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 = ;

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

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

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

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

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

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

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

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

AC代码