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I am making a program for nth Fibonacci number. I made the following program using recursion and memoization.
The main problem is that the value of n can go up to 10000 which means that the Fibonacci number of 10000 would be more than 2000 digit long.
With a little bit of googling, I found that i could use arrays and store every digit of the solution in an element of the array but I am still not able to figure out how to implement this approach with my program.
#include<iostream>
using namespace std;
long long int memo[101000];
long long int n;
long long int fib(long long int n)
{
if(n==1 || n==2)
return 1;
if(memo[n]!=0)
return memo[n];
return memo[n] = fib(n-1) + fib(n-2);
}
int main()
{
cin>>n;
long long int ans = fib(n);
cout<<ans;
}
How do I implement that approach or if there is another method that can be used to achieve such large values?
One thing that I think should be pointed out is there's other ways to implement fib that are much easier for something like C++ to compute
consider the following pseudo code
function fib (n) {
let a = 0, b = 1, _;
while (n > 0) {
_ = a;
a = b;
b = b + _;
n = n - 1;
}
return a;
}
This doesn't require memoisation and you don't have to be concerned about blowing up your stack with too many recursive calls. Recursion is a really powerful looping construct but it's one of those fubu things that's best left to langs like Lisp, Scheme, Kotlin, Lua (and a few others) that support it so elegantly.
That's not to say tail call elimination is impossible in C++, but unless you're doing something to optimise/compile for it explicitly, I'm doubtful that whatever compiler you're using would support it by default.
As for computing the exceptionally large numbers, you'll have to either get creative doing adding The Hard Way or rely upon an arbitrary precision arithmetic library like GMP. I'm sure there's other libs for this too.
Adding The Hard Way™
Remember how you used to add big numbers when you were a little tater tot, fresh off the aluminum foil?
5-year-old math
1259601512351095520986368
+ 50695640938240596831104
---------------------------
?
Well you gotta add each column, right to left. And when a column overflows into the double digits, remember to carry that 1 over to the next column.
... <-001
1259601512351095520986368
+ 50695640938240596831104
---------------------------
... <-472
The 10,000th fibonacci number is thousands of digits long, so there's no way that's going to fit in any integer C++ provides out of the box. So without relying upon a library, you could use a string or an array of single-digit numbers. To output the final number, you'll have to convert it to a string tho.
(woflram alpha: fibonacci 10000)
Doing it this way, you'll perform a couple million single-digit additions; it might take a while, but it should be a breeze for any modern computer to handle. Time to get to work !
Here's an example in of a Bignum module in JavaScript
const Bignum =
{ fromInt: (n = 0) =>
n < 10
? [ n ]
: [ n % 10, ...Bignum.fromInt (n / 10 >> 0) ]
, fromString: (s = "0") =>
Array.from (s, Number) .reverse ()
, toString: (b) =>
b .reverse () .join ("")
, add: (b1, b2) =>
{
const len = Math.max (b1.length, b2.length)
let answer = []
let carry = 0
for (let i = 0; i < len; i = i + 1) {
const x = b1[i] || 0
const y = b2[i] || 0
const sum = x + y + carry
answer.push (sum % 10)
carry = sum / 10 >> 0
}
if (carry > 0) answer.push (carry)
return answer
}
}
We can verify that the Wolfram Alpha answer above is correct
const { fromInt, toString, add } =
Bignum
const bigfib = (n = 0) =>
{
let a = fromInt (0)
let b = fromInt (1)
let _
while (n > 0) {
_ = a
a = b
b = add (b, _)
n = n - 1
}
return toString (a)
}
bigfib (10000)
// "336447 ... 366875"
Expand the program below to run it in your browser
const Bignum =
{ fromInt: (n = 0) =>
n < 10
? [ n ]
: [ n % 10, ...Bignum.fromInt (n / 10 >> 0) ]
, fromString: (s = "0") =>
