algs4

Algorithms, Part I, https://online.princeton.edu/course/algorithms-part-i Algorithms, Part II, https://online.princeton.edu/course/algorithms-part-ii Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne https://algs4.cs.princeton.edu/ Union−Find Considering the dynamic connectivity problem, modeling of multiple objects connected in a space/network. Applications involve manipulating objects of all types. ・Pixels in a digital photo. ・Computers in a network. ・Friends in a social network. ・Transistors in a computer chip. Given a set of N objects. union(a, b): connect two objects. connected(p, q): is two objects connected?...

Memory Bit. 0 or 1. Byte. 8 bits. Megabyte (MB). 1 million or $2^{20}$ bytes. Gigabyte (GB). 1 billion or $2^{30}$ bytes. 64-bit machine. We assume a 64-bit machine with 8 byte pointers (References). ・Can address more memory. ・Pointers use more space (some JVMs “compress” ordinary object pointers to 4 bytes to avoid this cost). Typical memory usage for primitive types and arrays primitive types (bytes): boolean 1 byte 1 char 2 int 4 float 4 long 8 double 8...

假如有两种交税方式： 每天付 3 金币 每次付的金币呈指数级增长，但通知付款频率呈指数级下降 第1天：付 1 第2天：付 2 (累计 3) 第4天：付 4 (累积 7) 第8天：付 8 (累积 15) 哪种付的钱比较少？ 第二种比较划算，本质上等同于每天付 2，就是amortized constant。 A more rigorous examination of amortized analysis is done here, in three steps: Pick a cost model (like in regular runtime analysis) Compute the average cost of the i’th operation Show that this average (amortized) cost is bounded by a constant. 类似的应用在Array list 扩容中提到的 geometric resizing 方法(实际也是Python list 使用的方法)有体现, 所以使用一个因数来扩容数组, 可以让 ArrayList 的 add操作变为 amortized constant time....

Resource and Reference: CS61B Berkeley - Josh Hug Algorithms Princeton - ROBERT SEDGEWICK, KEVIN WAYNE 效率来源两个方面: 编程成本: 开发程序需要多长时间？代码是否容易阅读，修改和维护（大部分成本来自维护和可扩展性）？ 运行成本: 程序需要多长时间运行 (Time complexity)？ 需要多少内存 (Space complexity)？ Asymptotic Analysis Care about what happens for very large N (asymptotic behavior). We want to consider what types of algorithms would best handle scalability - Algorithms that scale well have better asymptotic runtime behavior. Simplification Summary Only consider the worst case. Pick a representative operation (aka: cost model) Ignore lower order terms Ignore multiplicative constants....