L6. More on the For-Loop Using the Count Variable Developing For-Loop Solutions.

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Presentation transcript:

L6. More on the For-Loop Using the Count Variable Developing For-Loop Solutions

First = input(‘Enter first year’); Last = input(‘Enter last year’); for y = First:Last fprintf(‘%5d\n’,y) end A Year-Printing Fragment

How It Works for y = First:Last fprintf(‘%5d\n’,y)) end Suppose First is 1999 and Last is First 2001 Last y

How It Works for y = First:Last fprintf(‘%5d\n’,y) end We enter the for-loop and y is initialized 1999 First 2001 Last 1999 y

How It Works for y = First:Last fprintf(‘%5d\n’,y)) end Is the value in y <= than the value in Last? 1999 First 2001 Last 1999 y

How It Works for y = First:Last fprintf(‘%5d\n’,y) end Yes. Execute the loop body and increment y First 2001 Last 2000 y 1999 Output

How It Works for y = First:Last fprintf(‘%5d\n’,y) end Is the value in y <= the value in Last? 1999 First 2001 Last 2000 y 1999 Output

How It Works for y = First:Last fprintf(‘%5d\n’,y) end Yes. Execute the loop body and increment y First 2001 Last 2001 y Output

How It Works for y = First:Last fprintf(‘%5d\n’,y) end Is the value in y <= the value in Last? 1999 First 2001 Last 2001 y Output

How It Works for y = First:Last fprintf(‘%5d\n’,y) end Yes. Execute the loop body and increment y First 2001 Last 2002 y Output

How It Works for y = First:Last fprintf(‘%5d\n’,y) end Is the value in y <= the value in Last? 1999 First 2001 Last 2002 y Output

How It Works for y = First:Last fprintf(‘%5d\n’,y) end No. The loop is finished First 2001 Last 2002 y Output

Problem Solving With the For-Loop The calculation to be repeated. end for count variable = expression for starting value : expression for ending value :

Developing For-Loop Solutions Illustrate the thinking associated with the design of for-loops The methodology of stepwise refinement. An example..

A Game: TriStick Pick three sticks each having a random length between zero and one. You win if you can form a triangle whose sides are the sticks. Otherwise you lose.

Win: Lose:

Problem Estimate the probability of winning a game of TriStick by simulating a million games and counting the number of wins.

Pseudocode Initialize running sum variable. Repeat 1,000,000 times: Play a game of TriStick by picking the three sticks. If you win increment the running sum Estimate the probability of winning

Refine… % Initialize running sum variable. Wins = 0; for n = 1: Play the nth game of TriStick by picking the three sticks. If you win increment the running sum. end % Estimate the prob of winning p = wins/

Refine the Loop Body Play the nth game of TriStick by picking the three sticks. If you win increment the running sum.

Refine the Loop Body % Play the nth game of TriStick % by picking the three sticks. a = rand; b = rand; c = rand; if (a<b+c) && (b<a+c) && (c<a+b) % No stick is longer than the % sum of the other two. wins = wins+1; end

Key Problem-Solving Strategy Progress from pseudocode to Matlab through a sequence of refinements. Comments have an essential role during the transitions. They “stay on” all the way to the finished fragment.