Methodology for problem solving: the case of iterator live-out value

888.11 seminars

[<< home] [Lecture 1] [Lecture 2] [Lecture 3] [Lecture 4] [Lecture 5] [Lecture 6]

Lecture 1: Overview and definition of the problem

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Assignment for next class

Note: students will present their solution for the exercices on the whiteboard during the class.

Exercise 1

Write at least three sample input C programs that respect the Static Control Part constraints, and the associated desired output. Each input program must contain at least 4 loops and one conditional.

Lecture 2: Writing algorithms

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Assignment for next class

Note: students will present their solution for the exercices on the whiteboard during the class.

Exercise 1

Write an algorithm which implements the description below:

The starting address of a matrix of integer A of size n x n
The starting address of a matrix of integer B of size n x n
A function matrix(16x16): getBlock(address:X, int:i, int:j) which returns a sub-matrix (a block) of the matrix starting at address X, of size 16 x 16 whose first element is at position (i,j)

An integer c, the sum of the diagonal elements of the product of A and B

Exercise 2

Write an algorithm which implements the description below:

An arbitrary binary search tree A with integer nodes
- The left subtree of a node contains only nodes with keys less than the node's key.
- The right subtree of a node contains only nodes with keys greater than the node's key.
- Both the left and right subtrees must also be binary search trees.

A balanced binary search tree B containing all elements in the nodes of A

Lecture 3: Solving the problem, part I

Find the slides here.

Assignment for next class

Note: students will present their solution for the exercices on the whiteboard during the class.

Exercise 1

Write an algorithm which implements the description below:

an AST A of a program such that:
- A represents a Static Control Part
- For each loop in A, the lower bound is always smaller than the upper bound
- Conditionals are always true
- There is no loop iterator symbol assigned outside its defining loop

an AST B containing A which is appended another AST that assigns to each loop iterator in A the value it takes when A is executed

Lecture 4: Solving the problem, part II

Find the slides here.

Assignment for next class

Note: students will present their solution for the exercices on the whiteboard during the class.

Exercise 1

Write an algorithm which implements the description below:

an AST A of a program such that:
- A represents a Static Control Part
- Conditionals are always true
- There is no loop iterator symbol assigned outside its defining loop

an AST B containing A which is appended another AST that assigns to each loop iterator in A the value it takes when A is executed

Lecture 5: General algorithm for the Live-out Iterator Problem

Find the slides here.

Assignment for Wednesday, Sept. 15th

Note: students will present their solution for the exercices on the whiteboard during the class.

Exercise 1

Write an algorithm which implements the description below:

an AST A of a program such that:
- A represents a Static Control Part
- There is no loop iterator symbol assigned outside its defining loop

an AST B containing A which is appended another AST that assigns to each loop iterator in A the value it takes when A is executed

Lecture 6: Proving your Algorithm

Find the slides here.

Assignment for Friday, Oct. 1st

Note: students will present their solution for the exercices on the whiteboard during the class.

Exercise 1

Given an algorithm which implements the description below, prove its correctness.

The starting address of a matrix of integer A of size n x n
The starting address of a matrix of integer B of size n x n
A function matrix(16x16): getBlock(address:X, int:i, int:j) which returns a sub-matrix (a block) of the matrix starting at address X, of size 16 x 16 whose first element is at position (i,j)

An integer c, the sum of the diagonal elements of the product of A and B