There have been many questions but i can't seem to find the why in the answers. It's usually: no, replace this with this or this should work.
My task is to create a program that asks the user to input a 3 digit positive integer (decimal) that converts it to octal.
For example, on paper: To convert the number 112 to octal. (8 is the base number for octal.)
These are the steps you would take:
112 / 8 = 14 remainder = 0
14 / 8 = 1 remainder = 6
1 / 8 = 0 remainder = 1
Remainder from bottom to up is the octal number that represents 112 in decimal.
So the octal number for 112 is 160.
I found the following program on the internet but i don't understand it fully.
The comments in the program are mine. Could anyone explain it to me please?
//declaration and initialization of variables but why is there an array?
int decimalNumber, quotient, i = 1, j;
int[] octalNumber = new int[100];
//input
Console.WriteLine("Enter a Decimal Number :");
decimalNumber = int.Parse(Console.ReadLine());
quotient = decimalNumber;
//as long as quotient is not equal to 0, statement will run
while (quotient != 0)
{
//this is how the remainder is calculated but it is then put in an array + 1, i don't understand this.
octalNumber[i++] = quotient % 8;
//divide the number given by the user with the octal base number
quotient = quotient / 8;
}
Console.Write("Equivalent Octal Number is ");
//i don't understand the code below here aswell.
for (j = i - 1; j > 0; j--)
Console.Write(octalNumber[j]);
Console.Read();
Any help is truly appreciated.
The first thing to understand is: this is a terrible way to solve this problem. The code is full of odd choices; it looks like someone took a bad C solution of this problem and translated it to C# without applying careful thought or using good practices. If you are trying to learn how to understand crappy code you find on the internet, this is a great example. If you are trying to learn how to design good code, this is a great example of what not to do.
//declaration and initialization of variables but why is there an array?
There's an array because we wish to store all the octal digits, and an array is a convenient mechanism for storing a number of data of the same type.
But we could ask some more pertinent questions here:
Why of size 100? It's not wrong, but that's enormously larger than necessary. What thought process led to 100 being chosen? Why wasn't that thought process documented anywhere?
Why an array of int? We're outputting text, which is a sequence of chars. It would seem more natural to have a bunch of chars.
Why an array? Since we are building a first-in-last-out data structure, a stack seems more appropriate. Or why not simply accumulate a string? That's inefficient if the string is large, but an octal string from a 32 bit integer is never large!
Why does the program produce output to the console? Surely a better factored program would have a method that takes an int and returns an octal string, which can then be printed.
Why do some of the variables have descriptive names and some have undescriptive names? Is the author of the code deliberately trying to confuse the reader? Or did they simply not think about it very carefully?
Why does i - apparently the current index into the array -- start at one?! This is simply bizarre. Arrays start at zero in C#.
What happens if you type in a negative number? Try it!
What happens if you type in zero?
We then go on to:
decimalNumber = int.Parse(Console.ReadLine());
This code presumes that the typed-in text is a legal integer, which is not guaranteed. So this program can crash. TryParse should be used, and the failure mode should be handled.
// this is how the remainder is calculated but it is
// then put in an array + 1, i don't understand this.
octalNumber[i++] = quotient % 8;
The author of the code thinks they are being clever. This is too much cleverness. Rewrite the code in your head to how it should have been implemented in the first place. First, rename i to currentIndex. Next, produce one side effect per statement, not two:
while (quotient != 0)
{
octalNumber[currentIndex] = quotient % 8;
currentIndex += 1;
quotient = quotient / 8;
}
Now it should be clear what is going on.
// I don't understand the code below here as well.
for (j = i - 1; j > 0; j--)
Console.Write(octalNumber[j]);
Do a little example. Suppose the number is 14, which is 16 in octal. First time through the loop we put 6 in slot 1. Next time through, we put 1 in slot 2. So the array is {0, 6, 1, 0, 0, 0, 0 ... } and i is 3. We wish to output 16. So we loop j from i-1 to 1, and print out 1 then 6.
