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to All Your Base in the Objective-C Track

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

Convert a number, represented as a sequence of digits in one base, to any other base.

Implement general base conversion. Given a number in base a, represented as a sequence of digits, convert it to base b.

Note

  • Try to implement the conversion yourself. Do not use something else to perform the conversion for you.

About Positional Notation

In positional notation, a number in base b can be understood as a linear combination of powers of b.

The number 42, in base 10, means:

(4 * 10^1) + (2 * 10^0)

The number 101010, in base 2, means:

(1 * 2^5) + (0 * 2^4) + (1 * 2^3) + (0 * 2^2) + (1 * 2^1) + (0 * 2^0)

The number 1120, in base 3, means:

(1 * 3^3) + (1 * 3^2) + (2 * 3^1) + (0 * 3^0)

I think you got the idea!

Yes. Those three numbers above are exactly the same. Congratulations!

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/all-your-base/AllYourBase.m

You can find the Exercism workspace by running exercism debug and looking for the line beginning with Workspace.

Submitting Incomplete Solutions

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

AllYourBaseTest.m

#import <XCTest/XCTest.h>

#if __has_include("AllYourBaseExample.h")
# import "AllYourBaseExample.h"
# else
# import "AllYourBase.h"
#endif

@interface AllYourBaseTest : XCTestCase

@end

@implementation AllYourBaseTest

- (void)testSingleBitOneToDecimal {
    NSArray<NSNumber *> *result = [AllYourBase outputDigitsForInputBase:2 inputDigits:@[@1] outputBase:10];
    NSArray<NSNumber *> *expected = @[@1];
    XCTAssertEqualObjects(result, expected);
}

- (void)testBinaryToSingleDecimal {
    NSArray<NSNumber *> *result = [AllYourBase outputDigitsForInputBase:2 inputDigits:@[@1, @0, @1] outputBase:10];
    NSArray<NSNumber *> *expected = @[@5];
    XCTAssertEqualObjects(result, expected);
}

- (void)testSingleDecimalToBinary {
    NSArray<NSNumber *> *result = [AllYourBase outputDigitsForInputBase:10 inputDigits:@[@5] outputBase:2];
    NSArray<NSNumber *> *expected = @[@1, @0, @1];
    XCTAssertEqualObjects(result, expected);
}

- (void)testBinaryToMultipleDecimal {
    NSArray<NSNumber *> *result = [AllYourBase outputDigitsForInputBase:2 inputDigits:@[@1, @0, @1, @0, @1, @0] outputBase:10];
    NSArray<NSNumber *> *expected = @[@4, @2];
    XCTAssertEqualObjects(result, expected);
}

- (void)testDecimalToBinary {
    NSArray<NSNumber *> *result = [AllYourBase outputDigitsForInputBase:10 inputDigits:@[@4, @2] outputBase:2];
    NSArray<NSNumber *> *expected = @[@1, @0, @1, @0, @1, @0];
    XCTAssertEqualObjects(result, expected);
}

- (void)testTrinaryToHexadecimal {
    NSArray<NSNumber *> *result = [AllYourBase outputDigitsForInputBase:3 inputDigits:@[@1, @1, @2, @0] outputBase:16];
    NSArray<NSNumber *> *expected = @[@2, @10];
    XCTAssertEqualObjects(result, expected);
}

- (void)testHexadecimalToTrinary {
    NSArray<NSNumber *> *result = [AllYourBase outputDigitsForInputBase:16 inputDigits:@[@2, @10] outputBase:3];
    NSArray<NSNumber *> *expected = @[@1, @1, @2, @0];
    XCTAssertEqualObjects(result, expected);
}

- (void)test15BitInteger {
    NSArray<NSNumber *> *result = [AllYourBase outputDigitsForInputBase:97 inputDigits:@[@3, @46, @60] outputBase:73];
    NSArray<NSNumber *> *expected = @[@6, @10, @45];
    XCTAssertEqualObjects(result, expected);
}

- (void)testEmptyList {
    NSArray<NSNumber *> *result = [AllYourBase outputDigitsForInputBase:2 inputDigits:@[] outputBase:10];
    NSArray<NSNumber *> *expected = @[];
    XCTAssertEqualObjects(result, expected);
}

- (void)testSingleZero {
    NSArray<NSNumber *> *result = [AllYourBase outputDigitsForInputBase:10 inputDigits:@[@0] outputBase:2];
    NSArray<NSNumber *> *expected = @[];
    XCTAssertEqualObjects(result, expected);
}

- (void)testMultipleZeros {
    NSArray<NSNumber *> *result = [AllYourBase outputDigitsForInputBase:10 inputDigits:@[@0, @0, @0] outputBase:2];
    NSArray<NSNumber *> *expected = @[];
    XCTAssertEqualObjects(result, expected);
}