Array.from (s) .reverse ()
, toString: (b) =>
b .reverse () .join ("")
, add: (b1, b2) =>
{
const len = Math.max (b1.length, b2.length)
let answer = []
let carry = 0
for (let i = 0; i < len; i = i + 1) {
const x = b1[i] || 0
const y = b2[i] || 0
const sum = x + y + carry
answer.push (sum % 10)
carry = sum / 10 >> 0
}
if (carry > 0) answer.push (carry)
return answer
}
}
const { fromInt, toString, add } =
Bignum
const bigfib = (n = 0) =>
{
let a = fromInt (0)
let b = fromInt (1)
let _
while (n > 0) {
_ = a
a = b
b = add (b, _)
n = n - 1
}
return toString (a)
}
console.log (bigfib (10000))
Try not to use recursion for a simple problem like fibonacci. And if you'll only use it once, don't use an array to store all results. An array of 2 elements containing the 2 previous fibonacci numbers will be enough. In each step, you then only have to sum up those 2 numbers. How can you save 2 consecutive fibonacci numbers? Well, you know that when you have 2 consecutive integers one is even and one is odd. So you can use that property to know where to get/place a fibonacci number: for fib(i), if i is even (i%2 is 0) place it in the first element of the array (index 0), else (i%2 is then 1) place it in the second element(index 1). Why can you just place it there? Well when you're calculating fib(i), the value that is on the place fib(i) should go is fib(i-2) (because (i-2)%2 is the same as i%2). But you won't need fib(i-2) any more: fib(i+1) only needs fib(i-1)(that's still in the array) and fib(i)(that just got inserted in the array).
So you could replace the recursion calls with a for loop like this:
int fibonacci(int n){
if( n <= 0){
return 0;
}
int previous[] = {0, 1}; // start with fib(0) and fib(1)
for(int i = 2; i <= n; ++i){
// modulo can be implemented with bit operations(much faster): i % 2 = i & 1
previous[i&1] += previous[(i-1)&1]; //shorter way to say: previous[i&1] = previous[i&1] + previous[(i-1)&1]
}
//Result is in previous[n&1]
return previous[n&1];
}
Recursion is actually discommanded while programming because of the time(function calls) and ressources(stack) it consumes. So each time you use recursion, try to replace it with a loop and a stack with simple pop/push operations if needed to save the "current position" (in c++ one can use a vector). In the case of the fibonacci, the stack isn't even needed but if you are iterating over a tree datastructure for example you'll need a stack (depends on the implementation though). As I was looking for my solution, I saw #naomik provided a solution with the while loop. That one is fine too, but I prefer the array with the modulo operation (a bit shorter).
Now concerning the problem of the size long long int has, it can be solved by using external libraries that implement operations for big numbers (like the GMP library or Boost.multiprecision). But you could also create your own version of a BigInteger-like class from Java and implement the basic operations like the one I have. I've only implemented the addition in my example (try to implement the others they are quite similar).
The main idea is simple, a BigInt represents a big decimal number by cutting its little endian representation into pieces (I'll explain why little endian at the end). The length of those pieces depends on the base you choose. If you want to work with decimal representations, it will only work if your base is a power of 10: if you choose 10 as base each piece will represent one digit, if you choose 100 (= 10^2) as base each piece will represent two consecutive digits starting from the end(see little endian), if you choose 1000 as base (10^3) each piece will represent three consecutive digits, ... and so on. Let's say that you have base 100, 12765 will then be [65, 27, 1], 1789 will be [89, 17], 505 will be [5, 5] (= [05,5]), ... with base 1000: 12765 would be [765, 12], 1789 would be [789, 1], 505 would be [505]. It's not the most efficient, but it is the most intuitive (I think ...)
