Iterating backwards over an array throwing exception - objective-c

Question

I am trying to make an add method that works like long addition, so I want to start the addition from the end and work my way backwards so I can get the carrys right and etc. So I am currently trying to start working backwards over the array.
For example what im trying to do.
two arrays with the character 123456789
and i want to add them starting at 9 + 9 then move to 8+8
So I'm pretty sure I'm using the right way to iterate backwards over an array, but everytime I try I get just the runtime error, index out of bounds, and I can't figure out why. Any help would be great, I just cant figure out why it keeps throwing the exception.
-(MPInteger *) add: (MPInteger *) x
{
NSMutableArray *a = self->intString;
NSMutableArray *b = x->intString;
NSMutableArray *c = [NSMutableArray arrayWithCapacity:100];
//for (int i = 0; i < [a count]; i++) {
for (NSInteger i = [a count] - 1; i > 0; i--) {
int num = 10;
NSNumber *ourNum = [NSNumber numberWithInt:num];
NSNumber *total = [NSNumber numberWithInt:[[a objectAtIndex:i] intValue] + [[b objectAtIndex:i] intValue]];
if ([total intValue] >= [ourNum intValue]) {
total = [NSNumber numberWithInt:([total intValue] - [ourNum intValue])];
[c addObject:[NSNumber numberWithInt:([total intValue])]];
} else {
[c addObject:[NSNumber numberWithInt:[[a objectAtIndex:i] intValue]+[[b objectAtIndex:i] intValue]]];
}
NSLog(#"%#", c[i]);
}
return x;
}

Answer 1

First, let's clean up this code.
- (MPInteger *)add:(MPInteger *)x {
NSMutableArray *a = self->intString;
NSMutableArray *b = x->intString;
NSMutableArray *c = [NSMutableArray arrayWithCapacity:100];
for (NSInteger i = [a count] - 1; i > 0; i--) {
int num = 10;
NSNumber *ourNum = #(num);
NSNumber *total = #([a[i] intValue] + [b[i] intValue]);
if ([total intValue] >= [ourNum intValue]) {
total = #([total intValue] - [ourNum intValue]);
[c addObject:#([total intValue])];
} else {
[c addObject:#([a[i] intValue] + [b[i] intValue])];
}
NSLog(#"%#", c[i]);
}
return x;
}
Next, let's remove redundant/duplicate code.
- (MPInteger *)add:(MPInteger *)x {
NSMutableArray *a = self->intString;
NSMutableArray *b = x->intString;
NSMutableArray *c = [NSMutableArray arrayWithCapacity:100];
for (NSInteger i = [a count] - 1; i > 0; i--) {
int num = 10;
NSNumber *total = #([a[i] intValue] + [b[i] intValue]);
if ([total intValue] >= num) {
total = #([total intValue] - num);
}
[c addObject:total];
NSLog(#"%#", c[i]);
}
return x;
}
Now we can clearly see all of the issues.
You're going from [a count] - 1 to 1. You should be going all the way to 0.
a and b might have different sizes, so if you only do [a count] - 1 to 0, then if for example [b count] < [a count], you'll get an index out of bounds error when you try to access b[i].
You're adding stuff to the end of c, but you should be adding it to the beginning of c since you're iterating backwards.
You don't store the carry anywhere.
You are accessing c[i], which doesn't exist.

Answer 2

You are starting with an empty array 'c', and you NSLog c[i] which is obviously out of bounds on the first iteration.