定义

template < typename Key >struct Splay ;

Splay 是关联容器，含有 key 类型对象的已排序集。用比较函数less<Key>进行排序。搜索、移除和插入拥有对数复杂度。 Splay 以Splay树实现。

成员类型

成员

可能的实现

template < typename Key >
struct Splay {
    int rt, tot, fa[MAXN], ch[MAXN][2], cnt[MAXN], sz[MAXN];
    Key val[MAXN];
    void maintain( int x ) {
        sz[x] = sz[ch[x][0]] + sz[ch[x][1]] + cnt[x];
    }
    bool get( int x ) {
        return x == ch[fa[x]][1];
    }
    void clear( int x ) {
        ch[x][0] = ch[x][1] = fa[x] = val[x] = sz[x] = cnt[x] = 0;
    }
    void rotate( int x ) {
        int y = fa[x], z = fa[y], chk = get( x );
        ch[y][chk] = ch[x][chk ^ 1];
        fa[ch[x][chk ^ 1]] = y;
        ch[x][chk ^ 1] = y;
        fa[y] = x;
        fa[x] = z;
        if ( z )
            ch[z][y == ch[z][1]] = x;
        maintain( x );
        maintain( y );
    }
    void splay( int x ) {
        for ( int f = fa[x]; f = fa[x], f; rotate( x ) )
            if ( fa[f] )
                rotate( get( x ) == get( f ) ? f : x );
        rt = x;
    }
    void ins( int k ) {
        if ( !rt ) {
            val[++tot] = k;
            cnt[tot]++;
            rt = tot;
            maintain( rt );
            return;
        }
        int cnr = rt, f = 0;
        while ( true ) {
            if ( val[cnr] == k ) {
                cnt[cnr]++;
                maintain( cnr );
                maintain( f );
                splay( cnr );
                break;
            }
            f = cnr;
            cnr = ch[cnr][val[cnr] < k];
            if ( !cnr ) {
                val[++tot] = k;
                cnt[tot]++;
                fa[tot] = f;
                ch[f][val[f] < k] = tot;
                maintain( tot );
                maintain( f );
                splay( tot );
                break;
            }
        }
    }
    int rk( int k ) {
        int res = 0, cnr = rt;
        while ( 1 ) {
            if ( k < val[cnr] ) {
                cnr = ch[cnr][0];
            }
            else {
                res += sz[ch[cnr][0]];
                if ( k == val[cnr] ) {
                    splay( cnr );
                    return res + 1;
                }
                res += cnt[cnr];
                cnr = ch[cnr][1];
            }
        }
    }
    int kth( int k ) {
        int cnr = rt;
        while ( 1 ) {
            if ( ch[cnr][0] && k <= sz[ch[cnr][0]] ) {
                cnr = ch[cnr][0];
            }
            else {
                k -= cnt[cnr] + sz[ch[cnr][0]];
                if ( k <= 0 )
                    return val[cnr];
                cnr = ch[cnr][1];
            }
        }
    }
    int pre() {
        int cnr = ch[rt][0];
        while ( ch[cnr][1] )
            cnr = ch[cnr][1];
        return cnr;
    }
    int nxt() {
        int cnr = ch[rt][1];
        while ( ch[cnr][0] )
            cnr = ch[cnr][0];
        return cnr;
    }
    void del( int k ) {
        rk( k );
        if ( cnt[rt] > 1 ) {
            cnt[rt]--;
            maintain( rt );
            return;
        }
        if ( !ch[rt][0] && !ch[rt][1] ) {
            clear( rt );
            rt = 0;
            return;
        }
        if ( !ch[rt][0] ) {
            int cnr = rt;
            rt = ch[rt][1];
            fa[rt] = 0;
            clear( cnr );
            return;
        }
        if ( !ch[rt][1] ) {
            int cnr = rt;
            rt = ch[rt][0];
            fa[rt] = 0;
            clear( cnr );
            return;
        }
        int x = pre(), cnr = rt;
        splay( x );
        fa[ch[cnr][1]] = x;
        ch[x][1] = ch[cnr][1];
        clear( cnr );
        maintain( rt );
    }
    int pre( int x ) {
        int ans;
        ins( x );
        ans = val[pre()];
        del( x );
        return ans;
    }
    int nxt( int x ) {
        int ans;
        ins( x );
        ans = val[nxt()];
        del( x );
        return ans;
    }
    bool empty() {
        return tot == 0;
    }
    int size() {
        return tot;
    }
};

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