Get the number of digits in an int - c++

How do I detect the length of an integer? In case I had le: int test(234567545);
How do I know how long the int is? Like telling me there is 9 numbers inside it???
*I have tried:**
char buffer_length[100];
// assign directly to a string.
sprintf(buffer_length, "%d\n", 234567545);
string sf = buffer_length;
cout <<sf.length()-1 << endl;
But there must be a simpler way of doing it or more clean...

How about division:
int length = 1;
int x = 234567545;
while ( x /= 10 )
length++;
or use the log10 method from <math.h>.
Note that log10 returns a double, so you'll have to adjust the result.

Make a function :
int count_numbers ( int num) {
int count =0;
while (num !=0) {
count++;
num/=10;
}
return count;
}

Nobody seems to have mentioned converting it to a string, and then getting the length. Not the most performant, but it definitely does it in one line of code :)
int num = -123456;
int len = to_string(abs(num)).length();
cout << "LENGTH of " << num << " is " << len << endl;
// prints "LENGTH of 123456 is 6"

You can use stringstream for this as shown below
stringstream ss;
int i = 234567545;
ss << i;
cout << ss.str().size() << endl;

if "i" is the integer, then
int len ;
char buf[33] ;
itoa (i, buf, 10) ; // or maybe 16 if you want base-16 ?
len = strlen(buf) ;
if(i < 0)
len-- ; // maybe if you don't want to include "-" in length ?

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
int main() {
int i=2384995;
char buf[100];
itoa(i, buf, 10); // 10 is the base decimal
printf("Lenght: %d\n", strlen(buf));
return 0;
}
Beware that itoa is not a standard function, even if it is supported by many compilers.

len=1+floor(log10(n));//c++ code lib (cmath)

looking across the internet it's common to make the mistake of initializing the counter variable to 0 and then entering a pre-condition loop testing for as long as the count does not equal 0. a do-while loop is perfect to avoid this.
unsigned udc(unsigned u) //unsigned digit count
{
unsigned c = 0;
do
++c;
while ((u /= 10) != 0);
return c;
}
it's probably cheaper to test whether u is less than 10 to avoid the uneccessary division, increment, and cmp instructions for cases where u < 10.
but while on that subject, optimization, you could simply test u against constant powers of ten.
unsigned udc(unsigned u) //unsigned digit count
{
if (u < 10) return 1;
if (u < 100) return 2;
if (u < 1000) return 3;
//...
return 0; //number was not supported
}
which saves you 3 instructions per digit, but is less adaptable for different radixes inaddition to being not as attractive, and tedious to write by hand, in which case you'd rather write a routine to write the routine before inserting it into your program. because C only supports very finite numbers, 64bit,32bit,16bit,8bit, you could simply limit yourself to the maximum when generating the routine to benefit all sizes.
to account for negative numbers, you'd simply negate u if u < 0 before counting the number of digits. of course first making the routine support signed numbers.
if you know that u < 1000,
it's probably easier to just write, instead of writing the routine.
if (u > 99) len = 3;
else
if (u > 9) len = 2;
else len = 1;

