Algorithm Design and Analysis CS 214 Dominik Scheder - - PowerPoint PPT Presentation

Algorithm Design and Analysis CS 214

Dominik Scheder dominik@cs.sjtu.edu.cn SEIEE Building 3, Room 526

http://basics.sjtu.edu.cn/~dominik/teaching/

Algorithm Design and Analysis CS 214

Dominik Scheder dominik@cs.sjtu.edu.cn SEIEE Building 3, Room 526

http://basics.sjtu.edu.cn/~dominik/teaching/

Algorithm Design and Analysis CS 214

Dominik Scheder dominik@cs.sjtu.edu.cn SEIEE Building 3, Room 526

http://basics.sjtu.edu.cn/~dominik/teaching/

Algorithm Design and Analysis CS 214

Dominik Scheder dominik@cs.sjtu.edu.cn SEIEE Building 3, Room 526

http://basics.sjtu.edu.cn/~dominik/teaching/

Grading and Homework

Grading and Homework

Grading: 40% homework assignment, 60 % final exam

Grading and Homework

Grading: 40% homework assignment, 60 % final exam Homework:

Grading and Homework

Grading: 40% homework assignment, 60 % final exam Homework: Handed out every two weeks

Grading and Homework

Grading: 40% homework assignment, 60 % final exam Homework: Handed out every two weeks You work on it in small groups (3-4 people)

Grading and Homework

Grading: 40% homework assignment, 60 % final exam Homework: Handed out every two weeks You work on it in small groups (3-4 people) Hand it back to me or Zhengyang a week later

Grading and Homework

Grading: 40% homework assignment, 60 % final exam Homework: Handed out every two weeks You work on it in small groups (3-4 people) Hand it back to me or Zhengyang a week later Each group presents solution at some point

Grading and Homework

Grading: 40% homework assignment, 60 % final exam Homework: Handed out every two weeks You work on it in small groups (3-4 people) Hand it back to me or Zhengyang a week later Each group presents solution at some point Please form small groups until next week!

Textbook

Algorithms Sanjoy Dasgupta Christos Papadimitriou Umesh Vazirani

Which programming languages do you know? Which algorithms do you know? (What is their running time?)

What are Algorithms?

What are Algorithms?

Example 1: A bad algorithm

What are Algorithms?

Example 1: A bad algorithm Example 2: A good algorithm

An Algorithmic Example

Sorting

Ye Zihao Li Huichen Xie Tiancheng Bai Yiwei Cai Wanxin Yu Hongzhong Xu Xiaojun Qiu Zhi Li Yunqi Zhao Xueyuan Liu Zhijian Wan Cheng Zhou Yuhao Zhu Qiuming Liu Haoming Lu Yizhou Tang Shuyang Xue Zhendong Gao Bicheng Sun Xingyuan Yang Runzhe You Xiaotian Zhang Xuan Chen Lequn Chen Tianyao Ke Songyu Huang Yuxiang Xu Shichao Qiu Wei Huang Junxiang Xu Bowen Pu Yifei You Yurong Zhang Jiaheng

Ye Zihao Li Huichen Xie Tiancheng Bai Yiwei Cai Wanxin Yu Hongzhong Xu Xiaojun Qiu Zhi Li Yunqi Zhao Xueyuan Liu Zhijian Wan Cheng Zhou Yuhao Zhu Qiuming Liu Haoming Lu Yizhou Tang Shuyang Xue Zhendong Gao Bicheng Sun Xingyuan Yang Runzhe You Xiaotian Zhang Xuan Chen Lequn Chen Tianyao Ke Songyu Huang Yuxiang Xu Shichao Qiu Wei Huang Junxiang Xu Bowen Pu Yifei You Yurong Zhang Jiaheng

Ye Zihao Li Huichen Xie Tiancheng Bai Yiwei Cai Wanxin Yu Hongzhong Xu Xiaojun Qiu Zhi Li Yunqi Zhao Xueyuan Liu Zhijian Wan Cheng Zhou Yuhao Zhu Qiuming Liu Haoming Lu Yizhou Tang Shuyang Xue Zhendong Gao Bicheng Sun Xingyuan Yang Runzhe You Xiaotian Zhang Xuan Chen Lequn Chen Tianyao Ke Songyu Huang Yuxiang Xu Shichao Qiu Wei Huang Junxiang Xu Bowen Pu Yifei You Yurong Zhang Jiaheng

Li Huichen Ye Zihao Xie Tiancheng Bai Yiwei Cai Wanxin Yu Hongzhong Xu Xiaojun Qiu Zhi Li Yunqi Zhao Xueyuan Liu Zhijian Wan Cheng Zhou Yuhao Zhu Qiuming Liu Haoming Lu Yizhou Tang Shuyang Xue Zhendong Gao Bicheng Sun Xingyuan Yang Runzhe You Xiaotian Zhang Xuan Chen Lequn Chen Tianyao Ke Songyu Huang Yuxiang Xu Shichao Qiu Wei Huang Junxiang Xu Bowen Pu Yifei You Yurong Zhang Jiaheng