So, exercise for you: write this program again, this time using the conventions of a well-designed C# program. Put your attempt on the code review site and people will be happy to give you tips on how to improve it.
This is already built into .NET, Convert.ToString already does this.
In your code, just after you have decimalNumber = int.Parse(...) you can do this:
Console.WriteLine(Convert.ToString(decimalNumber, 8));
Console.Read();
and then remove the rest of the code.
Now, if you're not asking how to do octal conversion in .NET but actually how that code works, here's how it works:
This loop does the heavy lifting:
1 while (quotient != 0)
{
//this is how the remainder is calculated but it is then put in an array + 1, i don't understand this.
2 octalNumber[i++] = quotient % 8;
//divide the number given by the user with the octal base number
3 quotient = quotient / 8;
}
I added some numbers to the lines to make it easier writing a description.
Basically, the loop does this (lines above correspond to points below).
As long as we have a number to convert (ie. we're still not done), loop.
Figure out the least significant digit, this is the remainder after dividing by 8, which is handled by the remainder operator, %, store this digit into the array in the next position.
Divide by 8 to get rid of that least significant digit and move all the other digits one up
Then loop back.
However, since we essentially found all the digits from the rightmost side towards the left, the loop at the end writes them back out in their opposite order.
As an exercise to the reader, try to figure out how the code in the question behaves if you:
Input a negative number
Input 0
(hint, it doesn't behave correctly but Convert.ToString does)
An array is used because they are calculating each digit every interation of the while loop. (e.g.) {0, 6, 1}
The last part of the program is printing each digit out, starting with the last item in the array and moving to the first. in this case it would print out:
160
Related
I'm trying to solve a simple question on leetcode.com (https://leetcode.com/problems/number-of-1-bits/) and I encounter a strange behavior which is probably my lack of understanding...
My solution to the question in the link is the following:
public int HammingWeight(uint n) {
int sum = 0;
while (n > 0) {
uint t = n % 10;
sum += t == 0 ? 0 : 1;
n /= 10;
}
return sum;
}
My solution was to isolate each number and if it's one increase the sum. When I ran this on my PC it worked (yes - I know it's not the optimal solution and there are more elegant solutions considering it's binary representation).
But when I tried running in the leetcode editor it returned a wrong answer for the following input (00000000000000000000000000001011).
No real easy way to debug other then printing to the console so I printed the value of n when entering the method and got the result of 11 instead of 1011 - on my PC I got 11. If I take a different solution - one that uses bitwise right shift or calculating mod by 2 then it works even when the printed n is still 11. And I would have expected those solutions to fail as well considering that n is "wrong" (different from my PC and the site as described).
Am I missing some knowledge regarding the representation of uint? Or binary number in a uint variable?
Your code appears to be processing it as base 10 (decimal), but hamming weight is about base 2 (i.e. binary). So: instead if doing % 10 and /= 10, you should be looking at % 2 and /= 2.
As for what uint looks like as binary: essentially like this, but ... the CPU is allowed to lie about where each of the octets actually is (aka "endianness"). The good news is: it doesn't usually expose that lie to you unless you cheat and look under the covers by looking at raw memory. As long as you use regular operators (include bitwise operators): the lie will remain undiscovered.
Side note: for binary work that is about checking a bit and shuffling the data down, & 1 and >> 1 would usually be preferable to % 2 and / 2. But as canton7 notes: there are also inbuilt operations for this specific scenario which uses the CPU intrinsic instruction when possible (however: using the built-in function doesn't help you increase your understanding!).
This Kata has a poor writing, in the examples the Inputs are printed in binary representation while the Outputs are in printed in decimal representation. And there is no clues to help understand that.
00000000000000000000000000001011b is 11 (in decimal, 8 + 2 + 1). That is why you get 11 as input for the first test case.