Here are a few different C++ implementations* of a function named digits() which takes a size_t as argument and returns its number of digits. If your number is negative, you are going to have to pass its absolute value to the function in order for it to work properly:
The While Loop
int digits(size_t i)
{
int count = 1;
while (i /= 10) {
count++;
}
return count;
}
The Exhaustive Optimization Technique
int digits(size_t i) {
if (i > 9999999999999999999ull) return 20;
if (i > 999999999999999999ull) return 19;
if (i > 99999999999999999ull) return 18;
if (i > 9999999999999999ull) return 17;
if (i > 999999999999999ull) return 16;
if (i > 99999999999999ull) return 15;
if (i > 9999999999999ull) return 14;
if (i > 999999999999ull) return 13;
if (i > 99999999999ull) return 12;
if (i > 9999999999ull) return 11;
if (i > 999999999ull) return 10;
if (i > 99999999ull) return 9;
if (i > 9999999ull) return 8;
if (i > 999999ull) return 7;
if (i > 99999ull) return 6;
if (i > 9999ull) return 5;
if (i > 999ull) return 4;
if (i > 99ull) return 3;
if (i > 9ull) return 2;
return 1;
}
The Recursive Way
int digits(size_t i) { return i < 10 ? 1 : 1 + digits(i / 10); }
Using snprintf() as a Character Counter
⚠ Requires #include <stdio.h> and may incur a significant performance penalty compared to other solutions. This method capitalizes on the fact that snprintf() counts the characters it discards when the buffer is full. Therefore, with the right arguments and format specifiers, we can force snprintf() to give us the number of digits of any size_t.
int digits(size_t i) { return snprintf (NULL, 0, "%llu", i); }
The Logarithmic Way
⚠ Requires #include <cmath> and is unreliable for unsigned integers with more than 14 digits.
// WARNING! There is a silent implicit conversion precision loss that happens
// when we pass a large int to log10() which expects a double as argument.
int digits(size_t i) { return !i? 1 : 1 + log10(i); }
Driver Program
You can use this program to test any function that takes a size_t as argument and returns its number of digits. Just replace the definition of the function digits() in the following code:
#include <iostream>
#include <stdio.h>
#include <cmath>
using std::cout;
// REPLACE this function definition with the one you want to test.
int digits(size_t i)
{
int count = 1;
while (i /= 10) {
count++;
}
return count;
}
// driver code
int main ()
{
const int max = digits(-1ull);
size_t i = 0;
int d;
do {
d = digits(i);
cout << i << " has " << d << " digits." << '\n';
i = d < max ? (!i ? 9 : 10 * i - 1) : -1;
cout << i << " has " << digits(i) << " digits." << '\n';
} while (++i);
}
* Everything was tested on a Windows 10 (64-bit) machine using GCC 12.2.0 in Visual Studio Code .

As long as you are mixing C stdio and C++ iostream, you can use the snprintf NULL 0 trick to get the number of digits in the integer representation of the number. Specifically, per man 3 printf If the string exceeds the size parameter provided and is truncated snprintf() will return
... the number of characters (excluding the terminating null byte)
which would have been written to the final string if enough space
had been available.
This allows snprintf() to be called with the str parameter NULL and the size parameter 0, e.g.
int ndigits = snprintf (NULL, 0, "%d", 234567545)
In your case where you simply wish to output the number of digits required for the representation, you can simply output the return, e.g.
#include <iostream>
#include <cstdio>
int main() {
std::cout << "234567545 is " << snprintf (NULL, 0, "%d", 234567545) <<
" characters\n";
}
Example Use/Output
$ ./bin/snprintf_trick
234567545 is 9 characters
note: the downside to using the snprintf() trick is that you must provide the conversion specifier which will limit the number of digits representable. E.g "%d" will limit to int values while "%lld" would allow space for long long values. The C++ approach using std::stringstream while still limited to numeric conversion using the << operator handles the different integer types without manually specifying the conversion. Something to consider.
second note: you shouldn't dangle the "\n" of the end of your sprintf() conversion. Add the new line as part of your output and you don't have to subtract 1 from the length...