The addition is then a bit like the addition on paper we learned at school:
begin with the lowest piece of the BigInt
add it with the corresponding piece of the other one
the lowest piece of that sum(= the sum modulus the base) becomes the corresponding piece of the final result
the "bigger" pieces of that sum will be added ("carried") to the sum of the following pieces
go to step 2 with next piece
if no piece left, add the carry and the remaining bigger pieces of the other BigInt (if it has pieces left)
For example:
9542 + 1097855 = [42, 95] + [55, 78, 09, 1]
lowest piece = 42 and 55 --> 42 + 55 = 97 = [97]
---> lowest piece of result = 97 (no carry, carry = 0)
2nd piece = 95 and 78 --> (95+78) + 0 = 173 = [73, 1]
---> 2nd piece of final result = 73
---> remaining: [1] = 1 = carry (will be added to sum of following pieces)
no piece left in first `BigInt`!
--> add carry ( [1] ) and remaining pieces from second `BigInt`( [9, 1] ) to final result
--> first additional piece: 9 + 1 = 10 = [10] (no carry)
--> second additional piece: 1 + 0 = 1 = [1] (no carry)
==> 9542 + 1 097 855 = [42, 95] + [55, 78, 09, 1] = [97, 73, 10, 1] = 1 107 397
Here is a demo where I used the class above to calculate the fibonacci of 10000 (result is too big to copy here)
Good luck!
PS: Why little endian? For the ease of the implementation: it allows to use push_back when adding digits and iteration while implementing the operations will start from the first piece instead of the last piece in the array.
The following Pseudo and JavaScript code is a extract from the implementation of a algorithm , i want to convert it to C++ .
Pseudo Code :
for b from 0 to 2|R| do
for i from 0 to |R| do
if BIT-AT(b, i) = 1 then // b’s bit at index i
JavaScript Code :
for (var b = 0; b < Math.pow(2, orders[r].length); b++) // use b's bits for directions
{
for (var i = 0; i < orders[r].length; i++)
{
if (((b >> i) & 1) == 1) { // is b's bit at index i on?
I don't understand what is happening in the last line of this code , What Should be the C++ code for the above given JavaScript code . So far what i have written is :
for (int b = 0; b < pow(2, orders.at(r).size()); b++)
{
for (int i = 0; i < orders.at(r).size(); i++)
{
if (((b >> i) & 1) == 1)***//This line is not doing what it is supposed to do according to pseudo code***
The last line is giving me segmentation fault .
--
Edit:I apologize the problem was somewhere else , This code works fine .
(((b >> i) & 1) == 1)
| |
| |
| bitwise AND between the result of the shift and number 1.
|
shift b by i bits to the right
After that the result is compared with the number 1.
So if, for example, b is 8, and i is 2, it will do the following:
shift 8 (which is 00001000) by 2 bits to the right. The result will be 00000100.
apply the bitwise AND: 00000100 BITWISE_AND 00000001, the result will be 0.
Compare it with 1. Since 0 =/= 1, you will not enter that last if.
As for the logic behind this, the code ((b >> i) & 1) == 1) returns true if the bit number i of the b variable is 1, and false otherwise.
And I believe that c++ code will be the same, with the exception that we don't have Math class in c++, and you'll have to replace vars with the corresponding types.
>> is the right shift operator, i.e. take the left operand and move its bit n positions to the right (defined by the right operand).
So essentially, 1 << 5 would move 1 to 100000.
In your example (b >> i) & 1 == 1 will check whether the i-th bit is set (1) due to the logical and (&).
As for your code, you can use it (almost) directly in C or C++. Math.pow() would become pow() inside math.h, but (in this case) you could simply use the left shift operator:
for (int b = 0; b < (1 << orders[r].length); ++b) // added the brackets to make it easier to read
for (int i = 0; i < orders[r].length; ++i)
if (((b >> i) & 1) == 1) {
// ...
}
1 << orders[r].length will essentially be the same as pow(2, orders[r].length), but without any function call.
I was calculating the Fibonacci sequence, and stumbled across this code, which I saw a lot:
int Fibonacci (int x)
{
if (x<=1) {
return 1;
}
return Fibonacci (x-1)+Fibonacci (x-2);
}
What I don't understand is how it works, especially the return part at the end: Does it call the Fibonacci function again? Could someone step me through this function?
