More on Iteration Using "For" - Notes | CS 1112, Study notes of Computer Science

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„^ Previous Lecture:^ „^ Branching^ „^ Logical operators and values^ „^ Introduction to

for-loop

„^ Today’s Lecture:^ „^ More on iteration using

for

„^ Announcements^ „^ Register your clicker!

February 3, 3009^

Lecture 5^

Question

A stick of unit length is split into two pieces. Thebreakpoint is randomly selected. On average, howlong is the shorter piece?

February 3, 3009^

Lecture 5^

n= 10000;^

% number of trials

total= 0;^

% accumulated length so far

for^ k= 1:n% one trial of the experimentbreakPt= rand(1);shortPiece= min(breakPt, 1-breakPt);total= total + shortPiece;end aveLength= total/nfprintf(‘Average length is %f\n’, ...

aveLength)

February 3, 3009^

Lecture 5^

Example: “Accumulate” a solution %^ Average^10 numbers

from^ user^ input n=^ 10;^ %^ number

of^ data^ values for^ k=^ 1:n%^ read^ and^ process

input^ value num=^ input('Enter

a^ number:^ '); total=^ total^ + num; endave=^ total/n;^

%^ average^ of^ n numbers fprintf('Average

is^ %f\n',^ ave)

How many passesthrough the loop willbe completed?^ A:^0 B:^1 C:^9 D:^10 E:^11

February 3, 3009^

Lecture 5^

Important Features of Iteration „^ A task can be accomplished if some steps arerepeated; these steps form the loop body „^ Need a starting point „^ Need to know when to stop „^ Need to keep track of (and measure) progress—update

February 3, 3009^

Lecture 5^

Monte Carlo Estimation of

π^ Sq. area =

ThrowN^ darts^ N^ =^ L^ ×^ L Circle area =^ Nin^2^ =^ π^ L^ /

L^

L/

February 3, 3009^

Lecture 5^

Monte Carlo Approximation of PiFor each of N trialsThrow a dartIf it lands in circleadd^

1 to total # of hitsPi is 4*hits/N

February 3, 3009^

Lecture 5^

Monte Carlo Pi with N darts on L-by-L board for k = 1:N endmyPi = 4*hits/N;

February 3, 3009^

Lecture 5^

Monte Carlo Pi with N darts on L-by-L board for k = 1:N% Throw kth dartx = rand(1)L – L/2;y = rand(1)L – L/2;% Is it in the circle?endmyPi = 4*hits/N;

February 3, 3009^

Lecture 5^

Monte Carlo Pi with N darts on L-by-L board for k = 1:N% Throw kth dartx = rand(1)L – L/2;y = rand(1)L – L/2;% Is it in the circle?if sqrt(x^2+y^2) <= L/2hits = hits + 1;endendmyPi = 4*hits/N;

February 3, 3009^

Lecture 5^

Syntax of the

for^ loop

for^ < var >= < start value

>:< incr >:< end bound

statements to be executed repeatedly end

Loop body

February 3, 3009^

Lecture 5^

Syntax of the

for^ loop

for^ < var >= < start value

>:< incr >:< end bound

statements to be executed repeatedly end Loop header specifies all the values that the index variablewill take on, one for each pass of the loop.E.g, k= 3:1:7^ means^ k^ will take on the values 3, 4, 5, 6,7, one at a time.

February 3, 3009^

Lecture 5^

% What will be printed?for k= 1:2:6fprintf(‘%d ’, k)end

A:^ 1 2 3 4 5 6B:^ 1 3 5 6C:^ 1 3 5 D:error(incorrect bounds)

February 3, 3009^

Lecture 5^

for^ loop examples

for k= 2:0.5:

k^ takes on the values 2,2.5,3 disp(k) Non-integer increment is OK

endfor k= 1:^

k^ takes on the values 1,2,3,

disp(k)^

Default increment is 1

endfor k= 0:-2:-

k^ takes on the values 0,-2,-4,-6 disp(k) “Increment” may be negative

endfor k= 0:-2:-

k^ takes on the values 0,-2,-4,-6 disp(k) Colon expression specifies a

bound

endfor k= 5:2:

The set of values for k is the empty disp(k) set: the loop body won’t execute

end