寻找最大的阶乘n，intiger允许！ C ++

Question

Sorry for bad English.
So my problem is that i need to find all possible factorials starting from 1. I need it to stop when Int have maximum memory used and print out maximum factorial value. My code is pretty simple, but i do not know how to get to stop loop when it reach maximum of Intiger values.

 #include <iostream>
 #include<climits>//
 #include <cmath>
 using namespace std;

 int main() {

int k,n=0;
unsigned  int factorial = 1;
unsigned  int factorial2=1;
unsigned  uval=INT_MAX;

cout << "Ievadi koeficentu k: ";
cin >> k;
for(int i = 1; i<=k; ++i) {
    factorial *= i;
}
cout << "Ievadita koeficenta " << k << " faktorials " << " = " <<factorial;

cout << "\nVisi iespejamie faktoriali no 1 - n: ";
for(int s = 1; s<=uval; ++s) {

    factorial2 *= s;
   if( s < uval / factorial2 ){
      cout  <<" \nkoeficenta " << s << " faktorials ir ==> " <<factorial2;
   }
}




return 0;
}

The problem is that the loop is going to calculate factorial to all UINT_MAX values, and most of the output will be 0 becouse memory is overloaded. But it should stop before it goes bigger that UINT_MAX memory! Hope you all understand my problem and will help me with this.

Answer 1

If factorial2 > UINT_MAX / (s+1) , the next factorial can't be calculated.

By the way, you should use unsigned int for factorial2

Answer 2

Before calculating the next factorial in the list, see if the previous one is greater than UINT_MAX / i . If it is, you know that the next multiplication will go out of bounds.

Answer 3

In a 32-bit signed integer, 12! is the largest possible.

You can check this by doing

if (INT_MAX / fact_so_far < n)
{
   std::cout << "Max factorial " << n-1 << std::endl;
}

[This code STOPS when it reaches the "unable to calculate", because INT_MAX / fact_so_far will not multiply without overflow].

if (INT_MAX / fact_so_far >= n)
{
    fact_so_far *= n;
}
else
{
    std::cout << n << " is too large to calculate factorial" << std::endl;
}

would be the other way to do this. [Obviously with suitable loop to increment n ]

Not that MAX_UINT is the max value for unsigned int , not for int [it's typically half that].

Edit to explain the logic:

The logic here is that if we divide INT_MAX with what our current factorial value is, it should produce a value larger than n [the current multiplier for the next factorial].

As a simple step through example, we pick a MAX_INT of 127:

Initial state:

factorial = 1, n = 1; 

Steps:

n = 2, MAX_INT / factorial = 127 -> factorial *= n => 2
n = 3, MAX_INT / factorial = 63 -> factorial *= n => 6
n = 4, MAX_INT / factorial = 21 -> factorial *= n => 24
n = 5, MAX_INT / factorial = 5 -> factorial *= n = 120
n = 6, MAX_INT / factorial = 1 -> FAIL - will overflow.

Answer 4

您正在将带符号的int与无符号的int进行比较，即您正在执行i <UINT_MAX（这是无符号的int的最大值），这是错误的，将导致溢出和错误的条件检查。

Answer 5

so i finaly did this with my code. Now it works but its not realy good. Maybe someone someday will need something like this as a start for his own max factorial programm. First program will ask you to insert a random number and then it calculate its factorial (only in max int borders). Then it prints out all possible int factorials. Its show only 11! as max but the max is 12! I add factorial 12! manualy, becouse the if statment cannot print out excatly the number 12 as max it prints one before. And in the end the programm shows you what is maxium possible factorial for intiger.

#include <iostream>
#include<climits>//
#include <cmath>
using namespace std;

int main() {
int k, max,s;
unsigned  int factorial = 1;
unsigned  int factorial2 = 1;
unsigned  uval=INT_MAX;

cout << "Ievadi koeficentu k: ";
cin >> k;
for(int i = 1; i<=k; ++i) {
    factorial *= i;
}
cout << "Ievadita koeficenta " << k << " faktorials " << " = " <<factorial;

cout << "\nVisi iespejamie faktoriali no 1 - n: ";
for( s = 1; s<=uval; ++s) {

    factorial2 *= s;
    max=factorial2;

if( s <= uval / factorial2 ){
cout  <<" \nkoeficenta " << s << " faktorials ir ==> " <<factorial2;

}
else {
        break;
}
    }
cout  <<" \nkoeficenta " << s << " faktorials ir ==> " <<factorial2;
cout  <<" \nMaksimalais faktorials ir skaitla " << s << " faktorials ==> " <<max;



return 0;
}

This is what the programm looks like!

![Programm][1]