3.cpp File Reference

#include <iostream>

Include dependency graph for 3.cpp:

Go to the source code of this file.

Functions
int	main ()

Function Documentation

main()

int main

(

void

)

Definition at line 9 of file 3.cpp.

          {
    int n,a,b,c;
    cin >> n;
    // given a+b+c=n and a<=b<=c
    // a+b>=c (triangle inequality)
    // a+b+c>=2c (add c)
    // c<=n/2 (obtain an upper bound of c)
 
    // since a*a+b*b=c*c therefore b*b<c*c b<c
    // assume a=b, then 2a*a=c*c, c=sqrt(2)*a
    // where c is not an integer, contradicts "int c" requirement
    // therefore a<=b can be simplified as a<b
 
    // assume b=c, then a*a=0 -> a=0 (rej.)
    // .'. b<=c can be simplifies as b<c
    // a+b+c=n -> 3c>n -> c>n/3
 
    // since c<=n/2 -> n-c>=n/2
    // a+b+c=n -> 2b>n-c -> b>n/4
 
    // we want output sort in ascending order of a
    // b+c=n-a -> 2b<n-a, when a increase b decrease
    // a+c=n-b -> 2c>=n-b, when b decrease c decrease
    // which means descending order of b and c
    for (c=n/2;c>n/3;c--){
        for (b=c-1;b>n/4;b--){
            a=n-c-b;
            // since the lower bound of b and c are too small, check a<b<c
            if ((a*a+b*b==c*c) && (a<b) && (b<c)){
                cout << a << " " << b << " " << c << "\n";
            }
        }
    }
    return 0;
}