查找大数的阶乘（位数> 20）

Question

我写了一些 C++ 代码来找到 int n 的阶乘。由于阶乘可能是一个非常大的数字，所以我决定将数字存储在一个向量中。但我的代码没有按预期工作。有些人请指出错误并指导我。我低调的感觉就像我搞砸了指针。 请建议是否有更优化的方法。 感谢社区。​​p>

守则：

    #include <iostream>
    #include <vector>
    #include <algorithm>
    using std::cout;
    using std::endl;
    using Digits = std::vector<int>;
    
    //define the length of the array, should be the maximum number of digits in the factorial(n)
    #define MAX 20
    
    void multiply(int x,Digits res,int res_size){
      int carry=0;
      for(int i=0;i<res_size;i++){
          int prod=carry+ x*res[i];
          res[i] = prod%10;
          carry = prod/10;
      }
    
      while(carry){
          res[res_size] = carry%10;
          carry/=10;
          (res_size)++;
      }
    }
    
    Digits factorial(int n){
      Digits res(MAX);  
      res[0] = 1;
      int res_size=1;
      for(int i=2;i<=n;i++){
          multiply(i,res,res_size);
      }
      reverse(res.begin(),res.end());
      return res;
    }
    
    int main(){
      for(auto i: factorial(20)){
        cout << i;     
      }cout << endl;
      return 0;
    }

输出：

10000000000000000000
 
[Done] exited with code=0 in 3.204 seconds

Answer 1

我看到一些错误：

#define MAX 20

    void multiply(int x,vector<int> res,int* res_size){ // should be .. void multiply(int x,vector<int> res,int &res_size)
      int carry=0;
      for(int i=0;i<*res_size;i++){
          int prod=carry+ x*res[i];
          res[i] = prod%10;
          carry = prod/10;
      }
    
      while(carry){
          res[*res_size] = carry%10;
          carry/=10;
          (*res_size)++;
      }
    }
    
    vector<int> factorial(int n){
      vector<int> res(MAX);
      res[0] = 1;
      int res_size=1;
      for(int i=2;i<=n;i++){
          multiply(i,res,&res_size); // should be ... multiply(i,res,res_size)
      }
      return res;
    }

总计：

void multiply(int x,vector<int> res,int &res_size){
cout << &res_size<< endl; // print address of "res_size"
  int carry=0;
  for(int i=0;i<res_size;i++){
      int prod=carry+ x*res[i];
      res[i] = prod%10;
      carry = prod/10;
  }

  while(carry){
      res[res_size] = carry%10;
      carry/=10;
      (res_size)++;
  }
}

vector<int> factorial(int n){
  vector<int> res(MAX);
  res[0] = 1;
  int res_size=1;
  for(int i=2;i<=n;i++){
      multiply(i,res,res_size);
  }
  return res;
}




cout << &res_size<< endl; // prints out the address where the value is stored.

int* res_size // stores the reference ( adddress )

Pointers

#include <iostream>
using namespace std;

    int main ()
    {
      int firstvalue, secondvalue;
      int * mypointer;
    
      mypointer = &firstvalue;
      *mypointer = 10;
      mypointer = &secondvalue;
      *mypointer = 20;
      cout << "firstvalue is " << firstvalue << '\n';
      cout << "secondvalue is " << secondvalue << '\n';
      return 0;
    }

指针可以远程控制原始值在哪里存储在 ram 中。

而不是在代码中到处复制。

看看这个视频，很不错
Introduction to pointers in C/C++

Pointers and dynamic memory - stack vs heap

mycodeschool

Answer 2

固定版本：

#include <vector>
#include <iostream>
using namespace std;

//define the length of the array, should be the maximum number of digits in the factorial(n)
#define MAX 20

void multiply(int x, vector<int>& res, int* res_size) {
    int carry = 0;
    for (int i = 0; i < *res_size; i++) {
        int prod = carry + x * res[i];
        res[i] = prod % 10;
        carry = prod / 10;
    }

    while (carry) {
        res[*res_size] = carry % 10;
        carry /= 10;
        (*res_size)++;
    }
}

vector<int> factorial(int n) {
    vector<int> res(MAX);
    res[0] = 1;
    int res_size = 1;
    for (int i = 2; i <= n; i++) {
        multiply(i, res, &res_size);
    }
    return res;
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    for (auto i : factorial(20)) {
        cout << i;
    }cout << endl;
    return 0;
}

要通过引用传递，只需在参数类型后添加&。 另请参阅 Why should I not #include <bits/stdc++.h>? 和 Why is "using namespace std;" considered bad practice?。

有关按值传递和按引用传递的更多信息，您可以查看此处：https://www.educative.io/edpresso/pass-by-value-vs-pass-by-reference。

基本上，按值传递会创建原始类型的副本，而按引用传递会传递对原始副本的引用，因此修改引用就是修改原始值。

此外，指针和引用非常相似，尽管当您想要修改传递给函数的变量时，我会使用引用。更多信息：https://www.tutorialspoint.com/pointers-vs-references-in-cplusplus#:~:text=References%20are%20used%20to%20refer,to%20store%20address%20of%20variable.&text=A%20reference%20shares%20the%20same,and%20size%20on%20the%20stack。