飞旋treap

虽然叫做非旋treap但是飞旋treap很带感所以就用这个名字了(SB)

这个东西是真的好写......

主要的两个函数只有两个，rotate和splay，split和merge。

merge就是大家都熟悉的左偏树合并，线段树合并......注意不能swap(x, y)

split分为splitV和splitS，按权值分，按大小分。

 inline void splitS(int o, int k, int &x, int &y) {
     if(!o) {
         x = y = ;
         return;
     }
     //pushdown(o);
     if(k <= siz[ls[o]]) {
         y = o;
         splitS(ls[y], k, x, ls[y]);
     }
     else {
         x = o;
         splitS(rs[x], k - siz[ls[o]] - , rs[x], y);
     }
     pushup(o);
     return;
 }

splitS

 inline void splitV(int o, int k, int &x, int &y) {
     if(!o) {
         x = y = ;
         return;
     }
     pushdown(o);
     if(val[o] <= k) {
         x = o;
         splitV(rs[x], k, rs[x], y);
     }
     else {
         y = o;
         splitV(ls[y], k, x, ls[y]);
     }
     pushup(o);
     return;
 }

splitV

 inline int merge(int x, int y) {
     if(!x || !y) {
         return x | y;
     }
     if(rd[x] >= rd[y]) {
         pushdown(x);
         rs[x] = merge(rs[x], y);
         pushup(x);
         return x;
     }
     else {
         pushdown(y);
         ls[y] = merge(x, ls[y]);
         pushup(y);
         return y;
     }
 }

merge

这个东西写着一般不去重。

接下来放例题。

 #include <cstdio>
 #include <algorithm>
 #include <climits>
 #include <cstdlib>
 #include <ctime>

 typedef long long LL;
 const int N = , INF = 0x3f3f3f3f;

 int ls[N], rs[N], val[N], rd[N], siz[N], tot, root;

 inline void pushup(int o) {
     siz[o] = siz[ls[o]] + siz[rs[o]] + ;
     return;
 }

 inline void pushdown(int o) {
     return;
 }

 inline void splitV(int o, int k, int &x, int &y) {
     if(!o) {
         x = y = ;
         return;
     }
     pushdown(o);
     if(val[o] <= k) {
         x = o;
         splitV(rs[x], k, rs[x], y);
     }
     else {
         y = o;
         splitV(ls[y], k, x, ls[y]);
     }
     pushup(o);
     return;
 }

 inline int merge(int x, int y) {
     if(!x || !y) {
         return x | y;
     }
     if(rd[x] >= rd[y]) {
         pushdown(x);
         rs[x] = merge(rs[x], y);
         pushup(x);
         return x;
     }
     else {
         pushdown(y);
         ls[y] = merge(x, ls[y]);
         pushup(y);
         return y;
     }
 }

 inline int np(int k) {
     int o = ++tot;
     siz[o] = ;
     rd[o] = (((LL)rand() << ) + rand()) % LONG_MAX;
     val[o] = k;
     return o;
 }

 inline int getLP(int x) {
     while(ls[x]) {
         x = ls[x];
     }
     return x;
 }

 inline int getRP(int x) {
     while(rs[x]) {
         x = rs[x];
     }
     return x;
 }

 inline int cal(int l, int r, int k) {
     if(l == -INF && r == INF) {
         return k;
     }
     return std::min(k - l, r - k);
 }

 inline void out(int x) {
     if(ls[x]) {
         out(ls[x]);
     }
     printf("%d ", val[x]);
     if(rs[x]) {
         out(rs[x]);
     }
     return;
 }

 int main() {
     srand(time());
     int n;
     scanf("%d", &n);
     int x = np(-INF), y = np(INF);
     root = merge(x, y);
     LL ans = ;
     for(int i = ; i <= n; i++) {
         int k;
         scanf("%d", &k);
         splitV(root, k, x, y);
         //printf("X : "); out(x); puts("");
         //printf("Y : "); out(y); puts("");
         int a = getRP(x), b = getLP(y);
         ans += cal(val[a], val[b], k);
         root = merge(merge(x, np(k)), y);
         //out(root); puts("");
     }
     printf("%lld\n", ans);
     return ;
 }

洛谷P2234 营业额统计

 #include <cstdio>
 #include <algorithm>
 #include <cstring>
 #include <cstdlib>
 #include <ctime>
 #include <climits>

 typedef long long LL;
 const int N = , INF = 0x3f3f3f3f;

 int ls[N], rs[N], siz[N], val[N], rd[N], tot, root;

 inline void pushup(int x) {
     siz[x] = siz[ls[x]] + siz[rs[x]] + ;
     return;
 }

 inline int merge(int x, int y) {
     if(!x || !y) {
         return x | y;
     }
     if(rd[x] >= rd[y]) {
         //pushdown(x);
         rs[x] = merge(rs[x], y);
         pushup(x);
         return x;
     }
     else {
         //pushdown(y);
         ls[y] = merge(x, ls[y]);
         pushup(y);
         return y;
     }
 }

 inline void splitV(int o, int k, int &x, int &y) {
     if(!o) {
         x = y = ;
         return;
     }
     //pushdown(o);
     //printf("o = %d \n", o);
     if(val[o] <= k) {
         x = o;
         splitV(rs[x], k, rs[x], y);
     }
     else {
         y = o;
         splitV(ls[y], k, x, ls[y]);
     }
     pushup(o);
     return;
 }

