图例
绝佳 | 不错 | 一般 | 不佳 | 糟糕 |
数据结构操作
数据结构 | 时间复杂度 | 空间复杂度 | |||||||
---|---|---|---|---|---|---|---|---|---|
平均 | 最差 | 最差 | |||||||
访问 | 搜索 | 插入 | 删除 | 访问 | 搜索 | 插入 | 删除 | ||
数组 | O(1) | O(n) | O(n) | O(n) | O(1) | O(n) | O(n) | O(n) | O(n) |
堆栈 | O(n) | O(n) | O(1) | O(1) | O(n) | O(n) | O(1) | O(1) | O(n) |
单链表 | O(n) | O(n) | O(1) | O(1) | O(n) | O(n) | O(1) | O(1) | O(n) |
双向链表 | O(n) | O(n) | O(1) | O(1) | O(n) | O(n) | O(1) | O(1) | O(n) |
跳跃表 | O(log(n)) | O(log(n)) | O(log(n)) | O(log(n)) | O(n) | O(n) | O(n) | O(n) | O(n log(n)) |
哈希表 | – | O(1) | O(1) | O(1) | – | O(n) | O(n) | O(n) | O(n) |
二叉搜索树 | O(log(n)) | O(log(n)) | O(log(n)) | O(log(n)) | O(n) | O(n) | O(n) | O(n) | O(n) |
笛卡尔树 | – | O(log(n)) | O(log(n)) | O(log(n)) | – | O(n) | O(n) | O(n) | O(n) |
B树 | 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) |
红黑树 | 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) |
伸展树 | – | O(log(n)) | O(log(n)) | O(log(n)) | – | O(log(n)) | O(log(n)) | O(log(n)) | O(n) |
AVL树 | 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) |
数组排序算法
算法 | 时间复杂度 | 空间复杂度 | ||
---|---|---|---|---|
最佳 | 平均 | 最差 | 最差 | |
Quicksort | O(n log(n)) | O(n log(n)) | O(n^2) | O(log(n)) |
归并排序 | O(n log(n)) | O(n log(n)) | O(n log(n)) | O(n) |
Timsort | O(n) | O(n log(n)) | O(n log(n)) | O(n) |
堆排序 | O(n log(n)) | O(n log(n)) | O(n log(n)) | O(1) |
冒泡排序 | O(n) | O(n^2) | O(n^2) | O(1) |
插入排序 | O(n) | O(n^2) | O(n^2) | O(1) |
选择排序 | O(n^2) | O(n^2) | O(n^2) | O(1) |
希尔排序 | O(n) | O((nlog(n))^2) | O((nlog(n))^2) | O(1) |
桶排序 | O(n+k) | O(n+k) | O(n^2) | O(n) |
基数排序 | O(nk) | O(nk) | O(nk) | O(n+k) |
图操作
节点 / 边界管理 | 存储 | 增加顶点 | 增加边界 | 移除顶点 | 移除边界 | 查询 |
---|---|---|---|---|---|---|
Adjacency list | O(|V|+|E|) | O(1) | O(1) | O(|V| + |E|) | O(|E|) | O(|V|) |
Incidence list | O(|V|+|E|) | O(1) | O(1) | O(|E|) | O(|E|) | O(|E|) |
Adjacency matrix | O(|V|^2) | O(|V|^2) | O(1) | O(|V|^2) | O(1) | O(1) |
Incidence matrix | O(|V| ⋅ |E|) | O(|V| ⋅ |E|) | O(|V| ⋅ |E|) | O(|V| ⋅ |E|) | O(|V| ⋅ |E|) | O(|E|) |
堆操作
类型 | 时间复杂度 | ||||||
---|---|---|---|---|---|---|---|
HEAPIFY | 查找最大值 | 分离最大值 | 提升键 | 插入 | 删除 | 合并 | |
Linked List (sorted) | – | O(1) | O(1) | O(n) | O(n) | O(1) | O(m+n) |
Linked List (unsorted) | – | O(n) | O(n) | O(1) | O(1) | O(1) | O(1) |
Binary Heap | O(n) | O(1) | O(log(n)) | O(log(n)) | O(log(n)) | O(log(n)) | O(m+n) |
Binomial Heap | – | O(1) | O(log(n)) | O(log(n)) | O(1) | O(log(n)) | O(log(n)) |
Fibonacci Heap | – | O(1) | O(log(n)) | O(1) | O(1) | O(log(n)) | O(1) |
大 O 复杂度图表
Big O Complexity Graph