Yes, the function calls itself. For example,
Fibonacci(4)
= Fibonacci(3) + Fibonacci(2)
= (Fibonacci(2) + Fibonacci(1)) + (Fibonacci(1) + Fibonacci(0))
= ((Fibonacci(1) + Fibonacci(0)) + 1) + (1 + 1)
= ((1 + 1) + 1) + 2
= (2 + 1) + 2
= 3 + 2
= 5
Note that the Fibonacci function is called 9 times here. In general, the naïve recursive fibonacci function has exponential running time, which is usually a Bad Thing.
This is a classical example of a recursive function, a function that calls itself.
If you read it carefully, you'll see that it will call itself, or, recurse, over and over again, until it reaches the so called base case, when x <= 1 at which point it will start to "back track" and sum up the computed values.
The following code clearly prints out the trace of the algorithm:
public class Test {
static String indent = "";
public static int fibonacci(int x) {
indent += " ";
System.out.println(indent + "invoked with " + x);
if (x <= 1) {
System.out.println(indent + "x = " + x + ", base case reached.");
indent = indent.substring(4);
return 1;
}
System.out.println(indent + "Recursing on " + (x-1) + " and " + (x-2));
int retVal = fibonacci(x-1) + fibonacci(x-2);
System.out.println(indent + "returning " + retVal);
indent = indent.substring(4);
return retVal;
}
public static void main(String... args) {
System.out.println("Fibonacci of 3: " + fibonacci(3));
}
}
The output is the following:
invoked with 3
Recursing on 2 and 1
invoked with 2
Recursing on 1 and 0
invoked with 1
x = 1, base case reached.
invoked with 0
x = 0, base case reached.
returning 2
invoked with 1
x = 1, base case reached.
returning 3
Fibonacci of 3: 3
A tree depiction of the trace would look something like
fib 4
fib 3 + fib 2
fib 2 + fib 1 fib 1 + fib 0
fib 1 + fib 0 1 1 1
1 1
The important parts to think about when writing recursive functions are:
1. Take care of the base case
What would have happened if we had forgotten if (x<=1) return 1; in the example above?
2. Make sure the recursive calls somehow decrease towards the base case
What would have happened if we accidentally modified the algorithm to return fibonacci(x)+fibonacci(x-1);
return Fibonacci (x-1)+Fibonacci (x-2);
This is terribly inefficient. I suggest the following linear alternative:
unsigned fibonacci(unsigned n, unsigned a, unsigned b, unsigned c)
{
return (n == 2) ? c : fibonacci(n - 1, b, c, b + c);
}
unsigned fibonacci(unsigned n)
{
return (n < 2) ? n : fibonacci(n, 0, 1, 1);
}
The fibonacci sequence can be expressed more succinctly in functional languages.
fibonacci = 0 : 1 : zipWith (+) fibonacci (tail fibonacci)
> take 12 fibonacci
[0,1,1,2,3,5,8,13,21,34,55,89]
This is classic function recursion. http://en.wikipedia.org/wiki/Recursive_function should get you started. Essentially if x less than or equal to 1 it returns 1. Otherwise it it decreases x running Fibonacci at each step.
As your question is marked C++, I feel compelled to point out that this function can also be achieved at compile-time as a template, should you have a compile-time variable to use it with.
template<int N> struct Fibonacci {
const static int value = Fibonacci<N - 1>::value + Fibonacci<N - 2>::value;
};
template<> struct Fibonacci<1> {
const static int value = 1;
}
template<> struct Fibonacci<0> {
const static int value = 1;
}
Been a while since I wrote such, so it could be a little out, but that should be it.
Yes, the Fibonacci function is called again, this is called recursion.
Just like you can call another function, you can call the same function again. Since function context is stacked, you can call the same function without disturbing the currently executed function.
Note that recursion is hard since you might call the same function again infinitely and fill the call stack. This errors is called a "Stack Overflow" (here it is !)
In C and most other languages, a function is allowed to call itself just like any other function. This is called recursion.
