write(T.query_val(i)-); }
        }
        putchar(' ');

        puts("");

        return ;

}