[Project Euler] Problem 9

A Pythagorean triplet is a set of three natural numbers, a b c, for which,

a² + b² = c²

For example, 3² + 4² = 9 + 16 = 25 = 5².

There exists exactly one Pythagorean triplet for which a + b + c = 1000.
Find the product abc.

寻找和为1000毕达哥拉斯三元数组，求它们的积

由于a b c，我们容易得到a的范围

a < 1000/(1+1+1.414); 估算有 a < 300;

   
     

    
      #include 
    
      <
    
      iostream
    
      >
    
      

    
      using
    
       
    
      namespace
    
       std;


    
      int
    
       main(){
 
    
      for
    
      (
    
      int
    
       a
    
      =
    
      1
    
      ; a
    
      <
    
      300
    
      ; a
    
      ++
    
      ){
 
    
      for
    
      (
    
      int
    
       b
    
      =
    
      (
    
      1000
    
      -
    
      a)
    
      /
    
      2
    
      ; b
    
      >
    
      a; b
    
      --
    
      ){
 
    
      if
    
      (a
    
      *
    
      a
    
      +
    
      b
    
      *
    
      b 
    
      ==
    
       (
    
      1000
    
      -
    
      a
    
      -
    
      b)
    
      *
    
      (
    
      1000
    
      -
    
      a
    
      -
    
      b)){
 cout 
    
      <<
    
       a
    
      *
    
      b
    
      *
    
      (
    
      1000
    
      -
    
      a
    
      -
    
      b) 
    
      <<
    
       endl;
 
    
      return
    
       
    
      0
    
      ;
 }
 }
 }
 
    
      return
    
       
    
      0
    
      ;
}
   
     

事实上，我们不能确认这样的数只有一组，所以中间那个 “return 0;”应该去掉