If it looks strange because it's different from the loop that you would write, you're right. This is not a very good application of recursion, because finding the n th Fibonacci number requires twice the time as finding the n-1th, leading to running time exponential in n.
Iterating over the Fibonacci sequence, remembering the previous Fibonacci number before moving on to the next improves the runtime to linear in n, the way it should be.
Recursion itself isn't terrible. In fact, the loop I just described (and any loop) can be implemented as a recursive function:
int Fibonacci (int x, int a = 1, int p = 0) {
if ( x == 0 ) return a;
return Fibonacci( x-1, a+p, a );
} // recursive, but with ideal computational properties
Or if you want to be more quick but use more memory use this.
int *fib,n;
void fibonaci(int n) //find firs n number fibonaci
{
fib= new int[n+1];
fib[1] = fib[2] = 1;
for(int i = 3;i<=n-2;i++)
fib[i] = fib[i-1] + fib[i-2];
}
and for n = 10 for exemple you will have :
fib[1] fib[2] fib[3] fib[4] fib[5] fib[6] fib[7] fib[8] fib[9] fib[10]
1 1 2 3 5 8 13 21 34 55``
After reading Hidden Features and Dark Corners of C++/STL on comp.lang.c++.moderated, I was completely surprised that the following snippet compiled and worked in both Visual Studio 2008 and G++ 4.4.
Here's the code:
#include <stdio.h>
int main()
{
int x = 10;
while (x --> 0) // x goes to 0
{
printf("%d ", x);
}
}
Output:
9 8 7 6 5 4 3 2 1 0
I'd assume this is C, since it works in GCC as well. Where is this defined in the standard, and where has it come from?
--> is not an operator. It is in fact two separate operators, -- and >.
The conditional's code decrements x, while returning x's original (not decremented) value, and then compares the original value with 0 using the > operator.
To better understand, the statement could be written as follows:
while( (x--) > 0 )
Or for something completely different... x slides to 0.
while (x --\
\
\
\
> 0)
printf("%d ", x);
Not so mathematical, but... every picture paints a thousand words...
That's a very complicated operator, so even ISO/IEC JTC1 (Joint Technical Committee 1) placed its description in two different parts of the C++ Standard.
Joking aside, they are two different operators: -- and > described respectively in §5.2.6/2 and §5.9 of the C++03 Standard.
x can go to zero even faster in the opposite direction in C++:
int x = 10;
while( 0 <---- x )
{
printf("%d ", x);
}
8 6 4 2
You can control speed with an arrow!
int x = 100;
while( 0 <-------------------- x )
{
printf("%d ", x);
}
90 80 70 60 50 40 30 20 10
;)
It's equivalent to
while (x-- > 0)
x-- (post decrement) is equivalent to x = x-1 (but returning the original value of x), so the code transforms to:
while(x > 0) {
x = x-1;
// logic
}
x--; // The post decrement done when x <= 0
It's
#include <stdio.h>
int main(void) {
int x = 10;
while (x-- > 0) { // x goes to 0
printf("%d ", x);
}
return 0;
}
Just the space makes the things look funny, -- decrements and > compares.
The usage of --> has historical relevance. Decrementing was (and still is in some cases), faster than incrementing on the x86 architecture. Using --> suggests that x is going to 0, and appeals to those with mathematical backgrounds.
Utterly geek, but I will be using this:
#define as ;while
int main(int argc, char* argv[])
{
int n = atoi(argv[1]);
do printf("n is %d\n", n) as ( n --> 0);
return 0;
}
while( x-- > 0 )
is how that's parsed.
One book I read (I don't remember correctly which book) stated: Compilers try to parse expressions to the biggest token by using the left right rule.
In this case, the expression:
x-->0
Parses to biggest tokens:
token 1: x
token 2: --
token 3: >
token 4: 0
conclude: x-- > 0
The same rule applies to this expression:
a-----b
After parse:
token 1: a
token 2: --
token 3: --
token 4: -
token 5: b
conclude: (a--)-- - b
This is exactly the same as
while (x--)
Anyway, we have a "goes to" operator now. "-->" is easy to be remembered as a direction, and "while x goes to zero" is meaning-straight.