Related

Formatting Commas into a long long integer

this is my first time posting a question. I was hoping to get some help on a very old computer science assignment that I never got around to finishing. I'm no longer taking the class, just want to see how to solve this.
Read in an integer (any valid 64-bit
integer = long long type) and output the same number but with commas inserted.
If the user entered -1234567890, your program should output -1,234,567,890. Commas
should appear after every three significant digits (provided more digits remain) starting
from the decimal point and working left toward more significant digits. If the number
entered does not require commas, do not add any. For example, if the input is 234 you
should output 234. The input 0 should produce output 0. Note in the example above
that the number can be positive or negative. Your output must maintain the case of the
input.
I'm relatively new to programming, and this was all I could come up with:
#include <iostream>
#include <cmath>
using namespace std;
int main()
{
long long n;
cout << "Enter an integer:" << endl;
cin >> n;
int ones = n % 10;
int tens = n / 10 % 10;
int hund = n / 100 % 10;
int thous = n / 1000 % 10;
int tthous = n / 10000 % 10;
cout << tthous << thous << "," << hund << tens << ones << endl;
return 0;
}
The original assignment prohibited the use of strings, arrays, and vectors, so please refrain from giving suggestions/solutions that involve these.
I'm aware that some sort of for-loop would probably be required to properly insert the commas in the necessary places, but I just do not know how to go about implementing this.
Thank you in advance to anyone who offers their help!
Just to give you an idea how to solve this, I've maiden a simple implementation. Just keep in mind that is just a simple example:
#include <iostream>
#include <cmath>
using namespace std;
int main()
{
long long n = -1234567890;
if ( n < 0 )
cout << '-';
n = abs(n);
for (long long i = 1000000000000; i > 0; i /= 1000) {
if ( n / i <= 0 ) continue;
cout << n / i ;
n = n - ( n / i) * i;
if ( n > 0 )
cout << ',';
}
return 0;
}
http://coliru.stacked-crooked.com/a/150f75db89c46e99
The easy solution would be to use ios::imbue to set a locale that would do all the work for you:
std::cout.imbue(std::locale(""));
std::cout << n << std::endl;
However, if the restraints don't allow for strings or vectors I doubt that this would be a valid solution. Instead you could use recursion:
void print(long long n, int counter) {
if (n > 0) {
print(n / 10, ++counter);
if (counter % 3 == 0) {
std::cout << ",";
}
std::cout << n%10;
}
}
void print(long long n) {
if (n < 0) {
std::cout << "-";
n *= -1;
}
print(n, 0);
}
And then in the main simply call print(n);
A small template class comma_sep may be a solution, the usage may be as simple as:
cout << comma_sep<long long>(7497592752850).sep() << endl;
Which outputs:
7,497,592,752,850
Picked from here:
https://github.com/arloan/libimsux/blob/main/comma_sep.hxx
template <class I = int, int maxdigits = 32>
class comma_sep
char buff[maxdigits + maxdigits / 3 + 2];
char * p;
I i;
char sc;
public:
comma_sep(I i, char c = ',') : p(buff), i(i), sc(c) {
if (i < 0) {
buff[0] = '-';
*++p = '\0';
}
}
const char * sep() {
return _sep(std::abs(i));
}
private:
const char * _sep(I i) {
I r = i % 1000;
I n = i / 1000;
if (n > 0) {
_sep(n);
p += sprintf(p, "%c%03d", sc, (int)r);
*p = '\0';
} else {
p += sprintf(p, "%d", (int)r);
*p = '\0';
}
return buff;
}
};
The above class handles only integeral numbers, float/double numbers need to use a partial specialized version:
template<int maxd>
class comma_sep<double, maxd> {
comma_sep<int64_t, maxd> _cs;
char fs[64];
double f;
public:
const int max_frac = 12;
comma_sep(double d, char c = ',') : _cs((int64_t)d, c) {
double np;
f = std::abs(modf(d, &np));
}
const char * sep(int frac = 3) {
if (frac < 1 || frac > max_frac) {
throw std::invalid_argument("factional part too too long or invalid");
}
auto p = _cs.sep();
strcpy(fs, p);
char fmt[8], tmp[max_frac+3];
sprintf(fmt, "%%.%dlf", frac);
sprintf(tmp, fmt, f);
return strcat(fs, tmp + 1);
}
};
The two above classes can be improved by adding type-traits like std::is_integral and/or std::is_floating_point, though.

How does C++ compiler represent int numbers in binary code?

I've written a program, which shows binary representation of a particular integer value, using bitwise operators in C++. For even numbers it works as I expect, but for odd it adds 1 to the left of the binary representation.
#include <iostream>
using std::cout;
using std::cin;
using std::endl;
int main()
{
unsigned int a = 128;
for (int i = sizeof(a) * 8; i >= 0; --i) {
if (a & (1UL << i)) { // if i-th digit is 1
cout << 1; // Output 1
}
else {
cout << 0; // Otherwise output 0
}
}
cout << endl;
system("pause");
return 0;
}
Results:
For a = 128: 000000000000000000000000010000000,
For a = 127: 100000000000000000000000001111111
You might prefer CHAR_BIT macro instead of raw 8 (#include <climits>).
Consider your start value! Assuming unsigned int having 32 bit, your start value is int i = 4*8, so 1U << i shifts the value out of range. This is undefined behaviour and could result in anything, obviously, your specific compiler or hardware shifts %32, thus you get an initial value & 1, resulting in the unexpected leading 1... Did you notice that you actually printed out 33 digits instead of only 32?
The problem is here:
for (int i = sizeof(a) * 8; i >= 0; --i) {
it should be:
for (int i = sizeof(a) * 8; i-- ; ) {
http://coliru.stacked-crooked.com/a/8cb2b745063883fa

