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stevenhuey's solution

to Perfect Numbers in the Objective-C Track

Published at Jul 13 2018 · 0 comments
Instructions
Test suite
Solution

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

  • Perfect: aliquot sum = number
    • 6 is a perfect number because (1 + 2 + 3) = 6
    • 28 is a perfect number because (1 + 2 + 4 + 7 + 14) = 28
  • Abundant: aliquot sum > number
    • 12 is an abundant number because (1 + 2 + 3 + 4 + 6) = 16
    • 24 is an abundant number because (1 + 2 + 3 + 4 + 6 + 8 + 12) = 36
  • Deficient: aliquot sum < number
    • 8 is a deficient number because (1 + 2 + 4) = 7
    • Prime numbers are deficient

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.

Setup

There are two different methods of getting set up to run the tests with Objective-C:

  • Create an Xcode project with a test target which will run the tests.
  • Use the ruby gem objc as a test runner utility.

Both are described in more detail here: http://exercism.io/languages/objective-c

Submitting Exercises

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.

Source

Taken from Chapter 2 of Functional Thinking by Neal Ford. http://shop.oreilly.com/product/0636920029687.do

Submitting Incomplete Solutions

It's possible to submit an incomplete solution so you can see how others have completed the exercise.

PerfectNumbersTest.m

#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
//
//  PerfectNumbers.m
//  Perfect Numbers
//
//  Created by Steven Huey on 6/17/16.
//  Copyright © 2016 Steve Huey. All rights reserved.
//

#import "PerfectNumbers.h"

@interface NumberClassifier ()
@property (assign) NSInteger numberToClassify;

- (NSArray*)factors;
- (NSInteger)sumOfFactors;
@end

@implementation NumberClassifier
- (instancetype)initWithNumber:(NSInteger)number
{
   self = [super init];
   
   if (self)
   {
      _numberToClassify = number;
   }
   
   return self;
}

- (NumberClassification)classification
{
   NSInteger sum = [self sumOfFactors];
   
   if (sum == self.numberToClassify)
   {
      return NumberClassificationPerfect;
   }
   else if (sum > self.numberToClassify)
   {
      return NumberClassificationAbundant;
   }
   else
   {
      return NumberClassificationDeficient;
   }
}

- (NSArray*)factors
{
   NSMutableArray* factors = [[NSMutableArray alloc] initWithCapacity:0];
   
   for (NSInteger i = 1; i <= self.numberToClassify; i++)
   {
      if (0 == self.numberToClassify % i)
      {
         [factors addObject:@(i)];
      }
   }
   
   return [NSArray arrayWithArray:factors];
}

- (NSInteger)sumOfFactors
{
   NSArray* factors = [self factors];
   NSInteger numberOfFactorsToSum = [factors count] - 1;
   NSRange range = NSMakeRange(0, numberOfFactorsToSum);
   
   __block NSInteger sum = 0;
   NSArray* factorsToSum = [factors subarrayWithRange:range];
   
   [factorsToSum enumerateObjectsUsingBlock:^(id obj, NSUInteger idx, BOOL * stop) {
      sum += [obj integerValue];
   }];
   
   return sum;
}
@end

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