Furthermore, it is a little more efficient than "for (x = 10; x > 0; x --)" on some platforms.
This code first compares x and 0 and then decrements x. (Also said in the first answer: You're post-decrementing x and then comparing x and 0 with the > operator.) See the output of this code:
9 8 7 6 5 4 3 2 1 0
We now first compare and then decrement by seeing 0 in the output.
If we want to first decrement and then compare, use this code:
#include <stdio.h>
int main(void)
{
int x = 10;
while( --x> 0 ) // x goes to 0
{
printf("%d ", x);
}
return 0;
}
That output is:
9 8 7 6 5 4 3 2 1
My compiler will print out 9876543210 when I run this code.
#include <iostream>
int main()
{
int x = 10;
while( x --> 0 ) // x goes to 0
{
std::cout << x;
}
}
As expected. The while( x-- > 0 ) actually means while( x > 0). The x-- post decrements x.
while( x > 0 )
{
x--;
std::cout << x;
}
is a different way of writing the same thing.
It is nice that the original looks like "while x goes to 0" though.
There is a space missing between -- and >. x is post decremented, that is, decremented after checking the condition x>0 ?.
-- is the decrement operator and > is the greater-than operator.
The two operators are applied as a single one like -->.
It's a combination of two operators. First -- is for decrementing the value, and > is for checking whether the value is greater than the right-hand operand.
#include<stdio.h>
int main()
{
int x = 10;
while (x-- > 0)
printf("%d ",x);
return 0;
}
The output will be:
9 8 7 6 5 4 3 2 1 0
C and C++ obey the "maximal munch" rule. The same way a---b is translated to (a--) - b, in your case x-->0 translates to (x--)>0.
What the rule says essentially is that going left to right, expressions are formed by taking the maximum of characters which will form a valid token.
Actually, x is post-decrementing and with that condition is being checked. It's not -->, it's (x--) > 0
Note: value of x is changed after the condition is checked, because it post-decrementing. Some similar cases can also occur, for example:
--> x-->0
++> x++>0
-->= x-->=0
++>= x++>=0
char sep = '\n' /1\
; int i = 68 /1 \
; while (i --- 1\
\
/1/1/1 /1\
/1\
/1\
/1\
/1\
/ 1\
/ 1 \
/ 1 \
/ 1 \
/1 /1 \
/1 /1 \
/1 /1 /1/1> 0) std::cout \
<<i<< sep;
For larger numbers, C++20 introduces some more advanced looping features.
First to catch i we can build an inverse loop-de-loop and deflect it onto the std::ostream. However, the speed of i is implementation-defined, so we can use the new C++20 speed operator <<i<< to speed it up. We must also catch it by building wall, if we don't, i leaves the scope and de referencing it causes undefined behavior. To specify the separator, we can use:
std::cout \
sep
and there we have a for loop from 67 to 1.
Instead of regular arrow operator (-->) you can use armor-piercing arrow operator: --x> (note those sharp barbs on the arrow tip). It adds +1 to armor piercing, so it finishes the loop 1 iteration faster than regular arrow operator. Try it yourself:
int x = 10;
while( --x> 0 )
printf("%d ", x);
Why all the complication?
The simple answer to the original question is just:
#include <stdio.h>
int main()
{
int x = 10;
while (x > 0)
{
printf("%d ", x);
x = x-1;
}
}
It does the same thing. I am not saying you should do it like this, but it does the same thing and would have answered the question in one post.
The x-- is just shorthand for the above, and > is just a normal greater-than operator. No big mystery!
There are too many people making simple things complicated nowadays ;)
Conventional way we define condition in while loop parenthesis"()" and terminating condition inside the braces"{}", but this -- & > is a way one defines all at once.
