可持久化線段樹學習筆記
阿新 • • 發佈:2018-11-04
可持久化線段樹,即主席樹。
每次修改的時候不修改原來的節點,暴力建新節點,充分運用了函數語言程式設計的思想。
模板題:給定一個數列,\(m\) 次詢問求區間 \([l,r]\) 內的第 \(k\) 大。
利用字首和思想:
#include <bits/stdc++.h> using namespace std; const int MAXN = 2e5 + 5; struct node { int val; node *lchild, *rchild; } *rt[MAXN]; int a[MAXN], subA[MAXN], n, m, cnt = 0; node *newNode(int val, node *lc, node *rc) { node *ptr = new node; ptr->lchild = lc; ptr->rchild = rc; ptr->val = val; return ptr; } void build(node *&cur, int l, int r) { if(l < r) { cur = newNode(0, NULL, NULL); int mid = (l + r) >> 1; build(cur->lchild, l, mid); build(cur->rchild, mid + 1, r); } else cur = newNode(0, NULL, NULL); } void modify(node *&cur, node *fa, int l, int r, int x) { cur = newNode(fa->val + 1, fa->lchild, fa->rchild); if(l != r) { int mid = (l + r) >> 1; if(x <= mid) modify(cur->lchild, cur->lchild, l, mid, x); else modify(cur->rchild, cur->rchild, mid + 1, r, x); } } int query(node *u, node *v, int l, int r, int k) { if(l == r) return l; int mid = (l + r) >> 1, lessSize = v->lchild->val - u->lchild->val; if(lessSize >= k) return query(u->lchild, v->lchild, l, mid, k); else return query(u->rchild, v->rchild, mid + 1, r, k - lessSize); } int main() { scanf("%d%d", &n, &m); for(int i = 0; i < n; i++) { scanf("%d", a + i); subA[i] = a[i]; } sort(subA, subA + n); int size = unique(subA, subA + n) - subA; for(int i = 0; i < n; i++) a[i] = lower_bound(subA, subA + size, a[i]) - subA + 1; build(rt[cnt++], 1, n); for(int i = 0; i < n; i++) { modify(rt[cnt], rt[cnt - 1], 1, n, a[i]); cnt++; } while(m--) { int x, y, k; scanf("%d%d%d", &x, &y, &k); printf("%d\n", subA[query(rt[x - 1], rt[y], 1, n, k) - 1]); } return 0; }