Out: 10/07 19:00
Due: 10/25 19:00

Instructions

Collaboration:

Collaboration on solving the assignment is allowed, after you have thought about the problem sets on your own. It is also OK to get clarification (but not solutions) from online resources, again after you have thought about the problem sets on your own. There are two requirements:

  • Cite your collaborators fully and completely (e.g., “XXX explained to me what is asked in problem set 3”). Or cite online resources (e.g., “I got inspired by reading XXX”) that helped you.

  • Write your scripts and report independently - the scripts and report must come from you only.

Submitting your assignment:

  • Please write a report PS1.pdf.

  • For problem set i, create a script named PS1_i.py.

  • Upload your Python scripts AND report to your Github ESE5023_Assignments_XXX repository (where XXX is your SUSTech ID) before the due time.

Late Submission:

Late submissions will not receive any credit. The submission time will be determined based on your latest GitHub file records.

1. Flowchart

[10 points] Write a function Print_values with arguments a, b, and c to reflect the following flowchart. Here the purple parallelogram operator is to print values in the given order. Report your output with some random a, b, and c values.

drawing

2. Matrix multiplication

2.1 [5 points] Make two matrices M1 (5 rows and 10 columns ) and M2 (10 rows and 5 columns ); both are filled with random integers from 0 and 50.

2.2 [10 points] Write a function Matrix_multip to do matrix multiplication, i.e., M1 * M2. Here you are ONLY allowed to use for loop, * operator, and + operator.

3. Pascal triangle

[20 points] One of the most interesting number patterns is Pascal’s triangle (named after Blaise Pascal). Write a function Pascal_triangle with an argument k to print the kth line of the Pascal triangle. Report Pascal_triangle(100) and Pascal_triangle(200).

4. Add or double

[20 points] If you start with 1 RMB and, with each move, you can either double your money or add another 1 RMB, what is the smallest number of moves you have to make to get to exactly x RMB? Here x is an integer randomly selected from 1 to 100. Write a function Least_moves to print your results. For example, Least_moves(2) should print 1, and Least_moves(5) should print 3.

5. Dynamic programming

Insert + or - operation anywhere between the digits 123456789 in a way that the expression evaluates to an integer number. You may join digits together to form a bigger number. However, the digits must stay in the original order.

5.1 [30 points] Write a function Find_expression, which should be able to print every possible solution that makes the expression evaluate to a random integer from 1 to 100. For example, Find_expression(50) should print lines include: \[ 1 - 2 + 34 + 5 + 6 + 7 + 8 - 9 = 50 \] and \[ 1 + 2 + 34 - 56 + 78 - 9 = 50 \]

5.2 [5 points] Count the total number of suitable solutions for any integer i from 1 to 100, assign the count to a list called Total_solutions. Plot the list Total_solutions, so which number(s) yields the maximum and minimum of Total_solutions?