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Problem Solving with Selection

Problem Set

The following problem sets are intended for practice. Attempt these on your own.

Largest of Three

Problem

Problem Description

Given three real numbers \(n_1\), \(n_2\), and \(n_3\), we want to find the largest of the three. Note that the largest one may not be unique, but we simply want the largest one. See the sample below.

  • \(n_1 = 0.1\)
  • \(n_2 = 0.3\)
  • \(n_3 = 0.2\)

Largest is \(0.3\)

  • \(n_1 = -0.1\)
  • \(n_2 = -0.2\)
  • \(n_3 = -0.3\)

Largest is \(-0.1\)

  • \(n_1 = 0\)
  • \(n_2 = 0\)
  • \(n_3 = 0\)

Largest is \(0\)

Task

Write Python code to compute and print the largest of the three number.

Assumptions

  • n1, n2, and n3 are floating point numbers.
  • n1, n2, and n3 are already initialized.
Hints
Hint #1

What is the condition to know if \(n_1\) is the largest number? Can you figure out the other conditions?

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n1 >= n2 and n1 >= n2

Note that we need to use >= because there is a possibility there are two numbers that are equal.

Hint #2

What constructs do you need to use? What about for the subsequenc check?

We need at least one if-statement. For the other, we need to use elif because there is a possibility there are two numbers that are equal.

Possible Solution 
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# Assume n1, n2, and n3 are initialized
if n1 >= n2 and n1 >= n3:
  print(n1)  # n1 is largest
elif n2 >= n1 and n2 >= n3:
  print(n2)  # n2 is largest
elif n3 >= n1 and n3 >= n2:
  print(n3)  # n3 is largest

There is an alternative solution by assuming that n1 is the largest. Then we challenge that by checking if n2 is the current largest. Finally, we challenge that by checking if n3 is the current largest. The advantage of this technique is that it can be extended easily to more numbers without changing the condition too much. Can you write the code based on this idea?

Assume Largest First 
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# Assume n1, n2, and n3 are initialized
largest = n1     # assume n1 is largest
if largest < n2: # check if n2 is larger
  largest = n2
if largest < n3: # check if n3 is larger
  largest = n3
print(largest)

Waist-to-Hip Ratio

Problem

Problem Description

Waist-to-hip ratio (WHR) is an alternative to body mass index (BMI) indicator to measure if a given person is of normal weight, overweight, or obese. The computation requires two values:

  • Waist measurement in cm.
  • Hip measurement in cm.

First we compute the ratio of waist to hip and determine the weight indicator using the table below. Note that the indicator depends on whether the patient is male or female.

Male Female Indicator
< 0.9 < 0.8 Normal
0.9 - 1.00 0.8 - 0.85 Overweight
> 1.00 > 0.85 Obese

Task

Write Python code to compute and print weight indicator given three variables is_male, waist, and hip.

Assumptions

  • is_male is a boolean.
  • waist and hip are positive floating point numbers (i.e., waist > 0 and hip > 0).
  • waist and hip are given in cm.
Hints
Hint #1

Can you compute the waist-to-hip ratio?

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ratio = waist / hip
Hint #2

Let us use nested if-statements. Consider checking is_male first. What should be the inner condition?

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# assume is_male is True
if ratio < 0.9:
  # Normal
elif 0.9 <= ratio and ratio <= 1.00:
  # Overweight
else:
  # Obese

The condition for when is_male is False is left as an exercise to the reader.

Possible Solution 
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# Assume is_male, waist, and hip are initialized
ratio = waist / hip
if is_male:
  if ratio < 0.9:
    print('Normal')
  elif 0.9 <= ratio and ratio <= 1.00:
    print('Overweight')
  else:
    print('Obese')
else:
  if ratio < 0.8:
    print('Normal')
  elif 0.8 <= ratio and ratio <= 0.85:
    print('Overweight')
  else:
    print('Obese')