Li Huichen Ye Zihao Xie Tiancheng Bai Yiwei Cai Wanxin Yu Hongzhong Xu Xiaojun Qiu Zhi Li Yunqi Zhao Xueyuan Liu Zhijian Wan Cheng Zhou Yuhao Zhu Qiuming Liu Haoming Lu Yizhou Tang Shuyang Xue Zhendong Gao Bicheng Sun Xingyuan Yang Runzhe You Xiaotian Zhang Xuan Chen Lequn Chen Tianyao Ke Songyu Huang Yuxiang Xu Shichao Qiu Wei Huang Junxiang Xu Bowen Pu Yifei You Yurong Zhang Jiaheng

Li Huichen Ye Zihao Xie Tiancheng Bai Yiwei Cai Wanxin Yu Hongzhong Xu Xiaojun Qiu Zhi Li Yunqi Zhao Xueyuan Liu Zhijian Wan Cheng Zhou Yuhao Zhu Qiuming Liu Haoming Lu Yizhou Tang Shuyang Xue Zhendong Gao Bicheng Sun Xingyuan Yang Runzhe You Xiaotian Zhang Xuan Chen Lequn Chen Tianyao Ke Songyu Huang Yuxiang Xu Shichao Qiu Wei Huang Junxiang Xu Bowen Pu Yifei You Yurong Zhang Jiaheng

Li Huichen Xie Tiancheng Ye Zihao Bai Yiwei Cai Wanxin Yu Hongzhong Xu Xiaojun Qiu Zhi Li Yunqi Zhao Xueyuan Liu Zhijian Wan Cheng Zhou Yuhao Zhu Qiuming Liu Haoming Lu Yizhou Tang Shuyang Xue Zhendong Gao Bicheng Sun Xingyuan Yang Runzhe You Xiaotian Zhang Xuan Chen Lequn Chen Tianyao Ke Songyu Huang Yuxiang Xu Shichao Qiu Wei Huang Junxiang Xu Bowen Pu Yifei You Yurong Zhang Jiaheng

Li Huichen Xie Tiancheng Ye Zihao Bai Yiwei Cai Wanxin Yu Hongzhong Xu Xiaojun Qiu Zhi Li Yunqi Zhao Xueyuan Liu Zhijian Wan Cheng Zhou Yuhao Zhu Qiuming Liu Haoming Lu Yizhou Tang Shuyang Xue Zhendong Gao Bicheng Sun Xingyuan Yang Runzhe You Xiaotian Zhang Xuan Chen Lequn Chen Tianyao Ke Songyu Huang Yuxiang Xu Shichao Qiu Wei Huang Junxiang Xu Bowen Pu Yifei You Yurong Zhang Jiaheng

Li Huichen Xie Tiancheng Ye Zihao Bai Yiwei Cai Wanxin Yu Hongzhong Xu Xiaojun Qiu Zhi Li Yunqi Zhao Xueyuan Liu Zhijian Wan Cheng Zhou Yuhao Zhu Qiuming Liu Haoming Lu Yizhou Tang Shuyang Xue Zhendong Gao Bicheng Sun Xingyuan Yang Runzhe You Xiaotian Zhang Xuan Chen Lequn Chen Tianyao Ke Songyu Huang Yuxiang Xu Shichao Qiu Wei Huang Junxiang Xu Bowen Pu Yifei You Yurong Zhang Jiaheng Li Huichen Xie Tiancheng Ye Zihao Bai Yiwei Cai Wanxin Yu Hongzhong Xu Xiaojun Qiu Zhi Li Yunqi Zhao Xueyuan Liu Zhijian Wan Cheng Zhou Yuhao Zhu Qiuming Liu Haoming Lu Yizhou Tang Shuyang Xue Zhendong Gao Bicheng Sun Xingyuan Yang Runzhe You Xiaotian Zhang Xuan Chen Lequn Chen Tianyao Ke Songyu Huang Yuxiang Xu Shichao Qiu Wei Huang Junxiang Xu Bowen Pu Yifei You Yurong Zhang Jiaheng

