二项式系数表的C程序

given with a positive integer value let’s say ‘val’ and the task is to print the value of binomial coefficient b(n, k) where, n and k be any value between 0 to val and hence display the result.

What is Binomial Coefficient

Binomial coefficient (n, k) is the order of choosing ‘k’ results from the given ‘n’ possibilities. The value of binomial coefficient of positive n and k is given by

$$C_k^n=\frac{n!}{(n-k)!k!}$$

where, n >= k

Example

示例

Input-: B(9,2)
Output-:

$$B_2^9=\frac{9!}{(9-2)!2!}$$ 

$$\frac{9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{6\times 5\times 4\times 3\times 2\times 1)\times 2\times 1}=\frac{362,880}{1440}=252$$

What is Binomial Coefficient Table

The Binomial Coefficient Table is formed for calculating the multiple values that can be generated between n and k.

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Example

示例

Input-: value = 5
Output-:

Approach used in the below program is as follows −

• Input the variable ‘val’ from the user for generating the table
• Start the loop from 0 to ‘val’ because the value of binomial coefficient will lie between 0 to ‘val’

• Apply the formula given, if n and k is not 0

  B(m, x) = B(m, x - 1) * (m - x + 1) / x

• Print the result

Algorithm

START
Step 1-> declare function for binomial coefficient table
   int bin_table(int val)
   Loop For int i = 0 and i <= val and i++
      print i
      Declare int num = 1
      Loop For int j = 0 and j <= i and j++
      If (i != 0 && j != 0)
         set num = num * (i - j + 1) / j
      End
         print num
   End
   print 

Step 2-> In main()
   Declare int value = 5
   call bin_table(value)
STOP

Example

示例

#include 
// Function for binomial coefficient table
int bin_table(int val) {
   for (int i = 0; i <= val; i++) {
      printf("%2d", i);
      int num = 1;
      for (int j = 0; j <= i; j++) {
         if (i != 0 && j != 0)
         num = num * (i - j + 1) / j;
         printf("%4d", num);
      }
      printf("
");
   }
}
int main() {
   int value = 5;
   bin_table(value);
   return 0;
}

输出