There is no numbers made of 0s and 1s in base 10 you have to decode as base 2 stuff here.
To solve the Kata, you just need to work in base 2 as you succeed to do and like #MarcGravell explained.
Please check below code, it will work for you.
Its very simple way to solve.
var result = 0;
for(var i = 0; i < 32; i++)
{
if ((n & 1) == 1) result++;
n = n >> 1;
}
return result;
I know you can convert the Int to a string and get the digit at position x using the indexer as if it was a char array, but this conversion becomes a bit of an overhead when you're dealing with multiple large numbers.
Is there a way to retrieve a digit at position x without converting the number to a string?
EDIT:
Thank you all, I will benchmark the proposed methods and check if it is any better than converting to a string. Thread will stay unanswered for 24h in case anyone has better ideas.
EDIT 2:
After some simple tests on ulong numbers, I have concluded that converting to strings and extracting the digit can be up to 50% slower compared to the methods provided below, see approved answer.
You could do something like this:
int ith_digit(int n, int i) {
return (int) (n / pow(10, i)) % 10;
}
We can get the ith digit by reducing the number down to a point where that digit we want becomes in the one's place, example:
Let's say you wanted the third digit in 12345, then by reducing it to 123 (by dividing it by 10 i number of times) we can then take the remainder of that number divided by ten to get the last digit, which is the digit we wanted.
I was trying to recreate my C++ factor program from a few years ago in my new language C#. All I could remember is that it possibly involved a modulo, and possibly didn't. I knew that it involved at least one for and if statement. However, when I started trying to recreate it I kept getting nothing near what should be. I thought it had something to do with me not understanding loops, but it turns out I understand loops just fine. What I don't understand is how to use the modulo when performing math operations.
for instance what am I doing when I say something like:
(ignore that it might not actually work, it's just an example)
if(12 % 2 == 0)
{
Console.WriteLine("I don't understand.");
}
This kind of thing I don't quite have a grasp of yet. I realize that it is taking the remainder, and that's all I can grasp, not how it's actually used in real programming. I managed to get my factor program to work in C# after a bit of thinking and tinkering, it again doesn't mean I understand this operator or its uses. I no longer have access to the old C++ file.
The % (modulo) operator yields the remainder from the division. In your example the remainder is equal to 0 and the if evaluates to true (0 == 0). A classic example is when it's used to see if a number is even or not.
if (number % 2 == 0) {
// even
} else {
// odd
}
Think of modulo like a circle with a pointer (spinner), easiest example is a clock.
Notice how at the top it is zero.
The modulo function maps any value to one of those values on the spinner, think of the value to the left of the % as the number of steps around the spinner, and the second value as the number of total steps in the spinner, so we have the following.
0 % 12 = 0
1 % 12 = 1
12 % 12 = 0
13 % 12 = 1
We always start at 0.
So if we go 0 steps around a 12 step spinner we are still at 0, if we go 1 step from zero we are on 1, if we go 12 steps we are back at 0. If we go 13 we go all the way around and end at 1 again.
I hope this helps you visualize it.
It helps when you are using structures like an array, and you want to cycle through them. Imagine you have an array of the days of the week, 7 elements (mon-sunday). You want to always display the day 3 days from the current day. well Today is tuesday, so the array element is days[1], if we want to get the day 3 days from now we do days[1+3]; now this is alright, but what if we are at saturday (days[5]) and want to get 3 days from there? well we have days[5+3] which is an index out of bounds error as our array has only 7 elements (max index of 6) and we tried to access the 8th element.
However, knowing what you know about modulos and spinners now you can do the following:
string threeDaysFromNow = days[(currentDay + 3)%7]; When it goes over the bounds of the array, it wraps around and starts at the beginning again. There are many applications for this. Just remember the visualization of spinners, that is when it clicked in my head.
The modulo operator % returns the remainder of a division operation. For example, where 13 / 5 = 2, 13 % 5 = 3 (using integer math).
