Fixed -universe successor problem Goal: maintain a dynamic subset s of size n of the universe 0=10, 1,.,u-1 of size u subject to these operations INSERT(X∈U\\S): Add x to s DELETE(X E S): Remove x from S

ynamic order statistics OS-SELECT(i, S): returns the i th smallest element in the dynamic set S. OS-RANK(, S): returns the rank ofx E S in the sorted order of s s elements IDEA: Use a red-black tree for the set S, but keep subtree sizes in the nodes

Binary-search-tree sort 7∈ b Create an empty Bst for i=i to n do trEe-INSert(,AiD) Perform an inorder tree walk of t Example:

Symbol-table problem Symbol table T holding n records

How fast can we sort? All the sorting algorithms we have seen so far are comparison sorts: only use comparisons to determine the relative order of elements E. g, insertion sort, merge sort, quicksort heapsort The best worst-case running time that weve seen for comparison sorting is O(nIgn) Is o(nlgn) the best we can do?

The divide-and-conquer design paradigm 1. Divide the problem(instance) into subproblems 2. Conquer the subproblems by solving them recursively 3. Combine subproblem solutions

Welcome to Introduction to Algorithms, Fall 2001 Handouts 1. Course Information 2. Calendar 3. Registration (MIT students only) 4. References 5. Objectives and Outcomes 6. Diagnostic Survey

第8章密钥管理习题 1.密钥管理为什么重要? 2.密钥的种类是如何区分的?有哪些分类标准? 3.对线性同余算法Xn+1= aXn mod24,问:a)该数列产生的最大周期是多少?

一、基本概念与简单算法 二、RSA公钥密码体制 三、离散对数公钥密码体制 四、可证明性安全公钥密码体制

一、分组密码的一般模型 二、DES与IDEA 三、AES 算法——Rijndael 四、分组密码分析方法* 五、分组密码工作模式