/*
 * pythagorean.c  | Jim Mahoney | Aug 2018
 * projecteuler.net #9 ; overflow example from "Computer Systems" text
 *
 *   $ gcc pythagorean.c -o pythagorean ; ./pythagorean
 *   sum =   1000  : a=200, b=375, c=425
 *
 * So far so good.
 *
 * Changing the "int sum = 1000;" line to make the sum bigger,
 * recompiling and rerunning gives these results:
 *
 *   sum =  10000  : a=2000, b=3750, c=4250
 *   sum = 100000  : a=5408,  b=69844, c=24748         b > c ???  OOPS!!
 *
 * The last result is clearly incorrect, since b is bigger than c.
 * But the code compiled and ran without warnings or errors.
 *
 * Your mission : explain what's going on, in detail.
 * 
 * Answer : It's all about integer sizes and overflow.
 * And the result will depend on your C compiler settings.
 * The printf() statements below illustrate the issue.
 *
 */
#include <stdio.h>
#include <stdlib.h>

int main(){
  int a, b, c;
  int sum = 100000;
  
  printf("sizeof(int) == %lu ; max is %lu \n",
  	 sizeof(int), (1lu << (8*sizeof(int)-1))-1);
  printf("sizeof(long int) == %lu ; max is %lu \n",
  	 sizeof(long int), (1lu << (8*sizeof(long int)-1))-1);
  printf("- - - - - - - - - - - \n");
  
  printf("Looking for a,b,c such that a**2+b**2=c**2 and a+b+c=%i ...\n", sum);
  for (a = 1; a < sum - 2; a++){
    for (b = a+1; b < sum - 2; b++){
      c = sum - a - b;
      if (a*a + b*b == c*c){
	printf("a = %i, b = %i, c = %i \n", a, b, c);
	
	printf(" a * a = %i \n", a*a);
	printf(" b * b = %i \n", b*b);
	printf(" c * c = %i \n", c*c);
	
	return 0;
      }
    }
  }
  printf("no solution found.\n");
  return 0;
}