C++ - how to find the length of an integer

I'm trying to find a way to find the length of an integer (number of digits) and then place it in an integer array. The assignment also calls for doing this without the use of classes from the STL, although the program spec does say we can use "common C libraries" (gonna ask my professor if I can use cmath, because I'm assuming log10(num) + 1 is the easiest way, but I was wondering if there was another way).
Ah, and this doesn't have to handle negative numbers. Solely non-negative numbers.
I'm attempting to create a variant "MyInt" class that can handle a wider range of values using a dynamic array. Any tips would be appreciated! Thanks!
Not necessarily the most efficient, but one of the shortest and most readable using C++:
std::to_string(num).length()
The number of digits of an integer n in any base is trivially obtained by dividing until you're done:
unsigned int number_of_digits = 0;
do {
++number_of_digits;
n /= base;
} while (n);
There is a much better way to do it
#include<cmath>
...
int size = trunc(log10(num)) + 1
....
works for int and decimal
If you can use C libraries then one method would be to use sprintf, e.g.
#include <cstdio>
char s[32];
int len = sprintf(s, "%d", i);
"I mean the number of digits in an integer, i.e. "123" has a length of 3"
int i = 123;
// the "length" of 0 is 1:
int len = 1;
// and for numbers greater than 0:
if (i > 0) {
// we count how many times it can be divided by 10:
// (how many times we can cut off the last digit until we end up with 0)
for (len = 0; i > 0; len++) {
i = i / 10;
}
}
// and that's our "length":
std::cout << len;
outputs 3
Closed formula for the longest int (I used int here, but works for any signed integral type):
1 + (int) ceil((8*sizeof(int)-1) * log10(2))
Explanation:
sizeof(int) // number bytes in int
8*sizeof(int) // number of binary digits (bits)
8*sizeof(int)-1 // discount one bit for the negatives
(8*sizeof(int)-1) * log10(2) // convert to decimal, because:
// 1 bit == log10(2) decimal digits
(int) ceil((8*sizeof(int)-1) * log10(2)) // round up to whole digits
1 + (int) ceil((8*sizeof(int)-1) * log10(2)) // make room for the minus sign
For an int type of 4 bytes, the result is 11. An example of 4 bytes int with 11 decimal digits is: "-2147483648".
If you want the number of decimal digits of some int value, you can use the following function:
unsigned base10_size(int value)
{
if(value == 0) {
return 1u;
}
unsigned ret;
double dval;
if(value > 0) {
ret = 0;
dval = value;
} else {
// Make room for the minus sign, and proceed as if positive.
ret = 1;
dval = -double(value);
}
ret += ceil(log10(dval+1.0));
return ret;
}
I tested this function for the whole range of int in g++ 9.3.0 for x86-64.
int intLength(int i) {
int l=0;
for(;i;i/=10) l++;
return l==0 ? 1 : l;
}
Here's a tiny efficient one
Being a computer nerd and not a maths nerd I'd do:
char buffer[64];
int len = sprintf(buffer, "%d", theNum);
Would this be an efficient approach? Converting to a string and finding the length property?
int num = 123
string strNum = to_string(num); // 123 becomes "123"
int length = strNum.length(); // length = 3
char array[3]; // or whatever you want to do with the length
How about (works also for 0 and negatives):
int digits( int x ) {
return ( (bool) x * (int) log10( abs( x ) ) + 1 );
}
Best way is to find using log, it works always
int len = ceil(log10(num))+1;
Code for finding Length of int and decimal number:
#include<iostream>
#include<cmath>
using namespace std;
int main()
{
int len,num;
cin >> num;
len = log10(num) + 1;
cout << len << endl;
return 0;
}
//sample input output
/*45566
5
Process returned 0 (0x0) execution time : 3.292 s
Press any key to continue.
*/
There are no inbuilt functions in C/C++ nor in STL for finding length of integer but there are few ways by which it can found
Here is a sample C++ code to find the length of an integer, it can be written in a function for reuse.
#include<iostream>
using namespace std;
int main()
{
long long int n;
cin>>n;
unsigned long int integer_length = 0;
while(n>0)
{
integer_length++;
n = n/10;
}
cout<<integer_length<<endl;
return 0;
}
Here is another way, convert the integer to string and find the length, it accomplishes same with a single line:
#include<iostream>
#include<cstring>
using namespace std;
int main()
{
long long int n;
cin>>n;
unsigned long int integer_length = 0;
// convert to string
integer_length = to_string(n).length();
cout<<integer_length<<endl;
return 0;
}
Note: Do include the cstring header file
The easiest way to use without any libraries in c++ is
#include <iostream>
using namespace std;
int main()
{
int num, length = 0;
cin >> num;
while(num){
num /= 10;
length++;
}
cout << length;
}
You can also use this function:
int countlength(int number)
{
static int count = 0;
if (number > 0)
{
count++;
number /= 10;
countlength(number);
}
return count;
}
#include <math.h>
int intLen(int num)
{
if (num == 0 || num == 1)
return 1;
else if(num < 0)
return ceil(log10(num * -1))+1;
else
return ceil(log10(num));
}
Most efficient code to find length of a number.. counts zeros as well, note "n" is the number to be given.
#include <iostream>
using namespace std;
int main()
{
int n,len= 0;
cin>>n;
while(n!=0)
{
len++;
n=n/10;
}
cout<<len<<endl;
return 0;
}