Li Huichen Xie Tiancheng Ye Zihao Bai Yiwei Cai Wanxin Yu Hongzhong Xu Xiaojun Qiu Zhi Li Yunqi Zhao Xueyuan Liu Zhijian Wan Cheng Zhou Yuhao Zhu Qiuming Liu Haoming Lu Yizhou Tang Shuyang Xue Zhendong Gao Bicheng Sun Xingyuan Yang Runzhe You Xiaotian Zhang Xuan Chen Lequn Chen Tianyao Ke Songyu Huang Yuxiang Xu Shichao Qiu Wei Huang Junxiang Xu Bowen Pu Yifei You Yurong Zhang Jiaheng Li Huichen Xie Tiancheng Ye Zihao Bai Yiwei Cai Wanxin Yu Hongzhong Xu Xiaojun Qiu Zhi Li Yunqi Zhao Xueyuan Liu Zhijian Wan Cheng Zhou Yuhao Zhu Qiuming Liu Haoming Lu Yizhou Tang Shuyang Xue Zhendong Gao Bicheng Sun Xingyuan Yang Runzhe You Xiaotian Zhang Xuan Chen Lequn Chen Tianyao Ke Songyu Huang Yuxiang Xu Shichao Qiu Wei Huang Junxiang Xu Bowen Pu Yifei You Yurong Zhang Jiaheng

Li Huichen Xie Tiancheng Ye Zihao Bai Yiwei Cai Wanxin Yu Hongzhong Xu Xiaojun Qiu Zhi Li Yunqi Zhao Xueyuan Liu Zhijian Wan Cheng Zhou Yuhao Zhu Qiuming Liu Haoming Lu Yizhou Tang Shuyang Xue Zhendong Gao Bicheng Sun Xingyuan Yang Runzhe You Xiaotian Zhang Xuan Chen Lequn Chen Tianyao Ke Songyu Huang Yuxiang Xu Shichao Qiu Wei Huang Junxiang Xu Bowen Pu Yifei You Yurong Zhang Jiaheng Li Huichen Xie Tiancheng Ye Zihao Bai Yiwei Cai Wanxin Yu Hongzhong Xu Xiaojun Qiu Zhi Li Yunqi Zhao Xueyuan Liu Zhijian Wan Cheng Zhou Yuhao Zhu Qiuming Liu Haoming Lu Yizhou Tang Shuyang Xue Zhendong Gao Bicheng Sun Xingyuan Yang Runzhe You Xiaotian Zhang Xuan Chen Lequn Chen Tianyao Ke Songyu Huang Yuxiang Xu Shichao Qiu Wei Huang Junxiang Xu Bowen Pu Yifei You Yurong Zhang Jiaheng

Li Huichen Xie Tiancheng Bai Yiwei Ye Zihao Cai Wanxin Yu Hongzhong Xu Xiaojun Qiu Zhi Li Yunqi Zhao Xueyuan Liu Zhijian Wan Cheng Zhou Yuhao Zhu Qiuming Liu Haoming Lu Yizhou Tang Shuyang Xue Zhendong Gao Bicheng Sun Xingyuan Yang Runzhe You Xiaotian Zhang Xuan Chen Lequn Chen Tianyao Ke Songyu Huang Yuxiang Xu Shichao Qiu Wei Huang Junxiang Xu Bowen Pu Yifei You Yurong Zhang Jiaheng

Li Huichen Xie Tiancheng Bai Yiwei Ye Zihao Cai Wanxin Yu Hongzhong Xu Xiaojun Qiu Zhi Li Yunqi Zhao Xueyuan Liu Zhijian Wan Cheng Zhou Yuhao Zhu Qiuming Liu Haoming Lu Yizhou Tang Shuyang Xue Zhendong Gao Bicheng Sun Xingyuan Yang Runzhe You Xiaotian Zhang Xuan Chen Lequn Chen Tianyao Ke Songyu Huang Yuxiang Xu Shichao Qiu Wei Huang Junxiang Xu Bowen Pu Yifei You Yurong Zhang Jiaheng

Li Huichen Bai Yiwei Xie Tiancheng Ye Zihao Cai Wanxin Yu Hongzhong Xu Xiaojun Qiu Zhi Li Yunqi Zhao Xueyuan Liu Zhijian Wan Cheng Zhou Yuhao Zhu Qiuming Liu Haoming Lu Yizhou Tang Shuyang Xue Zhendong Gao Bicheng Sun Xingyuan Yang Runzhe You Xiaotian Zhang Xuan Chen Lequn Chen Tianyao Ke Songyu Huang Yuxiang Xu Shichao Qiu Wei Huang Junxiang Xu Bowen Pu Yifei You Yurong Zhang Jiaheng

Li Huichen Bai Yiwei Xie Tiancheng Ye Zihao Cai Wanxin Yu Hongzhong Xu Xiaojun Qiu Zhi Li Yunqi Zhao Xueyuan Liu Zhijian Wan Cheng Zhou Yuhao Zhu Qiuming Liu Haoming Lu Yizhou Tang Shuyang Xue Zhendong Gao Bicheng Sun Xingyuan Yang Runzhe You Xiaotian Zhang Xuan Chen Lequn Chen Tianyao Ke Songyu Huang Yuxiang Xu Shichao Qiu Wei Huang Junxiang Xu Bowen Pu Yifei You Yurong Zhang Jiaheng

