I try to handle with big numbers in C++. One thing that I tried is installing the gmp library but this is not working properly on my computer (see this post). So I want to try another method and that is integer to string conversion.
But I dont get the idea of that. Let me make myself clear. For example we handle with a big integer. Lets say 2^1000. When, for example, I want to calculate 2^1000 mod 10 this is not possible (so far I know) with the normal libraries of c++. So my question is: Is it possible when converting my integer to a string and if the answer is yes:
How can I do arithmetic operations when I convert my integer to a string.
If you are using c++ predefined integer type, then 2^1000 is simply impossible. On your system maximum should be 2^16 or 2^32, max 2^64 (for long long). If you wanted to do that, you need to use (or implement yourself - what I don't recommend) infinite-precision integers.
You can convert normal int to string very easily with
... = std::to_string(/*Your int*/);
If you meant you want to do something like this:
amazing_to_string_conversion(1000000000000000000000000000000000000000000000)
It's not possible in any C++ implementation. The very number constant can't exist in code, it will many, many times overflow.
And if you consider implementing it yourself, it will probably K.O. you, because of very complicated calculations during division and non-trivial calculations like sqrt().
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Using extremely large integer holding 3001 digits
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How can i handle very large integers like 2^100000000 in c++?
I found no solution for this on internet that gives an exact answer.
Is there any mechanism that gives correct value in c++ for such large integers?
What you are looking for is called arbitrary precision arithmetic, you will find numerous libraries and educational resources with some googling.
You can represent given number as a string and convert it to array with integer digits. But the simplest way to google by keywords "long arithmetic c++ library" or something.
Maybe you want to use a Computer Algebra System (CAS), which would represent your expression like this:
class Pow : public Expr {
Number base;
Number exp;
};
Pow expr = new Pow(2, 100*1000*1000);
A CAS then allows you to manipulate these expressions structurally instead of the concrete values.
For example I have a factorial program that needs to save really huge integers that can be 50+ digits long. The absolute maximum primitive data type in C++ is unsigned long long int with a maximum value 18446744073709551615 which is only 20 digits long. Here's the link to the limits of C++: http://www.cplusplus.com/reference/climits/
How do I store numbers that are larger than that in a variable of some sort?
If you already have a boost dependency (which many people these days do), you can use the boost multi-precision library. In fact, it already has an example of a factorial program that can support output up to 128 bits, though extending it further is pretty trivial.
You'll have to use a bigint or bignum implementation. There are some libraries out there like this: http://gmplib.org/
Some more info and a list of libraries: http://en.wikipedia.org/wiki/Bignum
You can use array. First you should copy that giant number array,then use comma after 19 digits:
unsigned long long int num[]= {
7316717653133062491,9225119674426574742,3553491949349698352,0,312774506326239578,3180169848018694788,
5184385861560789112,9494954595017379583,3195285320880551112,5406987471585238630,5071569329096329522,
7443043557668966489,5044524452316173185,6403098711121722383,1136222989342338030,8135336276614282806,
4444866452387493035,8907296290491560440,7723907138105158593,0,7960866701724271218,8399879790879227492,
1901699720888093776,6572733300105336788,1220235421809751254,5405947522435258490,7711670556013604839,
5864467063244157221,5539753697817977846,1740649551492908625,6932197846862248283,9722413756570560574,
9026140797296865241,4535100474821663704,8440319989000889524,3450658541227588666,8811642717147992444,
2928230863465674813,9191231628245861786,6458359124566529476,5456828489128831426,0,7690042242190226710,
5562632111110937054,4217506941658960408,0,7198403850962455444,3629812309878799272,4428490918884580156,
1660979191338754992,0,0,5240636899125607176,0,6058861164671094050,7754100225698315520,0,0,
5593572972571636269,5618826704282524836,0,0,8232575304207529634,50};
There are many ways to store very big number which are below:
string
File
Link list
Vector/Dynamic array
Note: Please don't use array to avoid memory problem issues.
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Inputting large numbers in c++?
Arbitrary-precision arithmetic Explanation
I need to multiply two huge huge integers, like:
a=1212121212121212121212121212121212121212121212121212;
b=1212121212121212121212121212121212121212121212121212;
I think there are no data types in C and C++ to hold this huge an integer, so I thought to keep it as a string format like:-
char *number1="1212121212121212121212121212121212121212121212121212";
char *number2="1212121212121212121212121212121212121212121212121212";
during the time of multiplication I convert it into string with help of atoi() function like:
atoi(number1)*atoi(number2);
As usual the output of this multiplication will be obviously huge, so I need to change the output in string format.
I know there is an itoa() function which converts an integer to a string but it is not compatible with all compilers. Can any body tell me what I should do in this scenario?
I am using Ubuntu-10.04 and the g++ compiler.
Since C and C++ do not offer a native type that supports big numbers, it makes no sense to call atoi() to parse such numbers. atoi() returns a native int which is capped at 2,147,483,647 on 32-bit platforms.
You can use one of the numerous bignum libraries, like GMP for instance.
I think, the best variant besides using some math libraries is to split those numbers into int arrays with some fixed limit. Then just perform multiplication using basic math multiplication methods. And do not forget about overflows.
Multiplying the large numbers is very
difficult, however we can do it by
applying the logarithm of
multiplication of two numbers formula
and now we are going know how we
derived the product of two numbers’
logarithm.
Let us consider a, m and n are positive real numbers but a does not equal to 1 which means ‘a’ belongs to R+ – {1}. Logarithm of m and n to base a are x and y respectively by satisfying ax is equal to m and ay is equal to n condition.
loga (m.n) = x + y
As we already know x = loga m and y = loga n.
loga (m.n) = loga m + loga n
logarithm of multiplication of two values is equal to summation of the same values’ logarithms. The same logarithmic fundamental can now help us in multiplying the two large numbers by adding the logarithm of those values. If you don’t have a calculator, just take the logarithmic table help to perform this.
Using atoi() is also not helpful since the number itself won't fit in integer data type.
You have to simulate the method you did in elementary school.
121
*23
----
363
242*
----
2783
The implementation is left as an exercise. You would also need to know how to add big numbers.
I'm trying to write an algorithm for a number theory/computer science merged class that can factor large numbers in better than exponential time. I am using the g++ compiler on a 64 bit machine but when I chain together long it will only allow me to do up to 2 longs. Is there any way to tell it to use an arbitrary amount of space for a variable?
If you want just a collection of longs, you can declare an array of longs. But you don't want that. You want https://mattmccutchen.net/bigint/ BigIntegers :-)
Alternatives:
http://gmplib.org/
http://www.mpir.org/
(disclaimer: I haven't tested/used them)
Or if you want to implement them
How to implement big int in C++
I'll add that the C++ std library doesn't contain a big integer implementation (source STL big int class implementation )
You'll need a library. A good one is http://gmplib.org/