factorial of big numbers with strings in c++

I am doing a factorial program with strings because i need the factorial of Numbers greater than 250
I intent with:
string factorial(int n){
string fact="1";
for(int i=2; i<=n; i++){
b=atoi(fact)*n;
}
}
But the problem is that atoi not works. How can i convert my string in a integer.
And The most important Do I want to know if the program of this way will work with the factorial of 400 for example?
Not sure why you are trying to use string. Probably to save some space by not using integer vector? This is my solution by using integer vector to store factorial and print.Works well with 400 or any large number for that matter!
//Factorial of a big number
#include<iostream>
#include<vector>
using namespace std;
int main(){
int num;
cout<<"Enter the number :";
cin>>num;
vector<int> res;
res.push_back(1);
int carry=0;
for(int i=2;i<=num;i++){
for(int j=0;j<res.size();j++){
int tmp=res[j]*i;
res[j]=(tmp+carry)%10 ;
carry=(tmp+carry)/10;
}
while(carry!=0){
res.push_back(carry%10);
carry=carry/10;
}
}
for(int i=res.size()-1;i>=0;i--) cout<<res[i];
cout<<endl;
return 0;
}
Enter the number :400
Factorial of 400 :64034522846623895262347970319503005850702583026002959458684445942802397169186831436278478647463264676294350575035856810848298162883517435228961988646802997937341654150838162426461942352307046244325015114448670890662773914918117331955996440709549671345290477020322434911210797593280795101545372667251627877890009349763765710326350331533965349868386831339352024373788157786791506311858702618270169819740062983025308591298346162272304558339520759611505302236086810433297255194852674432232438669948422404232599805551610635942376961399231917134063858996537970147827206606320217379472010321356624613809077942304597360699567595836096158715129913822286578579549361617654480453222007825818400848436415591229454275384803558374518022675900061399560145595206127211192918105032491008000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
There's a web site that will calculate factorials for you: http://www.nitrxgen.net/factorialcalc.php. It reports:
The resulting factorial of 250! is 493 digits long.
The result also contains 62 trailing zeroes (which constitutes to 12.58% of the whole number)
3232856260909107732320814552024368470994843717673780666747942427112823747555111209488817915371028199450928507353189432926730931712808990822791030279071281921676527240189264733218041186261006832925365133678939089569935713530175040513178760077247933065402339006164825552248819436572586057399222641254832982204849137721776650641276858807153128978777672951913990844377478702589172973255150283241787320658188482062478582659808848825548800000000000000000000000000000000000000000000000000000000000000
Many systems using C++ double only work up to 1E+308 or thereabouts; the value of 250! is too large to store in such numbers.
Consequently, you'll need to use some sort of multi-precision arithmetic library, either of your own devising using C++ string values, or using some other widely-used multi-precision library (GNU GMP for example).
The code below uses unsigned double long to calculate very large digits.
#include<iostream.h>
int main()
{
long k=1;
while(k!=0)
{
cout<<"\nLarge Factorial Calculator\n\n";
cout<<"Enter a number be calculated:";
cin>>k;
if (k<=33)
{
unsigned double long fact=1;
fact=1;
for(int b=k;b>=1;b--)
{
fact=fact*b;
}
cout<<"\nThe factorial of "<<k<<" is "<<fact<<"\n";