For example:
int abc(){
int a = 5
while((a--) > 0){ // Decrement and comparison both at once
// Code
}
}
It says, decrement a and run the loop till the time a is greater than 0
Other way it should have been like:
int abc() {
int a = 5;
while(a > 0) {
a = a -1 // Decrement inside loop
// Code
}
}
Both ways, we do the same thing and achieve the same goals.
(x --> 0) means (x-- > 0).
You can use (x -->)
Output: 9 8 7 6 5 4 3 2 1 0
You can use (-- x > 0) It's mean (--x > 0)
Output: 9 8 7 6 5 4 3 2 1
You can use
(--\
\
x > 0)
Output: 9 8 7 6 5 4 3 2 1
You can use
(\
\
x --> 0)
Output: 9 8 7 6 5 4 3 2 1 0
You can use
(\
\
x --> 0
\
\
)
Output: 9 8 7 6 5 4 3 2 1 0
You can use also
(
x
-->
0
)
Output: 9 8 7 6 5 4 3 2 1 0
Likewise, you can try lot of methods to execute this command successfully.
This --> is not an operator at all. We have an operator like ->, but not like -->. It is just a wrong interpretation of while(x-- >0) which simply means x has the post decrement operator and this loop will run till it is greater than zero.
Another simple way of writing this code would be while(x--). The while loop will stop whenever it gets a false condition and here there is only one case, i.e., 0. So it will stop when the x value is decremented to zero.
Here -- is the unary post decrement operator.
while (x-- > 0) // x goes to 0
{
printf("%d ", x);
}
In the beginning, the condition will evaluate as
(x > 0) // 10 > 0
Now because the condition is true, it will go into the loop with a decremented value
x-- // x = 9
That's why the first printed value is 9
And so on. In the last loop x=1, so the condition is true. As per the unary operator, the value changed to x = 0 at the time of print.
Now, x = 0, which evaluates the condition (x > 0 ) as false and the while loop exits.
--> is not an operator, it is the juxtaposition of -- (post-decrement) and > (greater than comparison).
The loop will look more familiar as:
#include <stdio.h>
int main() {
int x = 10;
while (x-- > 0) { // x goes to 0
printf("%d ", x);
}
}
This loop is a classic idiom to enumerate values between 10 (the excluded upper bound) and 0 the included lower bound, useful to iterate over the elements of an array from the last to the first.
The initial value 10 is the total number of iterations (for example the length of the array), and one plus the first value used inside the loop. The 0 is the last value of x inside the loop, hence the comment x goes to 0.
Note that the value of x after the loop completes is -1.
Note also that this loop will operate the same way if x has an unsigned type such as size_t, which is a strong advantage over the naive alternative for (i = length-1; i >= 0; i--).
For this reason, I am actually a fan of this surprising syntax: while (x --> 0). I find this idiom eye-catching and elegant, just like for (;;) vs: while (1) (which looks confusingly similar to while (l)). It also works in other languages whose syntax is inspired by C: C++, Objective-C, java, javascript, C# to name a few.
That's what you mean.
while((x--) > 0)
We heard in childhood,
Stop don't, Let Go (روکو مت، جانے دو)
Where a Comma makes confusion
Stop, don't let go. (روکو، مت جانے دو)
Same Happens in Programming now, a SPACE makes confusion. :D
The operator you use is called "decrement-and-then-test". It is defined in the C99 standard, which is the latest version of the C programming language standard. The C99 standard added a number of new operators, including the "decrement-and-then-test" operator, to the C language. Many C++ compilers have adopted these new operators as extensions to the C++ language.
Here is how the code without using the "decrement-and-then-test" operator:
#include <stdio.h>
int main()
{
int x = 10;
while (x > 0)
{
printf("%d ", x);
x--;
}
}
In this version of the code, the while loop uses the > operator to test whether x is greater than 0. The x-- statement is used to decrement x by 1 at the end of each iteration of the loop.
