Advanced Data Structure and Algorithm Analysis (summer semester)

高级数据结构与算法分析

本文是ADS期末复习所做整理包含课程重点内容，习题错题等

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5-8 贪心算法 (Greedy Algorithm)

Make the best decision at each stage, under some greedy criterion

Key Points

• Doesn’t guarantee an optimal solution, however, it’s quite like the heuristics method. (Woeks when the local optimum is the global optimal)
• 跟Local Search的区别是Greedy Algorithm是在逐步地构建一个解，局部搜索是每次在局部去找更好的解（每次都是一个新的解）

Examples

1. Activity Selection Problem

   • By GA: ends first first $$O(NlogN)$$
   • By DP:

$$c_{1,j} = \begin{equation} \left\{ \begin{array}{lr} 1& if\ j=1\\ max\{c_{1,j-1},c_{1,k(j)}+1\} & if\ j>1 \end{array} \right. \end{equation}$$

​ If each activity has a weight:

c1,j={ 1max{ c1,j−1,c1,k(j)+w