3. basic data structures(2)
- 1. Basic Data Structures(2) 2016. 3. 24 장 홍 준
- 2. Contents • Stack • Queue • Time Complexity • Binary Heap • Binary Indexed Tree
- 3. Stack • LIFO(Last In First Out) • push(), pop(), top(), size() #include <stack> using namespace std; • Recursive Structure • Keeps a property(DFS, Convex hull, Convex hull Trick)
- 4. Queue • FIFO(First In First Out) • push(), pop(), front(), end() #include <queue> using namespace std; • BFS (너비우선탐색)
- 5. Time Complexity Big O notation 다항 시간, 지수 시간, 로그 시간 for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) k = i+j; } : O(n^2)
- 6. Time Complexity for (int i = 0; i < n; i++) { for (int j = i; j < i+k; j++) { O(1) process. } } : O(nk)
- 7. Time Complexity for (int i = 0; i < m; i++) { for (int j = 0; j < log(n); j++) { O(1) process. } } : O(mlog(n))
- 8. Binary Heap • Tree Structure A binary heap is a complete binary tree which satisfies the heap ordering property. The ordering can be one of two types: 1) the min-heap property: the value of each node is greater than or equal to the value of its parent, with the minimum-value element at the root. 2) the max-heap property: the value of each node is less than or equal to the value of its parent, with the maximum-value element at the root.
- 9. Binary Heap How to implement with an array : https://www.cs.cmu.edu/~adamchik/15-121/lectures/Binary%20Heaps/heaps.html 이 수업에서는 STL을 이용해서 어떻게 사용하는지를 알아보겠습니다.
- 10. Binary Heap #include <queue> using namespace std; ------------------------ priority_queue <int> Q; Q.push(1); Q.push(9); Q.push(7); Q.push(5); Q.pop(); int x = Q.top(), y = Q.size(); x = ?, y = ?
- 11. Binary Indexed Tree(Fenwick Tree) • 구간에 대한 최소/최대/합 • 많은 양의 질문 / 갱신 : 시간복잡도를 줄이자!...
- 12. Binary Indexed Tree(Fenwick Tree)
- 13. Binary Indexed Tree(Fenwick Tree) • 1~7까지의 합 • 4, 6, 7 • 1~8까지의 합 • 8 • 가장 오른쪽의 1
- 14. Binary Indexed Tree(Fenwick Tree) • 5를 갱신 • 5, 6, 8 • 3을 갱신 • 3, 4, 8 • 가장 오른쪽의 1
- 15. Binary Indexed Tree(Fenwick Tree) • 어떻게 구현…? • 가장 오른쪽의 1을 어떻게 알 수 있을까? • 2의 보수! cin >> x; int y = x & -x; cout << y;
- 16. Binary Indexed Tree(Fenwick Tree) • https://www.acmicpc.net/blog/view/21 • 연습문제를 직접 풀어보다가 모르는 게 생기면 질문합시다.