Bai Yiwei Li Huichen Xie Tiancheng Ye Zihao Cai Wanxin Yu Hongzhong Xu Xiaojun Qiu Zhi Li Yunqi Zhao Xueyuan Liu Zhijian Wan Cheng Zhou Yuhao Zhu Qiuming Liu Haoming Lu Yizhou Tang Shuyang Xue Zhendong Gao Bicheng Sun Xingyuan Yang Runzhe You Xiaotian Zhang Xuan Chen Lequn Chen Tianyao Ke Songyu Huang Yuxiang Xu Shichao Qiu Wei Huang Junxiang Xu Bowen Pu Yifei You Yurong Zhang Jiaheng

Bai Yiwei Li Huichen Xie Tiancheng Ye Zihao Cai Wanxin Yu Hongzhong Xu Xiaojun Qiu Zhi Li Yunqi Zhao Xueyuan Liu Zhijian Wan Cheng Zhou Yuhao Zhu Qiuming Liu Haoming Lu Yizhou Tang Shuyang Xue Zhendong Gao Bicheng Sun Xingyuan Yang Runzhe You Xiaotian Zhang Xuan Chen Lequn Chen Tianyao Ke Songyu Huang Yuxiang Xu Shichao Qiu Wei Huang Junxiang Xu Bowen Pu Yifei You Yurong Zhang Jiaheng

Bai Yiwei Li Huichen Xie Tiancheng Ye Zihao Cai Wanxin Yu Hongzhong Xu Xiaojun Qiu Zhi Li Yunqi Zhao Xueyuan Liu Zhijian Wan Cheng Zhou Yuhao Zhu Qiuming Liu Haoming Lu Yizhou Tang Shuyang Xue Zhendong Gao Bicheng Sun Xingyuan Yang Runzhe You Xiaotian Zhang Xuan Chen Lequn Chen Tianyao Ke Songyu Huang Yuxiang Xu Shichao Qiu Wei Huang Junxiang Xu Bowen Pu Yifei You Yurong Zhang Jiaheng

Bai Yiwei Li Huichen Xie Tiancheng Cai Wanxin Ye Zihao Yu Hongzhong Xu Xiaojun Qiu Zhi Li Yunqi Zhao Xueyuan Liu Zhijian Wan Cheng Zhou Yuhao Zhu Qiuming Liu Haoming Lu Yizhou Tang Shuyang Xue Zhendong Gao Bicheng Sun Xingyuan Yang Runzhe You Xiaotian Zhang Xuan Chen Lequn Chen Tianyao Ke Songyu Huang Yuxiang Xu Shichao Qiu Wei Huang Junxiang Xu Bowen Pu Yifei You Yurong Zhang Jiaheng

Bai Yiwei Li Huichen Xie Tiancheng Cai Wanxin Ye Zihao Yu Hongzhong Xu Xiaojun Qiu Zhi Li Yunqi Zhao Xueyuan Liu Zhijian Wan Cheng Zhou Yuhao Zhu Qiuming Liu Haoming Lu Yizhou Tang Shuyang Xue Zhendong Gao Bicheng Sun Xingyuan Yang Runzhe You Xiaotian Zhang Xuan Chen Lequn Chen Tianyao Ke Songyu Huang Yuxiang Xu Shichao Qiu Wei Huang Junxiang Xu Bowen Pu Yifei You Yurong Zhang Jiaheng

Bai Yiwei Li Huichen Cai Wanxin Xie Tiancheng Ye Zihao Yu Hongzhong Xu Xiaojun Qiu Zhi Li Yunqi Zhao Xueyuan Liu Zhijian Wan Cheng Zhou Yuhao Zhu Qiuming Liu Haoming Lu Yizhou Tang Shuyang Xue Zhendong Gao Bicheng Sun Xingyuan Yang Runzhe You Xiaotian Zhang Xuan Chen Lequn Chen Tianyao Ke Songyu Huang Yuxiang Xu Shichao Qiu Wei Huang Junxiang Xu Bowen Pu Yifei You Yurong Zhang Jiaheng

Bai Yiwei Li Huichen Cai Wanxin Xie Tiancheng Ye Zihao Yu Hongzhong Xu Xiaojun Qiu Zhi Li Yunqi Zhao Xueyuan Liu Zhijian Wan Cheng Zhou Yuhao Zhu Qiuming Liu Haoming Lu Yizhou Tang Shuyang Xue Zhendong Gao Bicheng Sun Xingyuan Yang Runzhe You Xiaotian Zhang Xuan Chen Lequn Chen Tianyao Ke Songyu Huang Yuxiang Xu Shichao Qiu Wei Huang Junxiang Xu Bowen Pu Yifei You Yurong Zhang Jiaheng

