Lecture 5 - Control Structure Applications

Transcription

1 Lecture 5 - Control Structure Applications Variable indexing and examples of program writing Variable Indexing & built in functions indexing positions in an array array Grade contains 6 locations to store information content Use: Grade( index ) Grade(4) refers to the content 89. i Grade( i ) refers to the content 5. Use a variable to reference specific locations within an array e.g. Grade( i ) instead of Grade(4) The variable index i must be an integer, as it is pointing to a location Calculate the mean value of a list of grades: >> clear >> Grade [ ]; >> total0; >> for i:6 >> total total + Grade(i); >> averagetotal/6; We can use a few built-in MATLAB functions (sum and length) to shorten the above code. >> clear >> Grade [ ]; >> average sum(grade)/length(grade); We can also average just the first scores by indexing a part of the array Grade >> average sum(grade(:)) / ; OR >> j :; >> average sum(grade(j)) / ; index to location of content Grade( 6. ) does not mean anything there is no 6. spot in array Grade The content of spot is 6. Index refers to location, regardless of content Lecture 5 - Control Structure Applications page of 7

2 Examples of program development, pseudocode use and control structure use Example : finding maximum value in a vector (list of numbers) Given a vector of any size with random numbers inside, write a program that will identify two things: ) The maximum value in the vector ) The location (index) of that maximum value in the vector Solution Procedure It helps to create a simple example to work with. Let s work with a vector that contains only six integers. >> Grade [ ]; Have MATLAB identify 98 as the maximum value, and find its index location to be 4 we will need the following tools: a) decisions b) a loop c) variable indexing d) some scalar variables to keep track of decisions Pseudo-code: English outline in statement-like order (not language specific) Independence of pseudo-code from computer language allows programmer to focus on logic rather than syntax Usually iterative procedure to form and sharpen logical flow Final pseudo-code very useful for writing the program - since the logic has been set, now just focus on the syntax Apply to the finding maximum problem ) input the student grades (keyboard, input file, etc.) ) find out how many grades there are ) look at each grade and compare it with the other grades a) pick the first two, save the bigger of the two as the current max save its location b) pick # spot and compare it with the current max, if # is bigger, save it as the new current max, and save the new location c) pick #4 and compare it to current max, repeat b) d) repeat for each remaining grade, updating current max if new max is found Note that c) and d) are repeating the instructions in b) as we iterate the location being compared (loop) Note that b) makes a decision (if current bigger than previous, then...) Lecture 5 - Control Structure Applications page of 7

3 Now let s refine the Pseudocode to reflect these observations ) Enter grades and determine total number ) Assume first grade is largest (assign max grade(), maxptr ) ) Loop from i to the final grade: compare grade(i) with max if grade(i) > max, new value for max is grade(i) new value for maxptr is i if grade(i) not > max move to next value to compare Now that we have a good pseudocode, we translate it into MATLAB >> grade[ ]; >> numgrade length(grade); >> maximum grade(); >> maxptr; >> for i : numgrades >> if(grade(i) > maximum) >> maximum grade(i); >> maxptr i; >> % >> %refer to max value as grade(maxptr) >> % or as maximum >> % >> disp([ the max grade is numstr(maximum)]); OR >> disp([ the max grade is numstr(grade(maxptr))]); >> disp([ it was student # numstr(maxptr)]; Isn t saving the location of the maximum, and the max itself a little redundant? We only need to save the location (index) of the number. Why not just save the location, and retrieve the value when needed? Pointer A variable whose purpose is to keep track of where a value is within an array, not the value itself Must be an INTEGER Let s re-work the maximum algorithm, but only save the location of the current maximum, not the max itself...using a pointer Lecture 5 - Control Structure Applications page 4 of 7

4 >> grade[ ]; >> numgrade length(grade); >> maxptr ; >> for i:numgrade >> if(grade(i) > grade(maxptr)) >> maxptr i; >> disp([ max. numstr(grade(maxptr))]); >> disp([ student # numstr(maxptr)]) This is a little more efficient (fewer steps) and reduces the number of variables needed (maximum is not used this time) For the sake of showing off MATLAB s nice features, let s use some more advanced built in functions to solve this problem. max is a built in function that finds the maximum value of a vector and returns its location within the vector. >> grade[ ]; >> [maxgrade, maxptr] max(grade); >> disp(maxgrade) >> disp(maxptr) This was much easier. We could also use the find command to try another approach >> maxptr find (grade max(grade)); >> maxgrade max(grade); The find command above returns the locations within grade where the condition (grade max(grade)) is true. These quicker methods that use built in MATLAB functions will be applied later on as we get more comfortable with basic programming. For now we ll do things the long way. The goal will be for you to be able to write programs that can do what max does and find does so you won t be dependent on existing built in stuff. Lecture 5 - Control Structure Applications page 5 of 7

5 Another algorithms - swapping and sorting swapping - switch the contents of two variables Given: x but I want x How can I swap x() with x()? Will this work?? >> x() x() >> x() x() Why not? >> x() x() > x() >> x() x() > x() What we need is some place to temporarily store one or the other >> temp x() >> x() x() >> x() temp >> temp x() > temp, x >> x() x() > temp, x >> x() temp > temp, x mission accomplished. what would pseudo-code look like? ) identify the variables to swap ) save the contents of # to a temporary location ) replace contents of # with that of # 4) replace the contents of # with that in the temporary location From now on, this entire pseudo-code can be a one word command... SWAP variabels # and # Lecture 5 - Control Structure Applications page 6 of 7

6 selection sort - re-order contents of a vector from low to high, or high to low. Combines the previous two algorithms: ) finding a maximum ) swapping. we have student grades G 7. we want to re-order from LOWEST to HIGHEST Pseudo-code: ) Find the location of the lowest value in the entire vector ) Swap the contents of that spot with the # spot ) find the location of the second lowest value in the entire vector a) or...find the lowest value in the entire vector, excluding # 4) Swap the contents of that spot with the # spot 5) Find the location of the lowest value remaining in the entire vector excluding spots # and #. 6) Swap the contents of that spot with # 7) repeat steps 5) and 6), moving down one spot each time Sorting - let s illustrate how we intend this algorithm to work... Given: G after iteration # G after iteration # G 7. after iteration # G 7. after iteration #4 G 7. we re done. # of iterations needed? One less than the number of values in the vector >> for i :(length(g)-) This selection sort code will be part of Homework #. Lecture 5 - Control Structure Applications page 7 of 7