“Computer Science is no more about
computers than astronomy is about
telescopes.”
— E. W. Dijkstra
Algorithms
CSE 130: Introduction to C Programming
Spring 2005
“Don’t sweat it — it’s only ones and
zeros.”
— P. Skelly
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Algorithms
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Algorithm Attributes
• Algorithms are the heart of computer
• An algorithm must be:
• complete
• precise
• finite
• An algorithm should describe exactly how
science
• An algorithm is a description of the steps
necessary to solve a problem
• “problem” = “task to be performed”
• An algorithm is a “blueprint” for a program
• A computer program embodies an algorithm
to perform a given procedure
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Developing an
Algorithm
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Algorithm Example 1
• Start with the input and desired output
• Divide and conquer the problem
• Iterative refinement of solution
• Present your solution as pseudocode
• When each solution step looks like a
• Compute the average of a list of numbers
• Input: a list of numbers
• Output: their average
program statement, you’re done!
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Divide and Conquer
Pseudocode Solution
1. Initialize total and count to 0
1. Add up the numbers
2. For each number:
2. Count the total number of values
1. Add it to the total
3. Average = total / count
2. Add 1 to count
3. Divide total by count
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Algorithm Example 2
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Making Change
1. Get the amount of money to return
• Problem: Given a monetary amount, print
2. Compute the number of quarters needed
the number and types of coins required to
make change
3. Compute the number of dimes needed
• Input: a number between 0 and 99 inclusive
• Output: a number of quarters, dimes,
4. Compute the number of nickels needed
5. Compute the number of pennies needed
nickels, and pennies equal to the input
6. Print the results
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Making Change, part 2
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Algorithm Example 3
• Problem: Create a receipt for a list of
purchased items. Print the total price,
compute the total with 8.25% tax, and print
the money tendered (plus any change
given)
1.
2. Compute the number of quarters needed
1. number of quarters = total / 25
• Input: a list of items and prices
• Output: a list of items and prices, plus the
2. remainder = remainder % 25
total, total with tax, and cash tendered
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Printing a Receipt
Printing a Receipt 2
1. Set the total to $0.00
5. Print total with tax
2. For each item:
6. Get cash tendered
1. Print the item name and price
7. Print cash tendered
2. Add item price to total
8. If cash tendered > total with tax:
3. Print total
1. Make change
4. Total with tax = 1.0825 * total
2. Print change
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Problem Solving
Process
The Feynman Problem-Solving
Algorithm:
• What is it?
• Analysis
• Design
• Implementation
• Testing
(1) write down the problem;
(2) think very hard;
(3) write down the answer.
— Murray Gell-mann
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Problem Solving
Process
• What is it?
– Analysis
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Problem Solving
Process
• What is it?
• Analysis
Determine the inputs, outputs, and other components of the
problem
Description should be sufficiently specific to allow you
to solve the problem
• Design
• Implementation
• Testing
Describe the components and associated processes
for solving the problem
Straightforward and flexible
– Design
• Implementation
• Testing
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Problem Solving
Process
Problem Solving
Process
• What is it?
• Analysis
• Design
• What is it?
• Analysis
• Design
• Implementation
Develop solutions for the components and use
those components to produce an overall solution
Straightforward and flexible
– Implementation
• Testing
– Testing
Test the components individually and collectively
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Problem Solving
Process
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Problem Solving
Methodologies
• How to do it?
• Depends upon your mode of thinking
• Bricolage approach
• Planned approach
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Problem Solving
Methodologies
Problem Solving
Methodologies
• How to do it?
• Depends upon your mode of thinking
• Bricolage approach
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• How to do it?
• Depends upon your mode of thinking
Problem features and aspects are repeatedly
tried and manipulated according to your
personal way of organizing information
• Bricolage approach
A mistake is not an error, but a correction
waiting to be made in the natural course
of solving the problem
• Planned approach
• Planned approach
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Uses logic, formalism, and engineering
coupled with a structured methodology
Inherent structure of the planned approach
offers makes it easier to show correctness
of solution
Dominant method in terms of teaching
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Tips
Tips
• Find out as much as you can
• Reuse what has been done before
• Expect future reuse
• Break complex problems into
• Find out as much as you can
Find out what is known about the problem
subproblems
Talk to the presenter
Determine what attempts have succeeded and what
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Tips
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Tips
• Find out as much as you can
• Find out as much as you can
Research can require significant time and generate questions
Consider:
The effort is worthwhile because the result is a better
understanding
Sketching a solution and then repeatedly refine its components
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Tips
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Tips
• Reuse what has been done before
• Reuse what has been done before
Your time is valuable
Correctness is probably even more valuable
Be open to indirect use of existing materials
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Tips
Tips
• Break complex problems into
• Expect future reuse
subproblems
Make as few assumptions as necessary
Divide-and-conquer
Maximizes the likelihood that your effort can be used in future situations
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Algorithm Building
Blocks
Programming Process
1. Specify the problem to be solved
1. Expressions
2. Develop an appropriate algorithm
2. Conditional (selection) statements
3. Code the algorithm using a
programming language (i.e., C)
3. Iteration (repetition) statements
4. Subprogram invocations
4. Test the resulting code
Closely related to expressions
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Next Time
• Programming Languages
• Creating Simple Programs
• Basic Input/Output
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