Question

I am trying Pascal Triangle solution in C, based on below formula:

I wrote the below code based on above formula:

#include <stdio.h>
#include <stdlib.h>

int pascalTriangle(int row, int col);

int main()
{
  int row, col;

  printf("Enter the row [0 to n]: ");
  scanf("%i", &row);
  printf("Enter the column [0 to m]: ");
  scanf("%i", &col);

  if(col > row) {
    printf("Error: column can be less than or equal to row\n");
    exit(1);
  }

  printf("Value = %i\n", pascalTriangle(row, col));
  return 0;
}

int pascalTriangle(int row, int col)
{
  int value[100];
  value[0]=1;
  int i=1;
  if(row==0 || row==col || col==0) {
    return value[0];
  } else {
row=row+1;
    while(i<=col) {
        printf("i = %i\trow = %i\tcol = %i\n", i, row, col);
        value[i]='\0';
        value[i]=(value[i-1]) * ((row-i)/i);
        printf("value[%i] = %i\tvalue[%i] = %i\n", i-1, value[i-1], i, value[i]);
        ++i;
    }
    return value[i-1];
  }
}

Here, upto some extent it is giving proper O/P. But, for many I/Ps I found wrong answers. I am unable to find the logical error, as on paper the logic is giving expected O/P. Example:- I give row=4 & col=2, O/P should be 6 but getting 4 as O/P.

Please help!!

Answer 1

The line

value[i]=(value[i-1]) * ((row-i)/i);

is wrong. row - ineed not be divisible by i (it generally isn’t). You need to first multiply and then divide,

value[i]=(value[i-1] * (row-i))/i;

(parentheses not necessary since they are implicitly placed thus), but then you have earlier overflow, so for larger values of row, compute the gcd,

int g = gcd(row - i, i)

and divide (row - i) / g, value[i-1]/(i/g)and multiply the results of these.