Loops - Execute a Set of Statements

6.1 While loops Loops - execute a set of statements between the keywords that delimit the beginning and end of the loop While loops - execute a list of statements ( the loop body) as long as the loop expression is true Loop expression - a logical expression following the while keyword that’s evaluates to true or false While loop while (expression) % statements to execute as long as expression is true end % statements here will execute after expression is false example x = 5; y = 18; while (y >= x) fprintf(‘%d ’, y); y = y - x; end Output : 18 13 8 problem 1) Write a while loop that continues to increment userValue by 5 as long as userValue is less than 10 function userValue = IncreaseValue(userValue) while userValue < 0 userValue = userValue + 5; end Command IncreaseValue(-13) = 2 IncreaseValue(-1) = 4 IncreaseValue(0) = 0 IncreaseValue(6) = 6 2) Write a while loop that multiple userValue by 2 while all of the following conditions are true: - userValue is not 10 - userValue is less than 25 function userValue = AdjustValue(userValue) while (userValue ~= 10) && (userValue < 25) userValue = userValue * 2; end Command AdjustValue(2) = 32 AdjustValue(5) = 10 AdjustValue(15) = 30 AdjustValue(10) = 10 AdjustValue(25) = 25 6.2 More while examples 3) Write a while loop that adjusts userValue while userValue is less than 0 or greater than 80. If userValue is greater than 80, then subtract 5 from userValue. If userValue is less than 0, then add 10 to userValue function userValue = AdjustValue(userValue) while (userValue < 0) || (userValue > 80) if userValue < 0 userValue = userValue + 10; end if userValue > 80 userValue = userValue - 5; end end 6.3 Counting Loop variable - a variable used to count the numbers of iterations while loop used for counting i = 1; while (i <= N) % Loop body statements go here i = i + 1; end example while loop that counts iterations :Savings interest program initSavings = 10000; interestRate = 0.05; fprintf(‘Initial savings of $%d\n’, initSavings); fprintf(‘at %f yearly interest. \n\n’, interestRate); years = input(‘Enter years: ’); i = 1; savings = initSavings; while (i <= years) fprintf(‘ Savings in year %d is %f\n’, i, savings); savings = savings + (savings * interestRate); i = i + 1; end *** a common error is to forget to include the loop variable update (e.g. i = i +1;) at the end of the loop ***another common error is to include the loop variable update at the beginning of the while loop before the loop’s statements are executed - counting is sometimes done by steps greater than 1 Problem 1) An insect population doubles every generation. Write a while loop that iterates numGeneration times. Inside the while loop, write a statement that doubles currentPopulation in each iteration of the while loop. function currentPopulation = CalculatePopulation(numGeneration, initialPopulation) % numGeneration : number of times the population is doubled % initialPopulation : starting population value i=1 currentPopulation = initialPopulation; while (i <= numGeneration ) currentPopulation = currentPopulation * 2; i = i + 1; end end 2) Write a while loop that assigns summedValue with the sum of all values from 1 to userNum. Assume userName is always greater than or equal to 1. Note : you may need to define additional variables. ex) if the userNum is 5, then summedValue is 15 (i.e. 1+2+3+4+5=15) function summedValue = SummationWithLoop(userNum) i = 1; summedValue = 0; while (i <= userNum) summedValue = summedValue + i; i = i + 1; end 6.4 For loops A for loop statement executes the loop’s statement for a fixed number of iterations using an index variable that iterates over a specified set of values. for loop with index increment for indexVar = startIndex: incrementValue: endIndex % Loop body statements go here end ex) for count = 2:1:8 - will iterate over the index values 2,3,4,5,6,7, and 8, executing 7 total iterations ex) for count = 2:2:10 - will iterate over the index values 2,4,6,8, and 10, executing 5 total iterations ex) for count = 12:-3:0 - will iterate over the index values 12,9,6,3, and 0, executing 