}
else
{
int numArr[10000];
int total,rem=0,count;
register int i;
//int i;
for(i=0;i<10000;i++)
numArr[i]=0;
numArr[10000]=1;
for(count=2;count<=k;count++)
{
while(i>0)
{
total=numArr[i]*count+rem;
rem=0;
if(total>9)
{
numArr[i]=total%10;
rem=total/10;
}
else
{
numArr[i]=total;
}
i--;
}
rem=0;
total=0;
i=10000;
}
cout<<"The factorial of "<<k<<" is \n\n";
for(i=0;i<10000;i++)
{
if(numArr[i]!=0 || count==1)
{
cout<<numArr[i];
count=1;
}
}
cout<<endl;
}
cout<<"\n\n";
}//while
return 0;
}
Output:
![Large Factorial Calculator
Enter a number be calculated:250
The factorial of 250 is
32328562609091077323208145520243684709948437176737806667479424271128237475551112
09488817915371028199450928507353189432926730931712808990822791030279071281921676
52724018926473321804118626100683292536513367893908956993571353017504051317876007
72479330654023390061648255522488194365725860573992226412548329822048491377217766
50641276858807153128978777672951913990844377478702589172973255150283241787320658
18848206247858265980884882554880000000000000000000000000000000000000000000000000
000000000000][1]
You can make atoi compile by adding c_str(), but it will be a long way to go till getting factorial. Currently you have no b around. And if you had, you still multiply int by int. So even if you eventually convert that to string before return, your range is still limited. Until you start to actually do multiplication with ASCII or use a bignum library there's no point to have string around.
Your factorial depends on conversion to int, which will overflow pretty fast, so you want be able to compute large factorials that way. To properly implement computation on big numbers you need to implement logic as for computation on paper, rules that you were tought in primary school, but treat long long ints as "atoms", not individual digits. And don't do it on strings, it would be painfully slow and full of nasty conversions
If you are going to solve factorial for numbers larger than around 12, you need a different approach than using atoi, since that just gives you a 32-bit integer, and no matter what you do, you are not going to get more than 2 billion (give or take) out of that. Even if you double the size of the number, you'll only get to about 20 or 21.
It's not that hard (relatively speaking) to write a string multiplication routine that takes a small(ish) number and multiplies each digit and ripples the results through to the the number (start from the back of the number, and fill it up).
Here's my obfuscated code - it is intentionally written such that you can't just take it and hand in as school homework, but it appears to work (matches the number in Jonathan Leffler's answer), and works up to (at least) 20000! [subject to enough memory].
std::string operator*(const std::string &s, int x)
{
int l = (int)s.length();
std::string r;
r.resize(l);
std::fill(r.begin(), r.end(), '0');
int b = 0;
int e = ~b;
const int c = 10;
for(int i = l+e; i != e;)
{
int d = (s[i]-0x30) * x, p = i + b;
while (d && p > e)
{
int t = r[p] - 0x30 + (d % c);
r[p] = (t % c) + 0x30;
d = t / c + d / c;
p--;
}
while (d)
{
r = static_cast<char>((d % c) +0x30)+r;
d /= c;
b++;
}
i--;
}
return r;
}
In C++, the largest integer type is 'long long', and it hold 64 bits of memory, so obviously you can't store 250! in an integer type. It is a clever idea to use strings, but what you are basically doing with your code is (I have never used the atoi() function, so I don't know if it even works with strings larger than 1 character, but it doesn't matter):