It's a common tactic to check a value against % 2 to see if it is even. If it is even, the remainder will be 0, otherwise it will be 1.
As for your specific use of it, you are doing 12 % 2 which is not only 0, but will always be 0. That will always make the if condition 12 % 2 == 0 true, which makes the if rather redundant.
as mentioned, it's commonly used for checking even/odd but also can use it to iterate loops at intervals, or split files into mod chunks. i personally use mod for clock face type problems as my data often navigates a circle.
the register is in mod for example an 8 bit register rolls over at 2^8 so so can force compliance into a register size var = mod(var, 256)
and the last thing i know about mod is that it is used in checksum and random number generation, but i haven't gone into the why for those. at all
An example where you could use this is in indexing arrays in certain for loops. For example, take the simple equation that defines the new pixel value of a resampled image using bicubic interpolation:
where
Don't worry what bicubic interpolation exactly is for the moment, we're just concerned about executing what seems to be two simple for loops: one for index i and one for index j. Note that the vector 'a' is 16 numbers long.
A simple for loop someone would try could be:
int n= 0;
for(int i = 0; i < 4; ++i)
{
for(int j = 0; i < 4; ++j)
{
pxy += a[n] * pow(x,i) * pow(y,j); // p(x,y)
n++; // n = 15 when finished
}
}
Or you could do it in one for loop:
for(int i = 0; i < 16; ++i)
{
int i_new = floor(i / 4.0); // i_new provides indices 0-3 incrementing every 4 iterations of loop
int j_new = i % 4; // j_new is reset to 0 when i is a multiple of 4
pxy += a[i] * pow(x,i_new) * pow(y,j_new); // p(x,y)
}
Printing i_new and j_new in the loop:
i_new j_new
0 0
0 1
0 2
0 3
1 0
1 1
1 2
1 3
2 0
2 1
2 2
2 3
3 0
3 1
3 2
3 3
As you can see, % can be very useful.
I may be using Math for evil... But, in a number written as 0.7000123
I need to get the "123" - That is, I need to extract the last 3 digits in the decimal portion of a number. The least significant digits, when the first few are what most people require.
Examples:
0.7500123 -> 123
0.5150111 -> 111
It always starts from digit 5. And yes, I'm storing secret information inside this number, in the part of the decimal that will not affect how the number is used - which is the potentially evil part. But it's still the best way around a certain problem I have.
I'm wondering whether math or string manipulation is the least dodgy way of doing this.
Performance is not an issue, at all, since I'm calling it once.
Can anyone see an easy mathematical way of doing this? eg A combination of Math functions (I've missed) in .NET?
It's a strange request to be sure. But one way to get an int value of the last 3 digits is like so:
int x = (int)((yourNumber * 10000000) % 1000);
I'm going to guess there's a better way to get the information you're looking for that's cleaner, but given what you've asked for, this should work.
First Convert Your number into the String.
string s = num.ToString();
string s1 = s.Substring(s.Length - 3, 3);
Now s1 Contains Last 3 Digits Of the Number
Using modulo will get you the last 3 digits:
var d = 0.7000123m;
d = d * 10000000 % 1000;
d will now hold the value 123.
Try this:
string value= "0.1234567";
string lastthreedigit= value.Substring(value.Length - 3);
I'm working on a simple game and I have the requirement of taking a word or phrase such as "hello world" and converting it to a series of numbers.
The criteria is:
Numbers need to be distinct
Need ability to configure maximum sequence of numbers. IE 10 numbers total.
Need ability to configure max range for each number in sequence.
Must be deterministic, that is we should get the same sequence everytime for the same input phrase.
