Check if any values have changed a certain amount - objective-c

Question

Does anyone know any efficient ways to check if any set of integers contains an integer that has changed by a certain amount.
For example I have:
int1 = 10;
int2 = 20;
int3 = 30;
And I want to know if any of these 3 integers change by 30
Now if int1 becomes 40 than the call should be triggered. At first I thought of just doing something like this.
if (abs((int1+int2+int3)-(newInt1+newInt2+newInt3)) >= 30) {
But many problems can arise from this...
False triggers (e.g. each new int value increases by 10, making the NET change greater than 30 but not necessarily any individual int greater than 30)
Untriggered reactions (e.g. one of the new integer values has increased by 50 so it should be called but then another new integer value is decreased by 50 (again, it should be called) but the net change is now zero because -50+50=0)
Does anyone have any efficient way of doing this? (Yes, I know obviously I could just check each value individually with OR statements...)
So far this is my best stab at it
if ((((abs(int1-newInt1))>=30)+((abs(int2-newInt2))>=30)+((abs(int3-newInt3))>=30))>0) {
But that's basically the same as using an OR statement (probably even takes a little longer than an OR statment.

Answer 1

I don't think that you can get any faster than that, and unless you're dealing with hundreds of millions of integers, this should not introduce a significant performance penalty.
However, you might want to be "clever". What if you somehow "checksum" the two sums? For example, multiply all the old and new numbers with the nth prime, then check if the difference of the new and old sum divided by the indexth prime is the amount you want.
int sum(int arr[], size_t n)
{
int n = 0;
for (int i = 0; i < n; i++)
n += primes[i] * arr[i];
return n;
}
int primes[3] = { 2, 3, 5 }; // or more
int olds[3] = { 10, 20, 30 };
int news[3] = { 40, 20, 30 };
int nth = 0; // check first
int change_expected = 30;
int oldsum = sum(olds, 3);
int newsum = sum(news, 3);
if ((newsum - oldsum) / primes[nth] == change_expected) {
// 1st value changed as expected
}
Note that this will take way more time and CPU cycles that your naive approach.

Answer 2

Since you are using objective-c, you can always create an object that does exactly what you want (see class below the example). The main benefit of doing it this way is that you don't have to check every integer every time one is set. You simply check each number as it is changed to see if it has changed too much.
Usage Example:
// myNumbers.confined will be true until you create a number, and THEN change it by 30 or more.
ARConfinedNumbers *myNumbers = [ARConfinedNumbers new];
[myNumbers addNumber:10];
[myNumbers addNumber:20];
[myNumbers addNumber:30];
[myNumbers replaceNumberAtIndex:0 withObject:40];
// No longer confined because we have changed 10 to 40
if (!myNumbers.confined)
NSLog(#"Not confined.");
// Reset
[myNumbers setConfined:YES];
Here is the class that I wrote to do this. Note that I used an NSArray, assuming that you were programming for iOS/MacOS but you can replace the NSArray with something else if you aren't using those classes. This should give you a great starting point though.
ARConfinedNumbers.h:
#import <Foundation/Foundation.h>
#interface ARConfinedNumbers : NSObject
// confined is true if the numbers have not been changed by more than 30.
// This can be reset by setting it to YES.
#property (nonatomic, assign) BOOL confined;
// Methods to manipulate the set of numbers
// Add more array-type-methods as needed
- (void)addNumber:(int)number;
- (void)replaceNumberAtIndex:(NSUInteger)index withObject:(int)number;
- (int)numberAtIndex:(NSUInteger)index;
- (NSUInteger)count;
#end
ARConfinedNumbers.m
#import "ARConfinedNumbers.h"
/* Private Methods */
#interface ARConfinedNumbers()
#property (nonatomic, strong) NSMutableArray *numbers;
#end
#implementation ARConfinedNumbers
- (id)init
{
self = [super init];
if (self)
{
_confined = YES;
_numbers = [NSMutableArray new];
}
return self;
}
- (void)addNumber:(int)number
{
[self.numbers addObject:#(number)];
}
- (void)replaceNumberAtIndex:(NSUInteger)index withObject:(int)number
{
if (index < self.numbers.count)
{
if (number)
{
int existingNumber = [self.numbers[index] intValue];
if (abs(existingNumber - number) >= 30)
self.confined = NO;
[self.numbers replaceObjectAtIndex:index withObject:#(number)];
}
}
}
- (int)numberAtIndex:(NSUInteger)index
{
if (index < self.numbers.count)
return [self.numbers[index] intValue];
return 0;
}
- (NSUInteger)count
{
return self.numbers.count;
}
#end