Nested Loops and Stepwise Refinement

1
Nested Loops and Stepwise Refinement
for(int row 1 row lt n row) for(int
col 1 col lt n col) // deal with
each row of matrix col by col // end for col
// end for row

• Nested Loops
• Loops defined
  inside the
  
  blocks of loops
  are referred to
  
  as "nested".
• A way to deal with the complexities of writing
  programs using nested loops is to follow the
  design paradigm of stepwise refinement
• write pseudo-programs in rough (highly abstract)
  steps
• continually refine steps until they end up as
  actual C code that solve problem. Remember to
  compile often!

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Example Hankel Matrix

• A Hankel matrix often used for statistical
  analysis is a matrix in which the (i,j)th entry
  depends only on
  the sum ij.
• The Hankel matrix defined by the numbers
  1, 2, ..., 2n-1 is
• Consider a program that reads in a value n (less
  than 50) from the user and print out the Hankel
  matrix defined by 1, 2, ..., 2n-1 to the screen

1 2 3 ... n 2 3 4 ... n1 ... n n1 n2 ...
2n-1
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Hankel Matrix Stepwise Refinement

• With stepwise refinement, 1st consider the
  problem from a highly abstract viewpoint
• Get a value for n, then
• compute Hankel matrix
• Gradually refine each abstraction

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Completed Hankel Solution

• Continue Refinement until all abstract concepts
  are concretely represented in the code

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ICE Trace this programs output

• include ltiostreamgt
• using namespace std
• int main()
• int n, i
• for (n2 nlt4 n)
• for (i7 igt6 i--)
• cout ltlt n ltlt " " ltlt i ltltendl
• cout ltlt "i is now " ltlt i ltlt endl
• // for n
• cout ltlt "n is now " ltlt n ltlt endl
• return 0

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ICE Nested Loops to Generate a Right Triangle

• Write a program that uses nested for loops to
  generate a right triangle with n asterisks such
  that the first row has one asterisk, the second
  has two, and so on.
• Right-align the asterisks on each row such as