常用演算法和資料結構的複雜度介紹
阿新 • • 發佈：2019-02-11
| 常用演算法和資料結構的複雜度 | |||||||||
| 演算法 | 資料結構 | 時間複雜度 | 空間複雜度 | ||||||
| 平均 | 最差 | 最差 | |||||||
| Graph of |V| vertices and |E| edges | - | O(|E| + |V|) | O(|V|) | ||||||
| Graph of |V| vertices and |E| edges | - | O(|E| + |V|) | O(|V|) | ||||||
| 二分查詢 | Sorted array of n elements | O(log(n)) | O(log(n)) | O(1) | |||||
| 窮舉查詢 | Array | O(n) | O(n) | O(1) | |||||
| Graph with |V| vertices and |E| edges | O((|V| + |E|) log |V|) | O((|V| + |E|) log |V|) | O(|V|) | ||||||
| Graph with |V| vertices and |E| edges | O(|V|^2) | O(|V|^2) | O(|V|) | ||||||
| Graph with |V| vertices and |E| edges | O(|V||E|) | O(|V||E|) | O(|V|) | ||||||
| 排序 | |||||||||
| 演算法 | 資料結構 | 時間複雜度 | 最壞情況下的輔助空間複雜度 | ||||||
| 最佳 | 平均 | 最差 | 最差 | ||||||
| 快速排序 | 陣列 | O(n log(n)) | O(n log(n)) | O(n^2) | O(n) | ||||
|
歸併排序 |
陣列 | O(n log(n)) | O(n log(n)) | O(n log(n)) | O(n) | ||||
| 堆排序 | 陣列 | O(n log(n)) | O(n log(n)) | O(n log(n)) | O(1) | ||||
| 氣泡排序 | 陣列 | O(n) | O(n^2) | O(n^2) | O(1) | ||||
| 插入排序 | 陣列 | O(n) | O(n^2) | O(n^2) | O(1) | ||||
| 選擇排序 | 陣列 | O(n^2) | O(n^2) | O(n^2) | O(1) | ||||
| 桶排序 | 陣列 | O(n+k) | O(n+k) | O(n^2) | O(nk) | ||||
| 基數排序 | 陣列 | O(nk) | O(nk) | O(nk) | O(n+k) | ||||
| 資料結構 | |||||||||
| 資料結構 | 時間複雜度 | 空間複雜度 | |||||||
| 平均 | 最差 | 最差 | |||||||
| 索引 | 查詢 | 插入 | 刪除 | 索引 | 查詢 | 插入 | 刪除 | ||
| 基本陣列 | O(1) | O(n) | - | - | O(1) | O(n) | - | - | O(n) |
| 動態陣列 | O(1) | O(n) | O(n) | O(n) | O(1) | O(n) | O(n) | O(n) | O(n) |
| 單鏈表 | O(n) | O(n) | O(1) | O(1) | O(n) | O(n) | O(1) | O(1) | O(n) |
| 雙鏈表 | O(n) | O(n) | O(1) | O(1) | O(n) | O(n) | O(1) | O(1) | O(n) |
| 跳錶 | O(log(n)) | O(log(n)) | O(log(n)) | O(log(n)) | O(n) | O(n) | O(n) | O(n) | O(n log(n)) |
| 雜湊表 | - | O(1) | O(1) | O(1) | - | O(n) | O(n) | O(n) | O(n) |
| 二叉搜尋樹 | O(log(n)) | O(log(n)) | O(log(n)) | O(log(n)) | O(n) | O(n) | O(n) | O(n) | O(n) |
| 笛卡爾樹 | - | O(log(n)) | O(log(n)) | O(log(n)) | - | O(n) | O(n) | O(n) | O(n) |
| B-樹 | O(log(n)) | O(log(n)) | O(log(n)) | O(log(n)) | O(log(n)) | O(log(n)) | O(log(n)) | O(log(n)) | O(n) |
| 紅黑樹 | O(log(n)) | O(log(n)) | O(log(n)) | O(log(n)) | O(log(n)) | O(log(n)) | O(log(n)) | O(log(n)) | O(n) |
| 伸展樹 | - | O(log(n)) | O(log(n)) | O(log(n)) | - | O(log(n)) | O(log(n)) | O(log(n)) | O(n) |
| AVL 樹 | O(log(n)) | O(log(n)) | O(log(n)) | O(log(n)) | O(log(n)) | O(log(n)) | O(log(n)) | O(log(n)) | O(n) |
| 堆 | |||||||||
| Heaps | 時間複雜度 | ||||||||
| 建堆 | 查詢最大值 | 提取最大值 | Increase Key | 插入 | 刪除 | 合併 | |||
| - | O(1) | O(1) | O(n) | O(n) | O(1) | O(m+n) | |||
| - | O(n) | O(n) | O(1) | O(1) | O(1) | O(1) | |||
| 二叉堆 | O(n) | O(1) | O(log(n)) | O(log(n)) | O(log(n)) | O(log(n)) | O(m+n) | ||
| 二項堆 | - | O(log(n)) | O(log(n)) | O(log(n)) | O(log(n)) | O(log(n)) | O(log(n)) | ||
| 斐波那契堆 | - | O(1) | O(log(n))* | O(1)* | O(1) | O(log(n))* | O(1) | ||
| 圖 | |||||||||
| 節點 / 邊 管理 | Storage | Add Vertex | Add Edge | Remove Vertex | Remove Edge | Query | |||
| 鄰接表 | O(|V|+|E|) | O(1) | O(1) | O(|V| + |E|) | O(|E|) | O(|V|) | |||
| 關聯表 | O(|V|+|E|) | O(1) | O(1) | O(|E|) | O(|E|) | O(|E|) | |||
| 鄰接矩陣 | O(|V|^2) | O(|V|^2) | O(1) | O(|V|^2) | O(1) | O(1) | |||
| 關聯矩陣 | O(|V| ⋅ |E|) | O(|V| ⋅ |E|) | O(|V| ⋅ |E|) | O(|V| ⋅ |E|) | O(|V| ⋅ |E|) | O(|E|) | |||