I've tried breaking down the problem like so:
Convert characters to ASCII number code: "hello world" = 104 101 108 108 111 32 119 111 114 108 100
Remove everyother number until we satisfy total numbers (10 in this case)
Foreach number if number > max number then divide by 2 until number <= max number
If any numbers are duplicated increase or decrease the first occurence until satisfied. (This could cause a problem as you could create a duplicate by solving another duplicate)
Is there a better way of doing this or am I on the right track? As stated above I think I may run into issues with removing distinction.
If you want to limit the size of the output series - then this is impossible.
Proof:
Assume your output is a series of size k, each of range r <= M for some predefined M, then there are at most k*M possible outputs.
However, there are infinite number of inputs, and specifically there are k*M+1 different inputs.
From pigeonhole principle (where the inputs are the pigeons and the outputs are the pigeonholes) - there are 2 pigeons (inputs) in one pigeonhole (output) - so the requirement cannot be achieved.
Original answer, provides workaround without limiting the size of the output series:
You can use prime numbers, let p1,p2,... be the series of prime numbers.
Then, convert the string into series of numbers using number[i] = ascii(char[i]) * p_i
The range of each character is obviously then [0,255 * p_i]
Since for each i,j such that i != j -> p_i * x != p_j * y (for each x,y) - you get uniqueness. However, this is mainly nice theoretically as the generated numbers might grow quickly, and for practical implementation you are going to need some big number library such as java's BigInteger (cannot recall the C# equivalent)
Another possible solution (with the same relaxation of no series limitation) is:
number[i] = ascii(char[i]) + 256*(i-1)
In here the range for number[i] is [256*(i-1),256*i), and elements are still distinct.
Mathematically, it is theoretically possible to do what you want, but you won't be able to do it in C#:
If your outputs are required to be distinct, then you cannot lose any information after encoding the string using ASCII values. This means that if you limit your output size to n numbers then the numbers will have to include all information from the encoding.
So for your example
"Hello World" -> 104 101 108 108 111 32 119 111 114 108 100
you would have to preserve the meaning of each of those numbers. The simplest way to do this would just 0 pad your numbers to three digits and concatenate them together into one large number...making your result 104101108111032119111114108100 for max numbers = 1.
(You can see where the issue becomes, for arbitrary length input you need very large numbers.) So certainly it is possible to encode any arbitrary length string input to n numbers, but the numbers will become exceedingly large.
If by "numbers" you meant digits, then no you cannot have distinct outputs, as #amit explained in his example with the pidgeonhole principle.
Let's eliminate your criteria as easily as possible.
For distinct, deterministic, just use a hash code. (Hash actually isn't guaranteed to be distinct, but is highly likely to be):
string s = "hello world";
uint hash = Convert.ToUInt32(s.GetHashCode());
Note that I converted the signed int returned from GetHashCode to unsigned, to avoid the chance of having a '-' appear.
Then, for your max range per number, just convert the base.
That leaves you with the maximum sequence criteria. Without understanding your requirements better, all I can propose is truncate if necessary:
hash.toString().Substring(0, size)
Truncating leaves a chance that you'll no longer be distinct, but that must be built in as acceptable to your requirements? As amit explains in another answer, you can't have infinite input and non-infinite output.
Ok, so in one comment you've said that this is just to pick lottery numbers. In that case, you could do something like this:
public static List<int> GenNumbers(String input, int count, int maxNum)
{
List<int> ret = new List<int>();
Random r = new Random(input.GetHashCode());
for (int i = 0; i < count; ++i)
{
int next = r.Next(maxNum - i);
foreach (int picked in ret.OrderBy(x => x))
{
if (picked <= next)
++next;
else
break;
}
ret.Add(next);
}
return ret;
}
The idea is to seed a random number generator with the hash code of the String. The rest of that is just picking numbers without replacement. I'm sure it could be written more efficiently - an alternative is to generate all maxNum numbers and shuffle the first count. Warning, untested.
I know newer versions of the .Net runtime use a random String hash code algorithm (so results will differ between runs), but I believe this is opt-in. Writing your own hash algorithm is an option.