Bai Yiwei Cai Wanxin Li Huichen Xie Tiancheng Ye Zihao Yu Hongzhong Xu Xiaojun Qiu Zhi Li Yunqi Zhao Xueyuan Liu Zhijian Wan Cheng Zhou Yuhao Zhu Qiuming Liu Haoming Lu Yizhou Tang Shuyang Xue Zhendong Gao Bicheng Sun Xingyuan Yang Runzhe You Xiaotian Zhang Xuan Chen Lequn Chen Tianyao Ke Songyu Huang Yuxiang Xu Shichao Qiu Wei Huang Junxiang Xu Bowen Pu Yifei You Yurong Zhang Jiaheng

Bai Yiwei Cai Wanxin Li Huichen Xie Tiancheng Ye Zihao Yu Hongzhong Xu Xiaojun Qiu Zhi Li Yunqi Zhao Xueyuan Liu Zhijian Wan Cheng Zhou Yuhao Zhu Qiuming Liu Haoming Lu Yizhou Tang Shuyang Xue Zhendong Gao Bicheng Sun Xingyuan Yang Runzhe You Xiaotian Zhang Xuan Chen Lequn Chen Tianyao Ke Songyu Huang Yuxiang Xu Shichao Qiu Wei Huang Junxiang Xu Bowen Pu Yifei You Yurong Zhang Jiaheng

Bai Yiwei Cai Wanxin Li Huichen Xie Tiancheng Ye Zihao Yu Hongzhong Xu Xiaojun Qiu Zhi Li Yunqi Zhao Xueyuan Liu Zhijian Wan Cheng Zhou Yuhao Zhu Qiuming Liu Haoming Lu Yizhou Tang Shuyang Xue Zhendong Gao Bicheng Sun Xingyuan Yang Runzhe You Xiaotian Zhang Xuan Chen Lequn Chen Tianyao Ke Songyu Huang Yuxiang Xu Shichao Qiu Wei Huang Junxiang Xu Bowen Pu Yifei You Yurong Zhang Jiaheng

Bai Yiwei Cai Wanxin Li Huichen Xie Tiancheng Ye Zihao Yu Hongzhong Xu Xiaojun Qiu Zhi Li Yunqi Zhao Xueyuan Liu Zhijian Wan Cheng Zhou Yuhao Zhu Qiuming Liu Haoming Lu Yizhou Tang Shuyang Xue Zhendong Gao Bicheng Sun Xingyuan Yang Runzhe You Xiaotian Zhang Xuan Chen Lequn Chen Tianyao Ke Songyu Huang Yuxiang Xu Shichao Qiu Wei Huang Junxiang Xu Bowen Pu Yifei You Yurong Zhang Jiaheng

Bai Yiwei Cai Wanxin Li Huichen Xie Tiancheng Ye Zihao Yu Hongzhong Xu Xiaojun Qiu Zhi Li Yunqi Zhao Xueyuan Liu Zhijian Wan Cheng Zhou Yuhao Zhu Qiuming Liu Haoming Lu Yizhou Tang Shuyang Xue Zhendong Gao Bicheng Sun Xingyuan Yang Runzhe You Xiaotian Zhang Xuan Chen Lequn Chen Tianyao Ke Songyu Huang Yuxiang Xu Shichao Qiu Wei Huang Junxiang Xu Bowen Pu Yifei You Yurong Zhang Jiaheng

Bai Yiwei Cai Wanxin Li Huichen Xie Tiancheng Ye Zihao Yu Hongzhong Xu Xiaojun Qiu Zhi Li Yunqi Zhao Xueyuan Liu Zhijian Wan Cheng Zhou Yuhao Zhu Qiuming Liu Haoming Lu Yizhou Tang Shuyang Xue Zhendong Gao Bicheng Sun Xingyuan Yang Runzhe You Xiaotian Zhang Xuan Chen Lequn Chen Tianyao Ke Songyu Huang Yuxiang Xu Shichao Qiu Wei Huang Junxiang Xu Bowen Pu Yifei You Yurong Zhang Jiaheng

Physical Exercise!

Analyzing Insertion Sort

blackboard

Analyzing Insertion Sort

Analyzing Insertion Sort

Sorting n items can require up to n(n−1)

2

comparisons.

Analyzing Insertion Sort

Sorting n items can require up to n(n−1)

2

comparisons. This class Set Size Comparisons

Analyzing Insertion Sort

Sorting n items can require up to n(n−1)

2

comparisons. This class 34 Set Size Comparisons

Analyzing Insertion Sort

Sorting n items can require up to n(n−1)

2

comparisons. This class 34 Set Size Comparisons 561

Analyzing Insertion Sort

Sorting n items can require up to n(n−1)

2

comparisons. This class 34 Set Size Comparisons 561 Jiaotong students

Analyzing Insertion Sort

Sorting n items can require up to n(n−1)

2

comparisons. This class 34 Set Size Comparisons 561 Jiaotong students 41297

Analyzing Insertion Sort

Sorting n items can require up to n(n−1)

