Pascal's triangle

Question

I am looking for a Pascal's triangle using a Python script.

I have done till here and don’t have any idea how to add on.

numstr = raw_input("Please enter the height: ")
height = int()

tri = []

row1 = [1]
row2 = [1, 1]
tri.append(row1)
tri.append(row2)

while len(tri) < height:

Answer 1

Note that the Pascal's Triangle is just the coefficients of the expansion of any binomial expression, so you can just use the formula for n choose k, that is, n!/k!(n-k)! where n represents the row, and k represents the column to actually print out the digits. You can then just make another function to space out the triangle properly, if you want(but the problem is, after 5 rows, it just becomes uneven due to the double digits). Here's a sort of pseudocode:

for row in rows:
number = 1
for space in rows-1 step -1:
    print " "
for column in row+1:
    print number
    number = row!/column!(row-column)!
print new line

Answer 2

This is Python code for Pascal's triangle:

# Python code for Pascal's triangle
# printPascal() function for printing Pascal's triangle.
def printPascal(N):
    # Declaring two arrays
    arr = [1]
    temp = []

    print("Pascal's triangle of", N, "Rows...")
    # Calculating the next rows.
    for i in range(N):
        # printing current row.
        print("rows", i+1, end=" : ")
        for j in range(len(arr)):
            print(arr[j], end=' ')
        print()

        # Calculating the next rows.
        temp.append(1)
        for j in range(len(arr)-1):
            temp.append(arr[j] + arr[j + 1])
        temp.append(1)

        # Copy the next row to the current row.
        arr = temp
        # Initialize temp to an empty array.
        temp = []


# Driver code
N = 9
printPascal(N)

For more details: https://algorithmdotcpp.blogspot.com/2021/07/print-n-rows-of-pascals-triangle-in-cpp-and-python.html

Answer 3

C# solution:

public IList<IList<int>> Generate(int numRows) {
    var result = new List<IList<int>>();
        var item1 = new List<int>();
        item1.Add(1);
        result.Add(item1);

        if (numRows == 1)
            return result;

        var item2 = new List<int>();
        item2.Add(1);
        item2.Add(1);
        result.Add(item2);

        if (numRows == 2)
            return result;

        var i = 2;
        while (i != numRows)
        {
            var data = result.Last().ToArray();
            var n = data.Length;
            var item = new int[n + 1];
            item[0] = 1;
            item[n] = 1;
            for (var x = 1; x < n; x++)
                item[x] = data[x - 1] + data[x];
            result.Add(item);
            i++;
        }

    return result;
}

Answer 4

Use:

// C++ code for Pascal's triangle
#include <stdio.h>
#include <ctype.h>
#include <conio.h>
#include <time.h>
#include <stdlib.h>

long unsigned int Factorial(long unsigned int Number)
{
    long unsigned int Fact = 0;
    if (Number == 0)
        return (long unsigned int) 1;
    else
    {
       Fact = Number*Factorial(Number-1);
       return Fact;
    }
}

long unsigned int Combination(long unsigned int num1, long unsigned int num2)
{
    long unsigned int Comb, num3;
    long unsigned int Factor1, Factor2, Factor3;
    Factor1 = Factorial(num1);
    Factor2 = Factorial(num2);
    num3 = num1 - num2;
    Factor3 = Factorial(num3);
    Comb = Factor1/(Factor2*Factor3);

    return(Comb);
}

int main()
{
    long unsigned int i, j, Num=0;
    long unsigned int **Matrix;
    clrscr();
    printf(" %d\n ", sizeof(long unsigned int));
    printf("Enter index of square matrix num: ");
    scanf("%lu", &Num);

    Matrix = (long unsigned int **) malloc(Num*Num*sizeof(long unsigned int *));

    for(i=0; i<Num; i++)
    {
        for (j=0; j<Num; j++)
        {
            *(*(Matrix+i)+j) = 0;
        }
    }

    for(i=0; i<Num; i++)
    {
        for(j=0; j<=i; j++)
        {
            printf(" %lu ", *(*(Matrix + i) + j));
        }

        printf("\n");
    }

    for(i=0; i<Num; i=i+1)
    {
        for(j=0; j<=i; j=j+1)
        {
            *(*(Matrix + i) + j) = Combination(i, j);
        }
        printf("\n");
    }

    for(i=0; i<Num; i++)
    {
        for(j=0; j<=i; j++)
        {
            //printf(" \n %lu  %lu \n", i, j);
            printf("  %lu  ", *(*(Matrix + i) + j));
        }
        printf("\n");
    }

    getch();
    return(0);
}

Answer 5

Here's the correct way to make Pascal's triangle.

Pascal's Triangle. And Its Patterns

Pascal's triangle

Answer 6

Try the SciPy 'pascal' module:

from scipy.linalg import pascal

pascal(6, kind='lower')

Output:

array([[ 1,  0,  0,  0,  0,  0],
   [ 1,  1,  0,  0,  0,  0],
   [ 1,  2,  1,  0,  0,  0],
   [ 1,  3,  3,  1,  0,  0],
   [ 1,  4,  6,  4,  1,  0],
   [ 1,  5, 10, 10,  5,  1]], dtype=uint64)

Answer 7

Here is my solution to generate a Pascal's triangle:

def factorial(x):

    return 1 if x == 0 else x * factorial(x - 1)

def triangle(n):

    return [[factorial(i) / (factorial(j) * factorial(i - j)) for j in range(i + 1)] for i in range(n)]

Answer 8

Actually, the next row is crossed axis sum of last row. For example, if the last row is [1, 1], the next row would be:

     [1, 1]
+ [1, 1]
-----------
= [1, 2, 1]

     [1, 2, 1]
+ [1, 2, 1]
--------------
= [1, 3, 3, 1]

So, the loop body can be like this:

tri.append(map(lambda x, y: x + y, [0] + tri[-1], tri[-1] + [0]))

Answer 9

You would have to take the last row there is in the triangle and create the next one like this:

1. Put a 1 at the start of the new row
2. For every number in the last row except the last, calculate the sum of the number and its right neighbor and put it into the new row
3. Put another 1 at the end of the new row

You could also calculate the new numbers using binomial coefficients, though that's likely a little more work to get right.