covert the string to integer (a string that if this code worked well, in one moment contains the value of 249!)
multiply the value of the string
So, after you are done multiplying, you don't even convert the integer back to string. And even if you did that, at one moment when you convert the string back to an integer, your program will crash, because the integer won't be able to hold the value of the string.
My suggestion is, to use some class for big integers. Unfortunately, there isn't one available in C++, so you'll have to code it by yourself or find one on the internet. But, don't worry, even if you code it by yourself, if you think a little, you'll see it's not that hard. You can even use your idea with the strings, which, even tough is not the best approach, for this problem, will still yield the results in the desired time not using too much memory.
This is a typical high precision problem.
You can use an array of unsigned long long instead of string.
like this:
struct node
{
unsigned long long digit[100000];
}
It should be faster than string.
But You still can use string unless you are urgent.
It may take you a few days to calculate 10000!.
I like use string because it is easy to write.
#include <bits/stdc++.h>
#pragma GCC optimize (2)
using namespace std;
const int MAXN = 90;
int n, m;
int a[MAXN];
string base[MAXN], f[MAXN][MAXN];
string sum, ans;
template <typename _T>
void Swap(_T &a, _T &b)
{
_T temp;
temp = a;
a = b;
b = temp;
}
string operator + (string s1, string s2)
{
string ret;
int digit, up = 0;
int len1 = s1.length(), len2 = s2.length();
if (len1 < len2) Swap(s1, s2), Swap(len1, len2);
while(len2 < len1) s2 = '0' + s2, len2++;
for (int i = len1 - 1; i >= 0; i--)
{
digit = s1[i] + s2[i] - '0' - '0' + up; up = 0;
if (digit >= 10) up = digit / 10, digit %= 10;
ret = char(digit + '0') + ret;
}
if (up) ret = char(up + '0') + ret;
return ret;
}
string operator * (string str, int p)
{
string ret = "0", f; int digit, mul;
int len = str.length();
for (int i = len - 1; i >= 0; i--)
{
f = "";
digit = str[i] - '0';
mul = p * digit;
while(mul)
{
digit = mul % 10 , mul /= 10;
f = char(digit + '0') + f;
}
for (int j = 1; j < len - i; j++) f = f + '0';
ret = ret + f;
}
return ret;
}
int main()
{
freopen("factorial.out", "w", stdout);
string ans = "1";
for (int i = 1; i <= 5000; i++)
{
ans = ans * i;
cout << i << "! = " << ans << endl;
}
return 0;
}
Actually, I know where the problem raised At the point where we multiply , there is the actual problem ,when numbers get multiplied and get bigger and bigger.
this code is tested and is giving the correct result.
#include <bits/stdc++.h>
using namespace std;
#define mod 72057594037927936 // 2^56 (17 digits)
// #define mod 18446744073709551616 // 2^64 (20 digits) Not supported
long long int prod_uint64(long long int x, long long int y)
{
return x * y % mod;
}
int main()
{
long long int n=14, s = 1;
while (n != 1)
{
s = prod_uint64(s , n) ;
n--;
}
}
Expexted output for 14! = 87178291200
The logic should be:
unsigned int factorial(int n)
{
unsigned int b=1;
for(int i=2; i<=n; i++){
b=b*n;
}
return b;
}
However b may get overflowed. So you may use a bigger integral type.
Or you can use float type which is inaccurate but can hold much bigger numbers.
But it seems none of the built-in types are big enough.