- (void)testLeadingZeros {
    NSArray<NSNumber *> *result = [AllYourBase outputDigitsForInputBase:7 inputDigits:@[@0, @6, @0] outputBase:10];
    NSArray<NSNumber *> *expected = @[@4, @2];
    XCTAssertEqualObjects(result, expected);
}

- (void)testNegativeDigit {
    NSArray<NSNumber *> *inputDigits = @[@1, @(-1), @1, @0, @1, @0];
    XCTAssertThrows([AllYourBase outputDigitsForInputBase:2 inputDigits:inputDigits outputBase:10]);
}

- (void)testInvalidPositiveDigit {
    NSArray<NSNumber *> *inputDigits = @[@1, @2, @1, @0, @1, @0];
    XCTAssertThrows([AllYourBase outputDigitsForInputBase:2 inputDigits:inputDigits outputBase:10]);
}

- (void)testFirstBaseIsOne {
    NSArray<NSNumber *> *inputDigits = @[];
    XCTAssertThrows([AllYourBase outputDigitsForInputBase:1 inputDigits:inputDigits outputBase:10]);
}

- (void)testSecondBaseIsOne {
    NSArray<NSNumber *> *inputDigits = @[@1, @0, @1, @0, @1, @0];
    XCTAssertThrows([AllYourBase outputDigitsForInputBase:2 inputDigits:inputDigits outputBase:1]);
}

- (void)testFirstBaseIsZero {
    NSArray<NSNumber *> *inputDigits = @[];
    XCTAssertThrows([AllYourBase outputDigitsForInputBase:0 inputDigits:inputDigits outputBase:10]);
}

- (void)testSecondBaseIsZero {
    NSArray<NSNumber *> *inputDigits = @[@7];
    XCTAssertThrows([AllYourBase outputDigitsForInputBase:10 inputDigits:inputDigits outputBase:0]);
}

- (void)testFirstBaseIsNegative {
    NSArray<NSNumber *> *inputDigits = @[@1];
    XCTAssertThrows([AllYourBase outputDigitsForInputBase:-2 inputDigits:inputDigits outputBase:10]);
}

- (void)testSecondBaseIsNegative {
    NSArray<NSNumber *> *inputDigits = @[@1];
    XCTAssertThrows([AllYourBase outputDigitsForInputBase:2 inputDigits:inputDigits outputBase:-7]);
}

@end
//
//  AllYourBase.m
//  AllYourBase
//
//  Created by Vui Nguyen on 1/4/17.
//  Copyright © 2017 Sunfish Empire. All rights reserved.
//

#import "AllYourBase.h"

@implementation AllYourBase

typedef NS_ENUM(NSInteger, AllYourBaseErrorCodes)
{
    negativeDigit,
    invalidPositiveDigit,
    invalidInputBase,
    invalidOutputBase,
    allZeroInput
};

// outputDigits is the function that the test file "AllYourBaseTest.m" calls, to
// return the array of digits given the following: input base, input digits, and output base
+(NSArray*) outputDigitsForInputBase: (int)inputBase inputDigits:(NSArray*)inputDigits outputBase:(int)outputBase
{
    // array of outputDigits to return
    NSMutableArray * outputDigits = [[NSMutableArray alloc] init];
    
    // a single digit in outputDigits
    int newDigit = 0;
    
    // this will be set to the original value represented by inputDigits and later
    // used in calculations to getoutputDigits
    double remainder = 0.0;
    
    // Declare our error and exception variables
    NSError * error = nil;
    NSException * exception = nil;
    
    // inputBase must be greater than 1
    if (inputBase < 2)
    {
        exception = [[NSException alloc] initWithName:@"InvalidInputBaseException" reason:@"Encountered Invalid Input Base" userInfo:nil];
        @throw exception;
    }
    
    // outputBase must be greater than 1
    if (outputBase < 2)
    {
        exception = [[NSException alloc] initWithName:@"InvalidOutputBaseException" reason:@"Encountered Invalid Output Base" userInfo:nil];
        @throw exception;
    }
    
    // If we have empty inputDigits, let's handle that
    if (inputDigits.count == 0)
    {
        NSLog(@"outputDigits are: @%@", outputDigits);
        return outputDigits;
    }
    
    // set remainder to our original value represented by inputDigits
    remainder = [self calcValueWithBaseDigits:inputBase inputDigits:inputDigits error:&error];
    
    // handle all errors returned by calcValueWithBaseDigits
    if (error)
    {
        if (error.code == allZeroInput)
        {
            NSLog(@"zero input digits, outputDigits are: @%@", outputDigits);
            return outputDigits; // return empty outputDigits as required by AllYourBaseTest.m
        }
        else if (error.code == negativeDigit)
        {
            exception = [[NSException alloc] initWithName:@"NegativeDigitException" reason:@"Encountered Negative Digit" userInfo:nil];
            @throw exception;
        }
        else if (error.code == invalidPositiveDigit)
        {
            exception = [[NSException alloc] initWithName:@"InvalidPositiveDigitException" reason:@"Encountered Invalid Positive Digit" userInfo:nil];
            @throw exception;
        }
    }

    int power = 0;
    