2

comparisons. This class 34 Set Size Comparisons 561 Jiaotong students 41297 852,700,456

Analyzing Insertion Sort

Sorting n items can require up to n(n−1)

2

comparisons. This class 34 Set Size Comparisons 561 Jiaotong students 41297 852,700,456 Runtime

Analyzing Insertion Sort

Sorting n items can require up to n(n−1)

2

comparisons. This class 34 Set Size Comparisons 561 Jiaotong students 41297 852,700,456 Runtime 1 second

Analyzing Insertion Sort

Sorting n items can require up to n(n−1)

2

comparisons. This class 34 Set Size Comparisons 561 Jiaotong students 41297 852,700,456 Runtime 1 second Shanghai Residents

Analyzing Insertion Sort

Sorting n items can require up to n(n−1)

2

comparisons. This class 34 Set Size Comparisons 561 Jiaotong students 41297 852,700,456 Runtime 1 second Shanghai Residents 24 mio

Analyzing Insertion Sort

Sorting n items can require up to n(n−1)

2

comparisons. This class 34 Set Size Comparisons 561 Jiaotong students 41297 852,700,456 Runtime 1 second Shanghai Residents 24 mio 294 × 1012

Analyzing Insertion Sort

Sorting n items can require up to n(n−1)

2

comparisons. This class 34 Set Size Comparisons 561 Jiaotong students 41297 852,700,456 Runtime 1 second Shanghai Residents 24 mio 294 × 1012 95 hours

Faster computers don’t solve this problem.

Faster computers don’t solve this problem. Better algorithms do.

A smarter sorting algorithm

• 1. Sort the first half

• 1. Sort the first half

• 1. Sort the first half

• 2. Sort the second half

• 1. Sort the first half

• 2. Sort the second half

• 1. Sort the first half

• 2. Sort the second half

• 3. Merge the sorted arrays.

• 1. Sort the first half

• 2. Sort the second half

• 3. Merge the sorted arrays.

• 1. Sort the first half

• 2. Sort the second half

• 3. Merge the sorted arrays.

• 1. Sort the first half

• 2. Sort the second half

• 3. Merge the sorted arrays.

Bai Yiwei

• 1. Sort the first half

• 2. Sort the second half

• 3. Merge the sorted arrays.

Bai Yiwei

• 1. Sort the first half

• 2. Sort the second half

• 3. Merge the sorted arrays.

Bai Yiwei

• 1. Sort the first half

• 2. Sort the second half

• 3. Merge the sorted arrays.

Bai Yiwei Cai Wanxin

• 1. Sort the first half

• 2. Sort the second half

• 3. Merge the sorted arrays.

Bai Yiwei Cai Wanxin

• 1. Sort the first half

• 2. Sort the second half

• 3. Merge the sorted arrays.

Bai Yiwei Cai Wanxin

• 1. Sort the first half

• 2. Sort the second half

• 3. Merge the sorted arrays.

Bai Yiwei Cai Wanxin Chen Lequn

• 1. Sort the first half

• 2. Sort the second half

• 3. Merge the sorted arrays.

Bai Yiwei Cai Wanxin Chen Lequn

• 1. Sort the first half

• 2. Sort the second half

• 3. Merge the sorted arrays.

Bai Yiwei Cai Wanxin Chen Lequn

• 1. Sort the first half

• 2. Sort the second half

• 3. Merge the sorted arrays.

Bai Yiwei Cai Wanxin Chen Lequn

• 1. Sort the first half

• 2. Sort the second half

• 3. Merge the sorted arrays.

Bai Yiwei Cai Wanxin Chen Lequn

How do we sort the two halves?