Using pow() for large number

I am trying to solve a problem, a part of which requires me to calculate (2^n)%1000000007 , where n<=10^9. But my following code gives me output "0" even for input like n=99.
Is there anyway other than having a loop which multilplies the output by 2 every time and finding the modulo every time (this is not I am looking for as this will be very slow for large numbers).
#include<stdio.h>
#include<math.h>
#include<iostream>
using namespace std;
int main()
{
unsigned long long gaps,total;
while(1)
{
cin>>gaps;
total=(unsigned long long)powf(2,gaps)%1000000007;
cout<<total<<endl;
}
}
You need a "big num" library, it is not clear what platform you are on, but start here:
http://gmplib.org/
this is not I am looking for as this will be very slow for large numbers
Using a bigint library will be considerably slower pretty much any other solution.
Don't take the modulo every pass through the loop: rather, only take it when the output grows bigger than the modulus, as follows:
#include <iostream>
int main() {
int modulus = 1000000007;
int n = 88888888;
long res = 1;
for(long i=0; i < n; ++i) {
res *= 2;
if(res > modulus)
res %= modulus;
}
std::cout << res << std::endl;
}
This is actually pretty quick:
$ time ./t
./t 1.19s user 0.00s system 99% cpu 1.197 total
I should mention that the reason this works is that if a and b are equivalent mod m (that is, a % m = b % m), then this equality holds multiple k of a and b (that is, the foregoing equality implies (a*k)%m = (b*k)%m).
Chris proposed GMP, but if you need just that and want to do things The C++ Way, not The C Way, and without unnecessary complexity, you may just want to check this out - it generates few warnings when compiling, but is quite simple and Just Works™.
You can split your 2^n into chunks of 2^m. You need to find: `
2^m * 2^m * ... 2^(less than m)
Number m should be 31 is for 32-bit CPU. Then your answer is:
chunk1 % k * chunk2 * k ... where k=1000000007
You are still O(N). But then you can utilize the fact that all chunk % k are equal except last one and you can make it O(1)
I wrote this function. It is very inefficient but it works with very large numbers. It uses my self-made algorithm to store big numbers in arrays using a decimal like system.
mpfr2.cpp
#include "mpfr2.h"
void mpfr2::mpfr::setNumber(std::string a) {
for (int i = a.length() - 1, j = 0; i >= 0; ++j, --i) {
_a[j] = a[i] - '0';
}
res_size = a.length();
}
int mpfr2::mpfr::multiply(mpfr& a, mpfr b)
{
mpfr ans = mpfr();
// One by one multiply n with individual digits of res[]
int i = 0;
for (i = 0; i < b.res_size; ++i)
{
for (int j = 0; j < a.res_size; ++j) {
ans._a[i + j] += b._a[i] * a._a[j];
}
}
for (i = 0; i < a.res_size + b.res_size; i++)
{
int tmp = ans._a[i] / 10;
ans._a[i] = ans._a[i] % 10;
ans._a[i + 1] = ans._a[i + 1] + tmp;
}
for (i = a.res_size + b.res_size; i >= 0; i--)
{
if (ans._a[i] > 0) break;
}
ans.res_size = i+1;
a = ans;
return a.res_size;
}
mpfr2::mpfr mpfr2::mpfr::pow(mpfr a, mpfr b) {
mpfr t = a;
std::string bStr = "";
for (int i = b.res_size - 1; i >= 0; --i) {
bStr += std::to_string(b._a[i]);
}
int i = 1;
while (!0) {
if (bStr == std::to_string(i)) break;
a.res_size = multiply(a, t);
// Debugging
std::cout << "\npow() iteration " << i << std::endl;
++i;
}
return a;
}
mpfr2.h
#pragma once
//#infdef MPFR2_H
//#define MPFR2_H
// C standard includes
#include <iostream>
#include <string>
#define MAX 0x7fffffff/32/4 // 2147483647
namespace mpfr2 {
class mpfr
{
public:
int _a[MAX];
int res_size;
void setNumber(std::string);
static int multiply(mpfr&, mpfr);
static mpfr pow(mpfr, mpfr);
};
}
//#endif
main.cpp
#include <iostream>
#include <fstream>
// Local headers
#include "mpfr2.h" // Defines local mpfr algorithm library
// Namespaces
namespace m = mpfr2; // Reduce the typing a bit later...
m::mpfr tetration(m::mpfr, int);
int main() {
// Hardcoded tests
int x = 7;
std::ofstream f("out.txt");
m::mpfr t;
for(int b=1; b<x;b++) {
std::cout << "2^^" << b << std::endl; // Hardcoded message
t.setNumber("2");
m::mpfr res = tetration(t, b);
for (int i = res.res_size - 1; i >= 0; i--) {
std::cout << res._a[i];
f << res._a[i];
}
f << std::endl << std::endl;
std::cout << std::endl << std::endl;
}
char c; std::cin.ignore(); std::cin >> c;
return 0;
}
m::mpfr tetration(m::mpfr a, int b)
{
m::mpfr tmp = a;
if (b <= 0) return m::mpfr();
for (; b > 1; b--) tmp = m::mpfr::pow(a, tmp);
return tmp;
}
I created this for tetration and eventually hyperoperations. When the numbers get really big it can take ages to calculate and a lot of memory. The #define MAX 0x7fffffff/32/4 is the number of decimals one number can have. I might make another algorithm later to combine multiple of these arrays into one number. On my system the max array length is 0x7fffffff aka 2147486347 aka 2^31-1 aka int32_max (which is usually the standard int size) so I had to divide int32_max by 32 to make the creation of this array possible. I also divided it by 4 to reduce memory usage in the multiply() function.
- Jubiman