What is Pascal Triangle?
The Pascal triangle is a triangular array of binomial coefficients. It looks like this:
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1 2 3 4 5 6 |
row -> 0 1 row -> 1 1 1 row -> 2 1 2 1 row -> 3 1 3 3 1 row -> 4 1 4 6 4 1 row -> 5 1 5 10 10 5 1 |
The following is a formula to compute the value at any given place in the triangle:
where n stands for the row number and k stands for the column number. Note that the rows start from 0 and also the leftmost column is 0. So, to find out the value at 4th row, 2nd col, we do this:
The following is a C program which prints the pascal triangle based upon the number of rows entered by the user:
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 |
/************************************** * C Program to print Pascal Triangle ***************************************/ #include<stdio.h> // include stdio.h unsigned long int factorial(unsigned long int); int main() { int n; printf("Enter number of rows: "); scanf("%d", &n); printf("\n"); // loop for number of rows for(int i = 0; i <= n; i++) { // loop to print leading spaces at each line for(int space = 0; space < n - i; space++) { printf(" "); } // loop to print numbers in each row for(int j = 0; j <= i; j++) { printf("%-5d ", factorial(i) / (factorial(j) * factorial(i-j) ) ); } // print newline character printf("\n"); } return 0; } unsigned long int factorial(unsigned long int n) { unsigned long int f = 1; while(n > 0) { f = f * n; n--; } return f; } |
Expected Output:
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1 2 3 4 5 6 7 8 9 10 11 12 13 |
Enter number of rows: 10 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1 1 9 36 84 126 126 84 36 9 1 1 10 45 120 210 252 210 120 45 10 1 |
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