Merge sort

Merge sort

Y, L, X, B, C, Q, Z, T

Merge sort

Y, L, X, B, C, Q, Z, T

Merge sort

Y, L, X, B, C, Q, Z, T Y, L, X, B C, Q, Z, T

Merge sort

Y, L, X, B, C, Q, Z, T Y, L, X, B C, Q, Z, T

Merge sort

Y, L, X, B, C, Q, Z, T Y, L, X, B C, Q, Z, T Y, L X, B

Merge sort

Y, L, X, B, C, Q, Z, T Y, L, X, B C, Q, Z, T Y, L X, B Y L

Merge sort

Y, L, X, B, C, Q, Z, T Y, L, X, B C, Q, Z, T Y, L X, B Y L L,Y

Merge sort

Y, L, X, B, C, Q, Z, T Y, L, X, B C, Q, Z, T Y, L X, B Y L L,Y X B

Merge sort

Y, L, X, B, C, Q, Z, T Y, L, X, B C, Q, Z, T Y, L X, B Y L L,Y X B B,X

Merge sort

Y, L, X, B, C, Q, Z, T Y, L, X, B C, Q, Z, T Y, L X, B Y L L,Y X B B,X B, L, X, Y

Merge sort

Y, L, X, B, C, Q, Z, T Y, L, X, B C, Q, Z, T Y, L X, B Y L L,Y X B B,X B, L, X, Y

Merge sort

Y, L, X, B, C, Q, Z, T Y, L, X, B C, Q, Z, T Y, L X, B Y L L,Y X B B,X B, L, X, Y C, Q Z, T

Merge sort

Y, L, X, B, C, Q, Z, T Y, L, X, B C, Q, Z, T Y, L X, B Y L L,Y X B B,X B, L, X, Y C, Q Z, T C Q

Merge sort

Y, L, X, B, C, Q, Z, T Y, L, X, B C, Q, Z, T Y, L X, B Y L L,Y X B B,X B, L, X, Y C, Q Z, T C Q C,Q

Merge sort

Y, L, X, B, C, Q, Z, T Y, L, X, B C, Q, Z, T Y, L X, B Y L L,Y X B B,X B, L, X, Y C, Q Z, T C Q C,Q Z T

Merge sort

Y, L, X, B, C, Q, Z, T Y, L, X, B C, Q, Z, T Y, L X, B Y L L,Y X B B,X B, L, X, Y C, Q Z, T C Q C,Q Z T T,Z

Merge sort

Y, L, X, B, C, Q, Z, T Y, L, X, B C, Q, Z, T Y, L X, B Y L L,Y X B B,X B, L, X, Y C, Q Z, T C Q C,Q Z T T,Z C, Q, T, Z

Merge sort

Y, L, X, B, C, Q, Z, T Y, L, X, B C, Q, Z, T Y, L X, B Y L L,Y X B B,X B, L, X, Y C, Q Z, T C Q C,Q Z T T,Z C, Q, T, Z B, C, L, Q, T, X, Y, Z

Pseudocode for Mergesort

Pseudocode for Mergesort

mergesort(array X):

• n := |X|
• if n = 1: return X
• else:

– A := mergesort (X [1 . . . ⌊n/2⌋]) – B := mergesort (X [⌊n/2⌋ + 1 . . . n]) – return merge(A, B)

Pseudocode for Mergesort

mergesort(array X):

• n := |X|
• if n = 1: return X
• else:

– A := mergesort (X [1 . . . ⌊n/2⌋]) – B := mergesort (X [⌊n/2⌋ + 1 . . . n]) – return merge(A, B)

Pseudocode for merge

Pseudocode for merge

merge(A, B):

• if |A| = 0 return B
• else if |B| = 0 return A
• else if A[1] < B[1]: return A[1] ◦ merge(A[2 . . .], B)
• else return B[1] ◦ merge(A, B[2 . . .])

How long does it take?

How long does it take? How many comparisons does it take?

How long does it take? How many comparisons does it take?

merge(A, B) requires at most |A| + |B| − 1 comparisons.

How long does it take? How many comparisons does it take?

merge(A, B) requires at most |A| + |B| − 1 comparisons.

blackboard

Y, L, X, B, C, Q, Z, T Y, L, X, B C, Q, Z, T Y, L X, B Y L L,Y X B B,X B, L, X, Y C, Q Z, T C Q C,Q Z T T,Z C, Q, T, Z B, C, L, Q, T, X, Y, Z

Y, L, X, B, C, Q, Z, T Y, L, X, B C, Q, Z, T Y, L X, B Y L L,Y X B B,X B, L, X, Y C, Q Z, T C Q C,Q Z T T,Z C, Q, T, Z B, C, L, Q, T, X, Y, Z

4 × 1

Y, L, X, B, C, Q, Z, T Y, L, X, B C, Q, Z, T Y, L X, B Y L L,Y X B B,X B, L, X, Y C, Q Z, T C Q C,Q Z T T,Z C, Q, T, Z B, C, L, Q, T, X, Y, Z

4 × 1 2 × 3

Y, L, X, B, C, Q, Z, T Y, L, X, B C, Q, Z, T Y, L X, B Y L L,Y X B B,X B, L, X, Y C, Q Z, T C Q C,Q Z T T,Z C, Q, T, Z B, C, L, Q, T, X, Y, Z

4 × 1 2 × 3 1 × 7

If n = 2d . . .

If n = 2d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

If n = 2d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

n 2 × 1

If n = 2d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

n 2 × 1

. . .

If n = 2d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

n 2 × 1

. . .

n 4 × 3

If n = 2d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

n 2 × 1

. . .

n 4 × 3 n 8 × 7

If n = 2d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

n 2 × 1

. . .

n 4 × 3 n 8 × 7

Blackboard

Mergesort requires at most n⌈log(n)⌉ comparisons.

