The exact value of the factorial of the "algorithmic race get started classic"

The exact value of the factorial of the "algorithmic race get started classic"

Problem description

Enter a positive integer of not more than 1000 N, output n! = 1x2x3x4x Accurate results of Xn.

Example input: 5
Sample output: 120

Algorithm analysis

We need to address two questions:

How to save Results

What is the multiplication process?

For the first question: because the factorial of 1000 is not saved with an integer, as with double, it will be more than 2000 bits, save the number of bits of the factorial value, we can only use an array, where a size of 3000 is used;

For the second question: we can simulate the mathematical multiplication process, take 1 as the base number, and deposit the array, starting with 2, then multiplying each bit in the array of the existing base number, setting a carry identifier, and then storing the result in the array; The first bit of storage, followed by 10 bits, hundred, thousands, and so on, the final result from the back to the output, the output needs to be the back of the excess 0 removed. (from the single-bit can also avoid meaningless 0 and a meaningful mix of 0, such as 5 of the factorial of 120, there is an array of 0, 1, 2, if it is in accordance with 120, the last 0 will be confused with the remaining 2,997 0, increasing the difficulty of processing)

Code implementation

#include <stdio.h>#include <string.h>#include <stdlib.h>Const intMAXN = the;intF[MAXN];intMain () {intI, J, N; while(scanf_s ("%d", &n)) {memset(F,0,sizeof(f)); f[0] =1; for(i =2; I <= N; i++) {//Multiply I            intc =0;//c is rounding .             for(j =0; J < Maxn; J + +) {ints = f[j] * i + C;//s is 3,000 bits multiplied by I plus carryF[J] = s%Ten;//Current bit storage bitsc = S/Ten;//Carry ID}        } for(j = maxn-1; J >=0; j--) {if(F[j]) Break;//From back to front, in turn remove the number of bits of 0}//Output Results         for(i = j; I >=0; i--)printf("%d", F[i]);printf("\ n"); } System ("Pause");return 0;}

The exact value of the factorial of the "algorithmic race get started classic"