洛谷P3721 单旋

什么毒瘤......

题意：模拟一棵单旋splay，求每次插入，splay最值，删除最值的操作次数。

解：乍一看感觉很神，又因为是LCT题单上的，然后就折磨了我好久，最后跑去看题解...

居然是手玩找规律题！我疯了。

是这样的，因为它只会单旋，而且只会splay最值，手玩一下就发现整个树的形态不变......就是把一个节点拿上去当根了，然后它的子节点代替它的位置。

插入，根据普通splay插入可知它一定接在前驱/后继的下面。找到深度大的那个就行了。

具体来说，用一棵值域线段树维护每个权值的深度。同时还要记录根，fa，son，树中节点数...

线段树要支持区间加，单点修改，查询第k大，区间求和，单点查询等功能。

大力分类讨论，注意一波细节，然后就A了...

#include <cstdio>
#include <algorithm>

const int N = 100010;

struct Node {
    int f, x;
}node[N];

int tag[N * 4], sum[N * 4], fa[N], s[N][2], X[N], temp;

inline void pushdown(int o) {
    if(tag[o]) {
        tag[o << 1] += tag[o];
        tag[o << 1 | 1] += tag[o];
        tag[o] = 0;
    }
    return;
}

int ask(int p, int l, int r, int o) {
    if(l == r) {
        if(!sum[o]) {
            tag[o] = 0;
        }
        return tag[o];
    }
    pushdown(o);
    int mid = (l + r) >> 1;
    if(p <= mid) {
        return ask(p, l, mid, o << 1);
    }
    else {
        return ask(p, mid + 1, r, o << 1 | 1);
    }
}

void change(int p, int v, int l, int r, int o) {
    if(l == r) {
        if(v == -1) {
            sum[o] = tag[o] = 0;
        }
        else {
            sum[o] = 1;
            tag[o] = v;
        }
        return;
    }
    pushdown(o);
    int mid = (l + r) >> 1;
    if(p <= mid) {
        change(p, v, l, mid, o << 1);
    }
    else {
        change(p, v, mid + 1, r, o << 1 | 1);
    }
    sum[o] = sum[o << 1] + sum[o << 1 | 1];
    return;
}

int getK(int k, int l, int r, int o) {
    if(l == r) {
        return r;
    }
    int mid = (l + r) >> 1;
    if(k <= sum[o << 1]) {
        return getK(k, l, mid, o << 1);
    }
    else {
        return getK(k - sum[o << 1], mid + 1, r, o << 1 | 1);
    }
}

int getSum(int L, int R, int l, int r, int o) {
    if(L <= l && r <= R) {
        return sum[o];
    }
    int mid = (l + r) >> 1, ans = 0;
    if(L <= mid) {
        ans += getSum(L, R, l, mid, o << 1);
    }
    if(mid < R) {
        ans += getSum(L, R, mid + 1, r, o << 1 | 1);
    }
    return ans;
}

void add(int L, int R, int v, int l, int r, int o) {
    if(L <= l && r <= R) {
        tag[o] += v;
        return;
    }
    pushdown(o);
    int mid = (l + r) >> 1;
    if(L <= mid) {
        add(L, R, v, l, mid, o << 1);
    }
    if(mid < R) {
        add(L, R, v, mid + 1, r, o << 1 | 1);
    }
    return;
}

int main() {
    int q, f, x, siz = 0, rt;
    scanf("%d", &q);
    for(int i = 1; i <= q; i++) {
        scanf("%d", &node[i].f);
        if(node[i].f == 1) {
            scanf("%d", &node[i].x);
            X[++temp] = node[i].x;
        }
    }
    std::sort(X + 1, X + temp + 1);
    temp = std::unique(X + 1, X + temp + 1) - X - 1;
    for(int i = 1; i <= q; i++) {
        f = node[i].f;
        if(f == 1) {
            x = std::lower_bound(X + 1, X + temp + 1, node[i].x) - X;
            int k = getSum(1, x, 1, temp, 1), d;
            if(!siz) {
                d = 1;
                rt = x;
            }
            else if(!k) {
                int r = getK(1, 1, temp, 1);
                d = ask(r, 1, temp, 1) + 1;
                fa[x] = r;
                s[r][0] = x;
            }
            else if(k == siz) {
                int l = getK(siz, 1, temp, 1);
                d = ask(l, 1, temp, 1) + 1;
                fa[x] = l;
                s[l][1] = x;
            }
            else {
                int l = getK(k, 1, temp, 1); 
                int r = getK(k + 1, 1, temp, 1);
                int dl = ask(l, 1, temp, 1);
                int dr = ask(r, 1, temp, 1);
                if(dl > dr) {
                    d = dl + 1;
                    fa[x] = l;
                    s[l][1] = x;
                }
                else {
                    d = dr + 1;
                    fa[x] = r;
                    s[r][0] = x;
                }
            }
            change(x, d, 1, temp, 1);
            printf("%d\n", d);
            siz++;
        }
        else if(f == 2) { // splay small 
            x = getK(1, 1, temp, 1);
            int d = ask(x, 1, temp, 1);
            if(d > 1) {
                int r = fa[x];
                if(s[x][1]) {
                    fa[s[x][1]] = r;
                }
                s[r][0] = s[x][1];
                add(r, temp, 1, 1, temp, 1);
                change(x, 1, 1, temp, 1);
                fa[x] = 0;
                s[x][1] = rt;
                fa[rt] = x;
                rt = x;
            }
            printf("%d\n", d);
        }
        else if(f == 3) {
            x = getK(siz, 1, temp, 1);
            int d = ask(x, 1, temp, 1);
            if(d > 1) {
                int l = fa[x];
                if(s[x][0]) {
                    fa[s[x][0]] = l;
                }
                s[l][1] = s[x][0];
                add(1, l, 1, 1, temp, 1);
                change(x, 1, 1, temp, 1);
                fa[x] = 0;
                s[x][0] = rt;
                fa[rt] = x;
                rt = x;
            }
            printf("%d\n", d);
        }
        else if(f == 4) {
            x = getK(1, 1, temp, 1);
            int d = ask(x, 1, temp, 1);
            if(d > 1) {
                int r = fa[x];
                if(s[x][1]) {
                    fa[s[x][1]] = r;
                } 
                s[r][0] = s[x][1];
                add(1, r - 1, -1, 1, temp, 1);
            }
            else {
                add(1, temp, -1, 1, temp, 1);
                rt = s[x][1];
                fa[s[x][1]] = 0;
            }
            change(x, -1, 1, temp, 1);
            printf("%d\n", d);
            siz--;
        }
        else if(f == 5) {
            x = getK(siz, 1, temp, 1);
            int d = ask(x, 1, temp, 1);
            if(d > 1) {
                int l = fa[x];
                if(s[x][0]) {
                    fa[s[x][0]] = l;
                }
                s[l][1] = s[x][0];
                add(l + 1, temp, -1, 1, temp, 1);
            }
            else {
                add(1, temp, -1, 1, temp, 1);
                rt = s[x][0];
                fa[s[x][0]] = 0;
            }
            change(x, -1, 1, temp, 1);
            printf("%d\n", d);
            siz--;
        }
    }
    return 0;
}