This class 34 Set Size Steps 561 Jiaotong students 41297 852 mio Runtime 1 second Shanghai Residents 24 mio 294 × 1012 95 hours insertion sort:

This class 34 Set Size Steps 561 Jiaotong students 41297 852 mio Runtime 1 second Shanghai Residents 24 mio 294 × 1012 95 hours insertion sort:

mergesort: n⌈log(n)⌉

This class 34 Set Size Steps 561 Jiaotong students 41297 852 mio Runtime 1 second Shanghai Residents 24 mio 294 × 1012 95 hours insertion sort:

mergesort: n⌈log(n)⌉ Steps Runtime

This class 34 Set Size Steps 561 Jiaotong students 41297 852 mio Runtime 1 second Shanghai Residents 24 mio 294 × 1012 95 hours insertion sort:

mergesort: n⌈log(n)⌉ Steps Runtime 204

This class 34 Set Size Steps 561 Jiaotong students 41297 852 mio Runtime 1 second Shanghai Residents 24 mio 294 × 1012 95 hours insertion sort:

mergesort: n⌈log(n)⌉ Steps Runtime 204 660,752 600 mio

This class 34 Set Size Steps 561 Jiaotong students 41297 852 mio Runtime 1 second Shanghai Residents 24 mio 294 × 1012 95 hours insertion sort:

mergesort: n⌈log(n)⌉ Steps Runtime 204 660,752 600 mio 1 second

This class 34 Set Size Steps 561 Jiaotong students 41297 852 mio Runtime 1 second Shanghai Residents 24 mio 294 × 1012 95 hours insertion sort:

mergesort: n⌈log(n)⌉ Steps Runtime 204 660,752 600 mio 1 second 15 minutes

This class 34 Set Size Steps 561 Jiaotong students 41297 852 mio Runtime 1 second Shanghai Residents 24 mio 294 × 1012 95 hours insertion sort:

mergesort: n⌈log(n)⌉ Steps Runtime 204 660,752 600 mio 1 second 15 minutes fast computer bad algorithm

This class 34 Set Size Steps 561 Jiaotong students 41297 852 mio Runtime 1 second Shanghai Residents 24 mio 294 × 1012 95 hours insertion sort:

mergesort: n⌈log(n)⌉ Steps Runtime 204 660,752 600 mio 1 second 15 minutes fast computer bad algorithm slow computer good algorithm

What will study this semester?

What will study this semester?

• 1. Which areas do will we study?

What will study this semester?

Sorting algorithms

• 1. Which areas do will we study?

What will study this semester?

Sorting algorithms Algorithms for numbers, matrices;

• 1. Which areas do will we study?

What will study this semester?

Sorting algorithms Algorithms for numbers, matrices; “algebraic algorithms”

• 1. Which areas do will we study?

What will study this semester?

Sorting algorithms Algorithms for numbers, matrices; “algebraic algorithms” Graph algorithms

• 1. Which areas do will we study?

What will study this semester?

Sorting algorithms Algorithms for numbers, matrices; “algebraic algorithms” Graph algorithms

• 1. Which areas do will we study?

Optimization algorithms

What will study this semester?

What will study this semester?

• 2. Which algorithmic ideas will we study?

What will study this semester?

• 2. Which algorithmic ideas will we study?

Divide-and-conquer algorithms (like mergesort)

What will study this semester?

• 2. Which algorithmic ideas will we study?

Divide-and-conquer algorithms (like mergesort) Greedy algorithms (always do the next best thing)

What will study this semester?

• 2. Which algorithmic ideas will we study?

Divide-and-conquer algorithms (like mergesort) Greedy algorithms (always do the next best thing) Dynamic programming (recursion unrolled)

What will study this semester?

• 2. Which algorithmic ideas will we study?

Divide-and-conquer algorithms (like mergesort) Greedy algorithms (always do the next best thing) Dynamic programming (recursion unrolled) many more . . .

What will study this semester?

• 3. Which aspects will we study?

What will study this semester?

• 3. Which aspects will we study?

Is our algorithm correct?

What will study this semester?

• 3. Which aspects will we study?

Is our algorithm correct? How fast is it?

What will study this semester?

• 3. Which aspects will we study?

Is our algorithm correct? How fast is it? How much memory does it use?

What will study this semester?

• 3. Which aspects will we study?

Is our algorithm correct? How fast is it? How much memory does it use?

Efficiency

What will study this semester?

• 3. Which aspects will we study?

Is our algorithm correct? How fast is it? How much memory does it use? Are there more efficient algorithms?

Efficiency

What will study this semester?

Why should we study algorithms?

Why should we study algorithms?

Most algorithms are already implemented in a library.

Why should we study algorithms?

Most algorithms are already implemented in a library. If I can implement an algorithm, why must I understand the proof of (1) correctness; (2) running time?

Why should we study algorithms?

Most algorithms are already implemented in a library. If I can implement an algorithm, why must I understand the proof of (1) correctness; (2) running time? You will always face new problems for which your library has no implemented solution!