ðŸŽ‰ Exercism Research is now launched. Help Exercism, help science and have some fun at research.exercism.io ðŸŽ‰

# KiligWY's solution

## 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.

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);
}

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

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);
}

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.h

#import <Foundation/Foundation.h>

@interface AllYourBase : NSObject

+ (NSArray *)outputDigitsForInputBase:(NSInteger)inputBase inputDigits:(NSArray *)inputDigits outputBase:(NSInteger)outputBase;

@end

### AllYourBase.m

#import "AllYourBase.h"

@implementation AllYourBase

+ (NSArray *)outputDigitsForInputBase:(NSInteger)inputBase inputDigits:(NSArray *)inputDigits outputBase:(NSInteger)outputBase {
NSAssert(inputBase > 1, @"inputBase > 1");
NSAssert(outputBase > 1, @"outputBase > 1");

NSInteger decimalNumber = 0;
for (NSInteger i = 0; i < inputDigits.count; ++i) {
NSInteger inputDigit = [inputDigits[i] integerValue];
NSAssert(inputDigit < inputBase && inputDigit >= 0, @"inputDigit > 0 && inputDigit < inputBase");
decimalNumber += (inputDigit * pow(inputBase, inputDigits.count - i - 1));
}

NSInteger index = 0;
for (; ; ++index) {
if (pow(outputBase, index) > decimalNumber) {
index--;
break;
}
}

NSMutableArray *result = [NSMutableArray array];
while (index >= 0) {
NSInteger value = pow(outputBase, index);
NSInteger digit = 0;
if (value > decimalNumber) {
value = 0;
} else {
digit = decimalNumber / value;
}
decimalNumber -= (value * digit);
index--;
}

return result;
}

@end