Pascal's triangle/Puzzle: Difference between revisions

=={{header|C}}==

This solution is based upon algebraic necessities, namely that a solution exists when (top - 4(a+b))/7 is integral. It also highlights the type difference between floating point numbers and integers in C.

<lang c>

/* Pascal's pyramid solver

*

* [top]

* [ ] [ ]

* [mid] [ ] [ ]

* [ ] [ ] [ ] [ ]

* [ x ] [ a ] [ y ] [ b ] [ z ]

* x + z = y

*

* This solution makes use of a little bit of mathematical observation,

* such as the fact that top = 4(a+b) + 7(x+z) and mid = 2x + 2a + z.

*/

#include <stdio.h>

#include <math.h>

void pascal(int a, int b, int mid, int top, int* x, int* y, int* z)

{

double ytemp = (top - 4 * (a + b)) / 7.;

if(fmod(ytemp, 1.) >= 0.0001)

{

x = 0;

return;

}

*y = ytemp;

*x = mid - 2 * a - *y;

*z = *y - *x;

}

int main()

{

int a = 11, b = 4, mid = 40, top = 151;

int x, y, z;

pascal(a, b, mid, top, &x, &y, &z);

if(x != 0)

printf("x: %d, y: %d, z: %d\n", x, y, z);

else printf("No solution\n");

return 0;

}

</lang>

Output:

<pre>

x: 3, y: 13, z: 10

</pre>