5 total iterations If the increment value is 1, a programmer can omit the second argument in the for loops using the following form: for indexVar = startIndex: endIndex % Loop body statements go here end Problems 1) The for loop calculates the amt of money in a saving account after numberYears given in initial balance of savingsBalance and an annual interest rate of 2.5%. Complete the for loop to iterate from 1 to numberYears (inclusive) function savingsBalance = CalculateBalance(numberYears, savingsBalance) % numberYears : numbers of year that interest is applied to savings % savingsBalance : initial savings in dollars interestRate = 0.025; % 2.5% annual interest rate for (i = 1:numberYears) savingsBalance = savingsBalance + (savingsBalance * interestRate); end end 2) Write a for loop that assigns summedValue with the sum of all odd values from 1 to userNum. Assume userNum is always greater than or equal to 1. ex) if userNum = 5, them summedValue = 9 (1+3+5=9) function summedValue = OddsSum(userNum) summedValue = 0; for i = 1:2:userNum summedValue = summedValue + i ; end end 3) A pin code consist of N integers between 1 and 9. In a valid pin code, no integer is allowed to repeat consecutively. Ex) the sequence 1,2,1,3 is valid because even though 1 occurs twice, it is not consecutive. However the sequence 1,2,2,1 is invalid because 2 occurs twice, consecutively. Utilize a for loop and branches statement to write a function called pinCodeCheck to detect and eliminate all the consecutive repeats occurs, and the row array pinCode. The function outputs should be two row arrays. The row array rePos contains the positions pinCode where the conservative occurs, and the row array pinCodeFix is a valid pin code with all the consecutive repeats removed in pinCode. Hint : the empty array operator [] is will be helpful to use function [ repPos, pinCodeFix] = pinCodeCheck(pinCode) repPos = [] pinCodeFix = [] for i = 2:length(pinCode) if pinCode(i-1) == pinCode(i) repPos = [repPos i]; else pinCodeFix = [pinCodeFix pinCode(i)]; end end end 6.5 Nested Loops Nested loops - loops in which one loop appears as part of the body of another loop - commonly referred to as inner loop and outer loop nested loop example - multiplication tables Problems 1) Write two nested for loops to calculate the following double summations: ex: if s is 3 and t is 2, then summationResult is 18. (1x1)+(1x2)+(2x1)+(2x2)+(3x1)+(3x2)=19 function summationResult = DoubleSum(s, t) summationResult = 0; for i = 1:s for j = 1:t summationResult = summationResult + ( i * j ); end end 2) A times table gives the product between two integers (ex. 5x5=25, 5x6=30, 12x12 etc.). Write a function called timesTable that output a times table up to size requested, given a positive integer sizeOfTable. The top row and left column have integers from 1 to desired size. If sizeOfTable is: - negative, then the absolute value of sizeOfTable should be used to calculate the table - is not an integer, the table should be calculated to the neared integer greater than or equal to sizeOfTable Restrictions: The timesTable function should only use while loops function outputMatrix = timesTable( sizeOfTable) % insert code to determine the size of the times table sizeOfTable = abs(sizeOfTable) % abs - absolute value/positive value sizeOfTable = floor(sizeOfTable) % floor - round down rows = sizeOfTable columns = sizeOfTable % inset code to initialize the table by filling all entries with zeros outputMatrix (1:rows, 1:columns) = [0]; %insert code to fill the first column and first row with conservative integers starting with 1 i = 1; while ( i <= sizeOfTable) outputMatrix(i, 1) = i; outputMatrix(1, i) = 1; i = i + 1; end i = 1; while ( i <= sizeOfTable) j = 1; while (j <= sizeOfTable) outputMatrix(i, j) = i * j; j = i + 1; end end end 6.6 Loops and Arrays When performing numerical calculations with arrays, in general much better numerical performance is obtained with array operations than making use of repetitive code provided while and for loops. However, there are some instances when using while and for loops is simpler than using array operations. 