Problem 45 Triangular, pentagonal, and hexagonal （暴力）

朱雀 2022-07-15 02:50 233阅读 0赞

## Triangular, pentagonal, and hexagonal ##

### Problem 45 ###

Triangle, pentagonal, and hexagonal numbers are generated by the following formulae:

<table> 
 <tbody> 
  <tr> 
   <td><span style="font-size:18px">Triangle</span></td> 
   <td><span style="font-size:18px"><br> </span></td> 
   <td><span style="font-size:18px">T<sub><em>n</em></sub>=<em>n</em>(<em>n</em>+1)/2</span></td> 
   <td><span style="font-size:18px"><br> </span></td> 
   <td><span style="font-size:18px">1, 3, 6, 10, 15, ...</span></td> 
  </tr> 
  <tr> 
   <td><span style="font-size:18px">Pentagonal</span></td> 
   <td><span style="font-size:18px"><br> </span></td> 
   <td><span style="font-size:18px">P<sub><em>n</em></sub>=<em>n</em>(3<em>n</em>−1)/2</span></td> 
   <td><span style="font-size:18px"><br> </span></td> 
   <td><span style="font-size:18px">1, 5, 12, 22, 35, ...</span></td> 
  </tr> 
  <tr> 
   <td><span style="font-size:18px">Hexagonal</span></td> 
   <td><span style="font-size:18px"><br> </span></td> 
   <td><span style="font-size:18px">H<sub><em>n</em></sub>=<em>n</em>(2<em>n</em>−1)</span></td> 
   <td><span style="font-size:18px"><br> </span></td> 
   <td><span style="font-size:18px">1, 6, 15, 28, 45, ...</span></td> 
  </tr> 
 </tbody> 
</table>

It can be verified that T285 = P165 = H143 = 40755.

Find the next triangle number that is also pentagonal and hexagonal.

<table> 
 <tbody> 
  <tr> 
   <td> 
    <table> 
     <tbody> 
      <tr> 
       <td> 
        <div style="text-align:right"> 
         <span style="font-size:18px">Answer:</span> 
        </div> </td> 
       <td><strong><span style="font-size:18px">1533776805</span></strong></td> 
      </tr> 
      <tr> 
       <td colspan="2"><span style="color:rgb(153,153,153)"><span style="font-size:18px">Completed on Sun, 30 Oct 2016, 12:17</span></span></td> 
      </tr> 
     </tbody> 
    </table> </td> 
  </tr> 
 </tbody> 
</table>

代码：

#include <iostream>
    #include <cmath>
    using namespace std;
     
    int main()
    {
        int n = 143;
        while (1)
        {
        	n++;
        	//Hexagonal
            double h = n * (2 * n - 1); 
            double Triangle = (sqrt(1 + 8 * h) - 1) / 2;
            double Pentagonal = (sqrt(1 + 24 * h) + 1) / 6;
            double T = (int)Triangle;
            double P = (int)Pentagonal;
     
            if (T == Triangle && P == Pentagonal)
            {
                long long ans = n * (2 * n - 1);  
                cout<<ans<<endl;
                break;
            } 
        }
        return 0;
    }

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