    // Calculate the digit that we will be starting at, or largest power
    // e.g. The largest "power" necessary to represent a value of 4792 (decimal) is 10^3
    // (the power is 3).
    // The floor function rounds the calculation down
    while ( floor( ( remainder / pow( outputBase, (power+1) ) ) )  > 0 )
    {
        power = power + 1;
    }
    
    double powerValue = 0.0;
    
    // Calculate the individual digits needed to represent the remainder returned by
    // calcValueWithBaseDigits, and append them to outputDigits
    // for example, if the remainder value is 4792, the first power we start with is 3
    while (power >= 0)
    {
        // calculate powerValue, e.g. 10^3 (1000) is the first powerValue in our example
        powerValue = pow(outputBase, power);
        
        // newDigit is the leftmost outputDigit remaining: the number 4 in our example
        // (4 * 10^3 = 4000)
        newDigit = (remainder / powerValue);
        
        // fmod acts like a modulus function to move the calculation to the next-right outputDigit
        // remainder in our example would be 792
        remainder = fmod(remainder, powerValue);
        
        // you have to go through all this trouble just to get "newDigit" added to outputDigits
        // newDigit is 4 in our example
        [outputDigits addObject:[NSNumber numberWithInteger:newDigit]];
        
        // decrement power.  It will go to 2 in our example
        power = power - 1;
    }
    
    NSLog(@"outputDigits: @%@", outputDigits);
    return outputDigits;
}

// This is a "helper" function called by the outputDigits function. Its purpose is to
// calculate the value of the number given by inputDigits. The value can then be
// represented in the desired base by outputDigits.
+(double) calcValueWithBaseDigits: (int)inputBase inputDigits:(NSArray*)inputDigits error:(NSError **)error
{
    // Error handling stuff
    NSString * errorDomain = @"com.sunfishempire.allyourbase.errordomain";
    NSInteger errorCode;
    NSDictionary *errorUserInfo = nil;
    
    // the "value" variable has to be declared a Double so we can do the
    // calculation further down with the pow() function, which returns a Double
    double value = 0.0;
    NSUInteger backwardsIndex = inputDigits.count - 1;
    
    // We need to reverse the digits in order to calculate the value correctly.
    // I decided to create a reverseDigits array to make this code
    // easier to follow rather than walking the array backwards.
    // This also allows us to check for most of the possible errors
    // before calling the pow() function, which is an expensive operation.
    // Now, let's initialize the array to hold the digits reversed.
    // For now, it's holding the same elements as inputDigits, but we'll change that shortly.
    NSMutableArray * reverseDigits = [NSMutableArray arrayWithArray:inputDigits];
    
    NSEnumerator * inputDigitsEnumerator = [inputDigits objectEnumerator];
    NSNumber * digit;
    int digitSum = 0;
    
    // Let's do most of our error checking here before we waste time with calculations
    // Now, let's populate the reverseDigits array
    while (digit = [inputDigitsEnumerator nextObject])
    {
        // test for existence of a negative digit in inputDigits
        if (digit.intValue < 0)
        {
            errorCode = negativeDigit;
            *error = [[NSError alloc] initWithDomain:errorDomain code:errorCode userInfo:errorUserInfo];
            return value;
        }
        
        // test for a digit that's too big for the input base (i.e., can't have a '2' digit for base 2!)
        if (digit.intValue > (inputBase-1))
        {
            errorCode = invalidPositiveDigit;
            *error = [[NSError alloc] initWithDomain:errorDomain code:errorCode userInfo:errorUserInfo];
            return value;
        }
        
        // digitSum is needed to figure out if inputDigits array is all zeros
        digitSum = digitSum + [digit intValue];
        // insert digit n of inputDigits into the <size>-n slot of reverseDigits array
        reverseDigits[backwardsIndex] = digit;
        backwardsIndex = backwardsIndex - 1;
    }
    
    // test if the inputDigits array is all zeros.
    if (digitSum == 0)
    {
        errorCode = allZeroInput;
        *error = [[NSError alloc] initWithDomain:errorDomain code:errorCode userInfo:errorUserInfo];
        return value;
    }
    
    NSEnumerator * reverseDigitsEnumerator = [reverseDigits objectEnumerator];
    int index = 0;
    
    // calculating the value of the input number represented by inputDigits
    // Using 62 (decimal) as an example,
    while (digit = [reverseDigitsEnumerator nextObject])
    {
        // cast the integer digit as a double for the pow() function
        // in our example, the smallest digit is 2
        double digitDouble = [digit doubleValue];
        // The value is the existing value (0 to begin with), plus the digit (2) times
        // the inputBase (10) to the index power (0): 2 * 10^0 = 2
        value = value + (digitDouble * ( pow( (inputBase), (index) ) ));
        // increment the index (and thus the power) for the next iteration
        index = index + 1;
    }
    
    return value;
}

@end

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