Warning

# Computer Lab 05, Non-trivial loops

## Practical work

### Sum of digits in a string

Let s be a string containg several characters some of which may be digits. Write a function that returns the sum of all digits in that string.

def sum_digits_in_string(s):
"""Return sum of all digits in a string.
:param s: string containing the digits and other characters
:return: numeric value, sum of all digits

Examples:
>>> sum_digits_in_string('1')
1
>>> sum_digits_in_string('hi 1 hello 2')
3
>>> sum_digits_in_string('Values: 1.26, 2.3, 1.76')
28
"""

### Sum of decimal numbers in a string

Let s be a string containing decimal numbers separated by commas, e.g. s = '1.26,2.3,1.76'. Write a function that returns the sum of all decimal numbers in that string.

def sum_decimals_in_string(s):
"""Return sum of decimal numbers in a string.
:param s: string containing the decimal numbers separated by ','
:return: float, sum of all decimals

Examples:
>>> sum_decimals_in_string('1.2')
1.2
>>> sum_decimals_in_string('1.2,3.4')
4.6
>>> sum_decimals_in_string('1,2,0.000001')
3.000001
"""

### Character triangles

Using nested loops, write function print_left_triangle(n_rows, char) which prints the triangle depicted below. E.g. when you call that function like this:

>>> print_left_triangle(n_rows=5, char='T')
T
TT
TTT
TTTT
TTTTT

Again, using nested loops, write function print_right_triangle(n_rows, char) which prints the triangle depicted below. E.g. when you call that function like this:

>>> print_right_triangle(n_rows=5, char='T')
T
TT
TTT
TTTT
TTTTT

### Chemical compounds

Write a function combine_elements(el1, el2) which takes 2 iterables (e.g. lists) of chemical elements, and returns a list of all possible compounds that can arise by combining an element from the first list with an element from the second list.

def combine_elements(el1, el2):
"""Return a list of possible compounds each containg a single element from both the first and second list.
:param el1: list of strings, symbols of chemical elements for the first place of compound
:param el2: list of strings, symbols of chemical elements for the second place of compound
:return: list of strings, possible chemical compounds

Example:
>>> metals = 'Li Na K'.split()
>>> halogens = 'F Cl Br'.split()
>>> print(combine_elements(metals, halogens))
['LiF', 'LiCl', 'LiBr', 'NaF', 'NaCl', 'NaBr', 'KF', 'KCl', 'KBr']
"""

### Production maximization

Your small company produces wooden chairs and tables. Profit from a single chair is profit_per_chair, profit from a single table is profit_per_table. To build a single chair, you need to invest wood_per_chair units of wood and manhours_per_chair manhours of labour, to build a single table you need to invest wood_per_table units of wood and manhours_per_table manhours of labour. How many chairs and tables (n_chairs, n_tables) should you produce per day to maximize your profit, if you can invest available_manhours manhours a day and available_wood units of wood a day, and if you want the numbers of chairs and tables to be integers?

Write a function that returns the optimal values given all the parameter values as arguments.

def compute_optimal_production(profit_per_chair, profit_per_table,
wood_per_chair, wood_per_table,
manhours_per_chair, manhours_per_table,
available_wood, available_manhours):
"""Return numbers of chairs and tables to be produced per day to maximize profit.
:param profit_per_chair: Company profit for a single chair produced.
:param profit_per_chair: Company profit for a single table produced.
:param wood_per_chair: Amount of wood required to build a single chair.
:param wood_per_table: Amount of wood required to build a single table.
:param manhours_per_chair: Amount of work required to build a single chair.
:param manhours_per_table: Amount of work required to build a single chair.
:param available_wood: Total amount of wood available for production each day.
:param available_manhours: Total amount of work available each day.
:return: (n_chairs, n_tables) tuple containing the optimal number of chairs and tables produced each day.

Example:
>>> profit_per_chair, profit_per_table = 20, 30
>>> wood_per_chair, manhours_per_chair = 1, 3
>>> wood_per_table, manhours_per_table = 6, 1
>>> available_wood, available_manhours = 288, 99
>>> print(compute_optimal_production(
profit_per_chair, profit_per_table, wood_per_chair, wood_per_table,
manhours_per_chair, manhours_per_table, available_wood, available_manhours))
(18, 45)
"""

Suggestion: Proceed in smaller steps.

• Create helper function to compute the total profit from x chairs and y tables.
• Create a helper function telling you, whether when producing x chairs and y tables, the available amount of wood is or is not exceeded.
• Create a helper function telling you, whether when producing x chairs and y tables, the available manhours are or are not exceeded.
• Compute the maximal number of chairs and tables that can be produced per day, if you decided to produce only chairs/only tables.
• Then combine it all to complete function compute_optimal_production(). Perform exhaustive search among all feasible pairs of values for n_chairs and n_tables.