牛客-Forsaken的数列（Treap）

题目传送门

sol:第一次看题还真信了是用线段树来做，但是没什么想法，看了题解发现是我不会的Treap，然后花了几天时间学习了一下并补掉题目

• 无旋Treap

  #include <bits/stdc++.h>
  using namespace std;
  typedef long long LL;
  const int MAXN = 2e5 + 10;
  struct Treap {
      int ls, rs;
      int rand, size;
      LL sum, val, lazy;
  } node[MAXN];
  int root, tot;
  int add_node(int v) {
      int i = ++tot;
      node[i].ls = node[i].rs = 0;
      node[i].rand = rand();
      node[i].sum = node[i].val = v;
      node[i].lazy = 0;
      node[i].size = 1;
      return i;
  }
  void push_down(int rt) {
      int ls = node[rt].ls;
      int rs = node[rt].rs;
      if (ls != 0) {
          node[ls].lazy += node[rt].lazy;
          node[ls].val += node[rt].lazy;
          node[ls].sum += node[ls].size * node[rt].lazy;
      }
      if (rs != 0) {
          node[rs].lazy += node[rt].lazy;
          node[rs].val += node[rt].lazy;
          node[rs].sum += node[rs].size * node[rt].lazy;
      }
      node[rt].lazy = 0;
  }
  void push_up(int rt) {
      int ls = node[rt].ls;
      int rs = node[rt].rs;
      node[rt].size = node[ls].size + node[rs].size + 1;
      node[rt].sum = node[ls].sum + node[rs].sum + node[rt].val;
  }
  void split(int rt, int& a, int& b, int s) {
      if (rt == 0) {
          a = b = 0;
          return;
      }
      push_down(rt);
      int size = node[node[rt].ls].size;
      if (size < s) {
          a = rt;
          split(node[rt].rs, node[a].rs, b, s - size - 1);
      } else {
          b = rt;
          split(node[rt].ls, a, node[b].ls, s);
      }
      push_up(rt);
  }
  void merge(int& rt, int a, int b) {
      if (a == 0 || b == 0) {
          rt = a + b;
          return;
      }
      push_down(a);
      push_down(b);
      if (node[a].rand < node[b].rand) {
          rt = a;
          merge(node[rt].rs, node[a].rs, b);
      } else {
          rt = b;
          merge(node[rt].ls, a, node[b].ls);
      }
      push_up(rt);
  }
  void insert(int p, int v) {
      int x = 0, y = 0;
      split(root, x, y, p - 1);
      merge(root, x, add_node(v));
      merge(root, root, y);
  }
  void add(int l, int r, int v) {
      int x = 0, y = 0, z = 0;
      split(root, root, z, r);
      split(root, x, y, l - 1);
      node[y].lazy += v;
      node[y].val += v;
      node[y].sum += node[y].size * v;
      merge(root, x, y);
      merge(root, root, z);
  }
  LL query(int l, int r) {
      int x = 0, y = 0, z = 0;
      split(root, root, z, r);
      split(root, x, y, l - 1);
      LL sum = node[y].sum;
      merge(root, x, y);
      merge(root, root, z);
      return sum;
  }
  int main() {
      int n, q;
      scanf("%d", &n);
      for (int i = 1; i <= n; i++) {
          int v; scanf("%d", &v);
          merge(root, root, add_node(v));
      }
      scanf("%d", &q);
      for (int i = 1; i <= q; i++) {
          int opt; scanf("%d", &opt);
          if (opt == 1) {
              int pos; scanf("%d", &pos);
              insert(pos, 0);
          } else if (opt == 2) {
              int l, r, v;
              scanf("%d%d%d", &l, &r, &v);
              add(l, r, v);
          } else {
              int l, r;
              scanf("%d%d", &l, &r);
              printf("%lld\n", query(l, r));
          }
      }
      return 0;
  }

  在前置知识都掌握的情况下Treap还是挺好懂的，而且之前感觉lazy标记挺乱的，看了这题之后感觉理清了