Question

“The sigma notation is shorthand for a summation. Its use here means to add the values
of 1/2^i, where i varies from 1 to n. That is, add 1/2 + 1/4 + 1/8 …. If you make the
value of n large enough, the sum of this series should approach 1. Let’s experiment with
different values for n to see how close we get.”

#import <Foundation/Foundation.h>
// Define the Fraction class
@interface Fraction : NSObject
{
int numerator;
int denominator;
}
@property int numerator, denominator;
-(void) print;
-(void) setTo: (int) n over: (int) d;
-(Fraction*) add: (Fraction *) f;
-(void) reduce;
@end    

#import "Fraction.h"
@implementation Fraction
@synthesize numerator, denominator;
-(void) print
{
NSLog (@"%i/%i", numerator, denominator);
}
-(void) setTo: (int) n over: (int) d
{
numerator = n;
denominator = d;
}
-(Fraction *) add: (Fraction *) f
{
// To add two fractions:
// a/b + c/d = ((a*d) + (b*c)) / (b * d)
// result will store the result of the addition
Fraction *result = [[Fraction alloc] init];
result.numerator = numerator * f.denominator +
denominator * f.numerator;
result.denominator = denominator * f.denominator;
[result reduce];
return result; 
}

#import "Fraction.h"
int main (int argc, char *argv[])
{
NSAutoreleasePool * pool = [[NSAutoreleasePool alloc] init];
Fraction *aFraction = [[Fraction alloc] init];
Fraction *sum = [[Fraction alloc] init], *sum2;
int i, n, pow2;
[sum setTo: 0 over: 1]; // set 1st fraction to 0
NSLog (@"Enter your value for n:");
scanf ("%i", &n);
pow2 = 2;

for (i = 1; i <= n; ++i) {
[aFraction setTo: 1 over: pow2];
sum2 = [sum add: aFraction];
[sum release]; // release previous sum
sum = sum2;
pow2 *= 2;
}

NSLog (@"After %i iterations, the sum is %g", n, [sum convertToNum]);
[aFraction release];
[sum release];
[pool drain];
return 0;
}

Question: Why do we have to create additional variable sum2 that we are using in the “for” loop? Why do we need “release previous sum” here and then again give it a value that we just released? :

sum2 = [sum add: aFraction];
[sum release]; // release previous sum
sum = sum2;

Is it just for the sake of avoiding memory leakage? (method “add” initializes a variable that is stored in sum2)

Answer 1

Without seeing how Fraction is defined, I can’t be sure, but I’d guess that a Fraction object is immutable so that sum can’t simply be changed. If we did sum = [sum add:aFraction], it would leak the object that sum used to point to (it had a positive retain count, still does, and we no longer have a pointer to it).