1-D arrays and for loops n = 10; sampleArray = [ ]; % note the empty operator for i = 1:1:n sampleArray = [sampleArray, i^2]; end sampleArray The reverse order is produced by the following loop n = 10; sampleArray = [ ]; % note the empty operator for i = n:-1:1 sampleArray = [sampleArray, i^2]; end sampleArray If the number of loop iterations is large, resizing the array during each loop iteration adversely affects program speed. Such repeated resizing requires the interpreter to spend extra time looking for larger contiguous blocks of memory, and them moving the array into those blocks. changing the size of arrays in an iterative loop may result in a slow-running program tic n = 10^5; sampleArray = [ ]; for i = 1:n sampleArray = [sampleArray, i^2]; end toc To avoid such repeated resizing, the programmer can pre-allocate the array size before the loop. Such pre-allocation can be achieved by initially filling the array with zeros (or ones). Because the interpreter need only allocate memory once before the loop, and not repeatedly within the loop, program speed can be dramatically improved. Notes: - The ones function created an array of the specified size, filled with 1s - The zeros function create an array of the given size filled with 0s pre-allocating an array before entering a loop with many iterations can improve speed tic n = 10^5; sampleArray = zeros(1, n); for i = 1:n sampleArray(i) = i^2; end toc ***Good Practices - avoid programming for and while loops that incrementally increase the size of an array each time through the loop - if for and while loops must be used to perform array operations, pre-allocate the maximum amount of space required for the array before loop is executed - maximize use array operators to initialize and manipulate large arrays array operations may be faster than loops tic n = 10^5; sampleArray = ones(1, n); sampleArray = sampleArray.^2; toc Example - 2D array initialization with a for loop clear m = 5; n =5; matHilbert = zeros(m,n) for i = 1:m for j = 1:n matHilbert(i, j) = 1/(i+j-1); end end format rat % set output to approximation by ration of small interpersonal matHilbert format % resets format to default settings Problems 1) Write a for loop to populate multiplicationTable with the multiples of baseValue from 0 to 5 function multiplicationTable = CreateTable(baseValue) % multiples of baseValue used to populate multiplicationTable multiplicationTable = zeros(1, 6); % preallocate multiplicationTable with 6 elements for i = 0:5 multiplicationTable(1, i+1) = baseValue * i; end end Answer - CreateTable(2) = [0, 2, 4, 6, 8, 10] 2) Assign numMatches with the number of elements in userValues that equal matchValue ex) if matchValue = 2 and userVals = [2,2,1,2], then numMatches = 3 function numMatches = FindValues(userValue, matchValues) arraySize = 4 numMatches = 0; for (i = 1:arraySize) if (userValue(i) == matchValue) userValue(i) = userValue(i); else userValue(i) = NaN end end numMatches = sum(double(~isnan(userValue)));; end 3) Write a for loop that iterates from iterates from 1 to numberSamples to double any element’s value in dataSamples that is minValue ex) if minValue = 10, then dataSample = [2,12,9,20] becomes [4,12,18,20] function dataSamples = AdjustMinValue(numberSample, userSamples, minValue) dataSamples = userSamples; for i = 1:numberSamples if dataSamples(i) < minValue dataSamples(i) = dataSamples(i) * 2; else dataSamples(i) = dataSamples(i); end end end 6.7 Break and Continue A Break Statement in a loop (either while loop or for loop) causes an immediate exit of the loop. Statements in the loop after the break statement do not execute. A break statement can sometimes yield a loop that is easier to understand. A Continue Statement in a loop causes an immediate jump to the loop condition check. A continue statement can sometimes improve the readability of a loop. ex) Simon Say user_score = 0; simon_pattern = ‘RRGBRYYBGY’; user_pattern = ‘RRGBBRYBGY’; for i = 1:10 if simon_pattern(i) == user_pattern(i) user_score = user_score + 1; else break end end fprintf(‘User Score: %d \n’, user_Score)