How to resolve the algorithm 100 doors step by step in the Objective-C programming language

Published on 12 May 2024 09:40 PM
#Objective-c

How to resolve the algorithm 100 doors step by step in the Objective-C programming language

Table of Contents

Problem Statement

There are 100 doors in a row that are all initially closed. You make 100 passes by the doors. The first time through, visit every door and  toggle  the door  (if the door is closed,  open it;   if it is open,  close it). The second time, only visit every 2nd door   (door #2, #4, #6, ...),   and toggle it.
The third time, visit every 3rd door   (door #3, #6, #9, ...), etc,   until you only visit the 100th door.

Answer the question:   what state are the doors in after the last pass?   Which are open, which are closed?

Alternate:
As noted in this page's   discussion page,   the only doors that remain open are those whose numbers are perfect squares. Opening only those doors is an   optimization   that may also be expressed; however, as should be obvious, this defeats the intent of comparing implementations across programming languages.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm 100 doors step by step in the Objective-C programming language

Source code in the objective-c programming language

@import Foundation;

int main(int argc, const char * argv[]) {
    @autoreleasepool {
        
        // Create a mutable array
        NSMutableArray *doorArray = [@[] mutableCopy];
        
        // Fill the doorArray with 100 closed doors
        for (NSInteger i = 0; i < 100; ++i) {
            doorArray[i] = @NO;
        }
        
        // Do the 100 passes
        for (NSInteger pass = 0; pass < 100; ++pass) {
            for (NSInteger door = pass; door < 100; door += pass+1) {
                doorArray[door] = [doorArray[door]  isEqual: @YES] ? @NO : @YES;
            }
        }
        
        // Print the results
        [doorArray enumerateObjectsUsingBlock:^(id obj, NSUInteger idx, BOOL *stop) {
            if ([obj isEqual: @YES]) {
                NSLog(@"Door number %lu is open", idx + 1);
            }
        }];
    }
}

@import Foundation;

#pragma mark - Classes
////////////////////////////////////////////////////
// Model class header - A we are using a category to add a method to MSMutableArray
@interface NSMutableArray (DoorModelExtension)

- (void)setNumberOfDoors:(NSUInteger)doors;

@end

// Model class implementation
@implementation NSMutableArray (DoorModelExtension)

- (void)setNumberOfDoors:(NSUInteger)doors {
    // Fill the doorArray with 100 closed doors
    for (NSInteger i = 0; i < doors; ++i) {
        self[i] = @NO;
    }
}
@end
////////////////////////////////////////////////////

// View class header - A simple class to handle printing our values
@interface DoorViewClass : NSObject

- (void)printResultsOfDoorTask:(NSMutableArray *)doors;

@end

// View class implementation
@implementation DoorViewClass

- (void)printResultsOfDoorTask:(NSMutableArray *)doors {

    // Print the results, using an enumeration block for easy index tracking
    [doors enumerateObjectsUsingBlock:^(id obj, NSUInteger idx, BOOL *stop) {
        if ([obj isEqual: @YES]) {
            NSLog(@"Door number %lu is open", idx + 1);
        }
    }];
}

@end
////////////////////////////////////////////////////

#pragma mark - main
// With our classes set we can use them from our controller, in this case main
int main(int argc, const char * argv[]) {
    
    // Init our classes
    NSMutableArray *doorArray = [NSMutableArray array];
    DoorViewClass *doorView = [DoorViewClass new];
    
    // Use our class category to add the doors
    [doorArray setNumberOfDoors:100];
    
    // Do the 100 passes
    for (NSUInteger pass = 0; pass < 100; ++pass) {
        for (NSUInteger door = pass; door < 100; door += pass+1) {
            doorArray[door] = [doorArray[door]  isEqual: @YES] ? @NO : @YES;
        }
    }
    
    // Print the results
    [doorView printResultsOfDoorTask:doorArray];
   
}

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