Range out of bounds, Project Euler 4 - objective-c

Question

I've been attempting to solve Problem 4 on Project Euler which is:
A palindromic number reads the same both ways. The largest palindrome >made from the product of two 2-digit numbers is 9009 = 91 × 99.
Find the largest palindrome made from the product of two 3-digit numbers.
I've been doing this using Objective-C and I thought I had come up with an solution but for some reason I get a Thread 1: signal SIGABRT-error a bit in and I was hoping that you guys could help me figure out what's wrong with my code:
#import <Foundation/Foundation.h>
int main(int argc, const char * argv[]) {
#autoreleasepool {
NSMutableArray *palindromes = [[NSMutableArray alloc] init];
for (int i = 1; i < 1000; i++) {
for (int j = 1; j < 1000; j++) {
int k = i * j;
NSString *number = [NSString stringWithFormat:#"%d", k];
NSUInteger length = [number length];
NSUInteger half = (length / 2);
NSString *part1 = [number substringWithRange:NSMakeRange(0, half)];
//It's at the line below that I get the error
NSString *part2 = [number substringWithRange:NSMakeRange(half, [number length])];
if (part1 == part2) {
[palindromes addObject:number];
}
}
}
for (int l = 0; l < [palindromes count]; l++) {
NSLog(#"%d", l);
}
}
return 0;
}
What I want my code to do, is to multiply first 1 with 1, 2, 3, ... 999 and then do the same with 2, 3, 4 and so on up until 999. For each iteration the number of the current multiplication will be stored in k. k is then converted to a NSString named number. The length and half the length of number is then stored in the variables length respectively half. The first half of the current number is then stored in the NSString part1 and the second half in the NSString part2. I then compare these two substrings and if they are equal they get added to the palindrome-array and the array is later printed out.
However, when I try to run this in Xcode it stops when it gets to the line I have marked in my code and throws me a Thread 1: signal SIGABRT-error. The output in the console looks like this:
2015-12-30 17:26:41.522 Euler4[2075:167976] *** Terminating app due to uncaught exception 'NSRangeException', reason: '-[NSTaggedPointerString substringWithRange:]: Range {1, 2} out of bounds; string length 2'
*** First throw call stack:
(
0 CoreFoundation 0x00007fff8e6a9ae2 __exceptionPreprocess + 178
1 libobjc.A.dylib 0x00007fff8a202f7e objc_exception_throw + 48
2 CoreFoundation 0x00007fff8e6a998d +[NSException raise:format:] + 205
3 CoreFoundation 0x00007fff8e644cfa -[NSTaggedPointerString substringWithRange:] + 394
4 Euler4 0x00000001000013fb main + 507
5 libdyld.dylib 0x00007fff946b85ad start + 1
)
libc++abi.dylib: terminating with uncaught exception of type NSException
(lldb)
I do get that the problem is that the range for part2 is out of bounds but I don't get how it can be that, since both the upper and lower limit should be dynamic and tailored for each and every number, right?
Any help will be greatly appreciated!

Answer 1

You should do :
NSString *part2 = [number substringWithRange:NSMakeRange(half, half)];
Since you start from half and you need to read till next half(then length).
However your code to check the palindrome is not correct.
The corrected code should be as:
NSMutableArray *palindromes = [[NSMutableArray alloc] init];
for (int i = 1; i < 1000; i++) {
for (int j = 1; j < 1000; j++) {
int k = i * j;
NSString *number = [NSString stringWithFormat:#"%d", k];
NSUInteger length = [number length];
NSUInteger half = (length / 2);
NSString *part1 = [number substringWithRange:NSMakeRange(0, half)];
NSString *part2 = [number substringWithRange:NSMakeRange(half, half)];
NSMutableString *reverseStringPart2 = [NSMutableString stringWithCapacity:[part2 length]];
//following blocks reverses the part2 and store it in reverseStringPart2
[part2 enumerateSubstringsInRange:NSMakeRange(0,[part2 length])
options:(NSStringEnumerationReverse | NSStringEnumerationByComposedCharacterSequences)
usingBlock:^(NSString *substring, NSRange substringRange, NSRange enclosingRange, BOOL *stop) {
[reverseStringPart2 appendString:substring];
}];
//note == is not used since you needed to compare two strings value not their addresses
if ([part1 isEqualToString:reverseStringPart2]) {
[palindromes addObject:number];
}
}
}
Edit:
Since you want to find the largest palindrome number formed by mulitplication of two 3-digits number. This can be done as simple as this:
for (int k = 999*999; k > 0; k--) {
NSString *number = [NSString stringWithFormat:#"%d", k];
NSUInteger length = [number length];
NSUInteger half = (length / 2);
NSString *part1 = [number substringWithRange:NSMakeRange(0, half)];
NSString *part2 = [number substringWithRange:NSMakeRange(half, half)];
NSMutableString *reverseStringPart2 = [NSMutableString stringWithCapacity:[part2 length]];
[part2 enumerateSubstringsInRange:NSMakeRange(0,[part2 length])
options:(NSStringEnumerationReverse | NSStringEnumerationByComposedCharacterSequences)
usingBlock:^(NSString *substring, NSRange substringRange, NSRange enclosingRange, BOOL *stop) {
[reverseStringPart2 appendString:substring];
}];
if ([part1 isEqualToString:reverseStringPart2]) {
NSLog(#"The largest palindrome of multiplicatin of two 3-digits number is: %#", number);
break;
}
}
*Note: You can find the above without creating a string and doing manipulations. Simply create an integer and with mathematical logic you can check if it is palindrome or not. Start from the 999*999 and move towards 1. The first one you find is the result, then break the loop.*

Answer 2

The arguments to NSMakeRange are location and length. If you set location to half, then the largest legal value for length is number.length - half. But if you change to use that, then for an odd-length string, you'll get the middle character in part2 and not in part1. You actually want to create your second NSRange as NSMakeRange(number.length - half, half).
Your next problem will be that you never find a palindrome, because you are testing for string equality with part1 == part2, but you need to test with [part1 isEqualToString:part2].
After you fix that, you'll find that your palindrome test is wrong. Your test will pass for 123123, but 123123 is not a palindrome. You need to test that [number isEqualToString: number.reversed]. (You don't have to mess with NSMakeRange at all!) But there is no reversed property on NSString, so you'll have to write your own code to reverse the string.
Incidentally, you might as well start your loops at 100 instead of at 1, because the problem says “the product of two 3-digit numbers”, and numbers in the range 1…99 are not 3-digit numbers.

Answer 3

The length member of the struct NSRange represents the length of the substring starting from location, the first member.
If the string is 1234 and half is 2 then NSRange(2, 4) is character 2 - 6, that's always out of bounds.
Calculate the remaining characters for example
NSMakeRange(half, length - half)

Answer 4

I think you might be misinterpreting NSRange and NSMakeRange. The two parameters of NSMakeRange are the start location and length of the range, not the start location and end location. If you make this change:
//NSString *part2 = [number substringWithRange:NSMakeRange(half, [number length])];//old line
NSString *part2 = [number substringWithRange:NSMakeRange(half, [number length] - half)];//new line
Then you should eliminate out of bounds errors.
As a side note, your palindrome checking logic has a few problems. You have to mirror the second part of the string before checking for equality (be careful how you do this with strings). You also have to be a little more sophisticated to handle numbers with an odd number of digits.