 inline void splitS(int o, int k, int &x, int &y) {
     if(!o) {
         x = y = ;
         return;
     }
     //pushdown(o);
     if(k <= siz[ls[o]]) {
         y = o;
         splitS(ls[y], k, x, ls[y]);
     }
     else {
         x = o;
         splitS(rs[x], k - siz[ls[o]] - , rs[x], y);
     }
     pushup(o);
     return;
 }

 inline int np(int k) {
     int o = ++tot;
     siz[o] = ;
     val[o] = k;
     rd[o] = (((LL)rand() << ) + rand()) % LONG_MAX;
     return o;
 }

 inline void insert(int k) {
     int x, y;
     splitV(root, k, x, y);
     root = merge(merge(x, np(k)), y);
     return;
 }

 inline int getLP(int x) {
     while(ls[x]) {
         x = ls[x];
     }
     return x;
 }

 inline int getRP(int x) {
     while(rs[x]) {
         x = rs[x];
     }
     return x;
 }

 inline int getVbyR(int k) {
     int x, y;
     splitS(root, k, x, y);
     int t = val[getLP(y)];
     root = merge(x, y);
     return t;
 }

 inline int getRbyV(int k) {
     int x, y;
     splitV(root, k - , x, y);
     int t = siz[x];
     root = merge(x, y);
     return t;
 }

 inline int getPre(int k) {
     int x, y;
     splitV(root, k - , x, y);
     int t = val[getRP(x)];
     root = merge(x, y);
     return t;
 }

 inline int getNex(int k) {
     int x, y;
     splitV(root, k, x, y);
     int t = val[getLP(y)];
     root = merge(x, y);
     return t;
 }

 inline void del(int k) {
     int x, y, z;
     splitV(root, k - , x, y);
     splitS(y, , z, y);
     root = merge(x, y);
     return;
 }

 int main() {
     srand(time());
     int n;
     scanf("%d", &n);
     root = merge(np(-INF), np(INF));

     for(int i = , f, x; i <= n; i++) {
         scanf("%d%d", &f, &x);
         if(f == ) insert(x);
         else if(f == ) del(x);
         else if(f == ) printf("%d\n", getRbyV(x));
         else if(f == ) printf("%d\n", getVbyR(x));
         else if(f == ) printf("%d\n", getPre(x));
         else if(f == ) printf("%d\n", getNex(x));
     }

     return ;
 }

洛谷P3369 普通平衡树

 #include <cstdio>
 #include <algorithm>
 #include <cstdlib>
 #include <ctime>
 #include <cstring>
 #include <climits>

 typedef long long LL;
 const int N = ;

 int ls[N], rs[N], val[N], rd[N], siz[N], tot, root;
 bool rev[N];

 inline void pushup(int x) {
     siz[x] = siz[ls[x]] + siz[rs[x]] + ;
     return;
 }

 inline void pushdown(int x) {
     if(rev[x]) {
         std::swap(ls[x], rs[x]);
         if(ls[x]) {
             rev[ls[x]] ^= ;
         }
         if(rs[x]) {
             rev[rs[x]] ^= ;
         }
         rev[x] = ;
     }
     return;
 }

 inline int merge(int x, int y) {
     if(!x || !y) {
         return x | y;
     }
     if(rd[x] >= rd[y]) {
         pushdown(x);
         rs[x] = merge(rs[x], y);
         pushup(x);
         return x;
     }
     else {
         pushdown(y);
         ls[y] = merge(x, ls[y]);
         pushup(y);
         return y;
     }
 }

 inline void splitS(int o, int k, int &x, int &y) {
     if(!o) {
         x = y = ;
         return;
     }
     pushdown(o);
     if(k <= siz[ls[o]]) {
         y = o;
         splitS(ls[y], k, x, ls[y]);
     }
     else {
         x = o;
         splitS(rs[x], k - siz[ls[o]] - , rs[x], y);
     }
     pushup(o);
     return;
 }

 inline int np(int k) {
     int o = ++tot;
     siz[o] = ;
     val[o] = k;
     rd[o] = (((LL)rand() << ) + rand()) % LONG_MAX;
     return o;
 }

 inline void reverse(int l, int r) {
     int x, y, z;
     splitS(root, l, x, y);
     splitS(y, r - l + , y, z);
     rev[y] ^= ;
     root = merge(merge(x, y), z);
     return;
 }

 inline void insert(int p, int k) {
     int x, y;
     splitS(root, p + , x, y);
     root = merge(merge(x, np(k)), y);
     return;
 }

 void out(int x) {
     pushdown(x);
     if(ls[x]) out(ls[x]);
     if(val[x]) printf("%d ", val[x]);
     if(rs[x]) out(rs[x]);
     return;
 }

 int main() {
     int n, m;
     scanf("%d%d", &n, &m);
     root = merge(np(), np());
     for(int i = ; i <= n; i++) {
         insert(i - , i);
     }
     for(int i = , x, y; i <= m; i++) {
         scanf("%d%d", &x, &y);
         reverse(x, y);
     }
     out(root);
     return ;
 }

洛谷P3391 文艺平衡树

注意不要把split里的o写成x.....