Determine if a number is perfect, abundant, or deficient based on Nicomachus' (60 - 120 CE) classification scheme for natural numbers.
The Greek mathematician Nicomachus devised a classification scheme for natural numbers, identifying each as belonging uniquely to the categories of perfect, abundant, or deficient based on their aliquot sum. The aliquot sum is defined as the sum of the factors of a number not including the number itself. For example, the aliquot sum of 15 is (1 + 3 + 5) = 9
Implement a way to determine whether a given number is perfect. Depending on your language track, you may also need to implement a way to determine whether a given number is abundant or deficient.
There are two different methods of getting set up to run the tests with Objective-C:
objc
as a test runner utility.Both are described in more detail here: http://exercism.io/languages/objective-c
When submitting an exercise, make sure your solution file is in the same directory as the test code.
The submit command will look something like:
exercism submit <path-to-exercism-workspace>/objective-c/perfect-numbers/PerfectNumbers.m
You can find the Exercism workspace by running exercism debug
and looking for the line beginning
with Workspace.
Taken from Chapter 2 of Functional Thinking by Neal Ford. http://shop.oreilly.com/product/0636920029687.do
It's possible to submit an incomplete solution so you can see how others have completed the exercise.
#import <XCTest/XCTest.h>
#if __has_include("PerfectNumbersExample.h")
# import "PerfectNumbersExample.h"
# else
# import "PerfectNumbers.h"
#endif
NS_ASSUME_NONNULL_BEGIN
@interface PerfectNumbersTest : XCTestCase
@end
@implementation PerfectNumbersTest
- (void)testPerfect {
NumberClassifier *numberClassifier = [[NumberClassifier alloc] initWithNumber:6];
NumberClassification expectedValue = NumberClassificationPerfect;
NumberClassification result = [numberClassifier classification];
XCTAssertEqual(result, expectedValue);
}
- (void)testPerfectAgain {
NumberClassifier *numberClassifier = [[NumberClassifier alloc] initWithNumber:28];
NumberClassification expectedValue = NumberClassificationPerfect;
NumberClassification result = [numberClassifier classification];
XCTAssertEqual(result, expectedValue);
}
- (void)testDeficient {
NumberClassifier *numberClassifier = [[NumberClassifier alloc] initWithNumber:13];
NumberClassification expectedValue = NumberClassificationDeficient;
NumberClassification result = [numberClassifier classification];
XCTAssertEqual(result, expectedValue);
}
- (void)testAbundant {
NumberClassifier *numberClassifier = [[NumberClassifier alloc] initWithNumber:12];
NumberClassification expectedValue = NumberClassificationAbundant;
NumberClassification result = [numberClassifier classification];
XCTAssertEqual(result, expectedValue);
}
@end
NS_ASSUME_NONNULL_END
#import "PerfectNumbers.h"
@interface NumberClassifier ()
@property (nonatomic, assign) NSInteger number;
@end
@implementation NumberClassifier
- (instancetype)initWithNumber:(NSInteger)number
{
self = [super init];
if (self) {
_number = number;
}
return self;
}
- (NumberClassification)classification
{
NSArray *divisors = [self divisors];
NSInteger sum = [[divisors valueForKeyPath:@"@sum.integerValue"] integerValue];
if (sum == self.number) {
return NumberClassificationPerfect;
}
if (sum > self.number) {
return NumberClassificationAbundant;
}
return NumberClassificationDeficient;
}
- (NSArray *)divisors
{
NSMutableArray *array = [NSMutableArray array];
for (NSInteger i = 1; i < self.number; i++) {
if ([self isDivisor:i]) {
[array addObject:@(i)];
}
}
return array;
}
- (BOOL)isDivisor:(NSInteger)number
{
return self.number % number == 0;
}
@end
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