I have two simple while loops in my program that I feel ought to be math equations, but I'm struggling to convert them:
float a = someValue;
int b = someOtherValue;
int c = 0;
while (a <= -b / 2) {
c--;
a += b;
}
while (a >= b / 2) {
c++;
a -= b;
}
This code works as-is, but I feel it could be simplified into math equations. The idea here being that this code is taking an offset (someValue) and adjusting a coordinate (c) to minimize the distance from the center of a tile (of size someOtherValue). Any help would be appreciated.
It can be proved that the following is correct:
c = floor((a+b/2)/b)
a = a - c*b
Note that floor means round down, towards negative infinity: not towards 0. (E.g. floor(-3.1)=-4. The floor() library functions will do this; just be sure not to just cast to int, which will usually round towards 0 instead.)
Presumably b is strictly positive, because otherwise neither loop will never terminate: adding b will not make a larger and subtracting b will not make a smaller. With that assumption, we can prove that the above code works. (And paranoidgeek's code is also almost correct, except that it uses a cast to int instead of floor.)
Clever way of proving it:
The code adds or subtracts multiples of b from a until a is in [-b/2,b/2), which you can view as adding or subtracting integers from a/b until a/b is in [-1/2,1/2), i.e. until (a/b+1/2) (call it x) is in [0,1). As you are only changing it by integers, the value of x does not change mod 1, i.e. it goes to its remainder mod 1, which is x-floor(x). So the effective number of subtractions you make (which is c) is floor(x).
Tedious way of proving it:
At the end of the first loop, the value of c is the negative of the number of times the loop runs, i.e.:
0 if: a > -b/2 <=> a+b/2 > 0
-1 if: -b/2 ≥ a > -3b/2 <=> 0 ≥ a+b/2 > -b <=> 0 ≥ x > -1
-2 if: -3b/2 ≥ a > -5b/2 <=> -b ≥ a+b/2 > -2b <=> -1 ≥ x > -2 etc.,
where x = (a+b/2)/b, so c is: 0 if x>0 and "ceiling(x)-1" otherwise. If the first loop ran at all, then it was ≤ -b/2 just before the last time the loop was executed, so it is ≤ -b/2+b now, i.e. ≤ b/2. According as whether it is exactly b/2 or not (i.e., whether x when you started was exactly a non-positive integer or not), the second loop runs exactly 1 time or 0, and c is either ceiling(x) or ceiling(x)-1. So that solves it for the case when the first loop did run.
If the first loop didn't run, then the value of c at the end of the second loop is:
0 if: a < b/2 <=> a-b/2 < 0
1 if: b/2 ≤ a < 3b/2 <=> 0 ≤ a-b/2 < b <=> 0 ≤ y < 1
2 if: 3b/2 ≤ a < 5b/2 <=> b ≤ a-b/2 < 2b <=> 1 ≤ y < 2, etc.,
where y = (a-b/2)/b, so c is: 0 if y<0 and 1+floor(y) otherwise. [And a now is certainly < b/2 and ≥ -b/2.]
So you can write an expression for c as:
x = (a+b/2)/b
y = (a-b/2)/b
c = (x≤0)*(ceiling(x) - 1 + (x is integer))
+(y≥0)*(1 + floor(y))
Of course, next you notice that (ceiling(x)-1+(x is integer)) is same as floor(x+1)-1 which is floor(x), and that y is actually x-1, so (1+floor(y))=floor(x), and as for the conditionals:
when x≤0, it cannot be that (y≥0), so c is just the first term which is floor(x),
when 0 < x < 1, neither of the conditions holds, so c is 0,
when 1 ≤ x, then only 0≤y, so c is just the second term which is floor(x) again.
So c = floor(x) in all cases.
c = (int)((a - (b / 2)) / b + 1);
a -= c * b;
Test case at http://pastebin.com/m1034e639
I think you want something like this:
c = ((int) a + b / 2 * sign(a)) / b
That should match your loops except for certain cases where b is odd because the range from -b/2 to b/2 is smaller than b when b is odd.
Assuming b is positive, abs(c) = floor((abs(a) - b/2) / b). Then, apply sign of a to c.