Pascal's Triangle is a mathematical concept represented as a triangular array where each row represents the coefficients of the binomial expansion. Each element in the triangle is obtained by adding the two elements directly above it in the previous row.
-
Input from the User:
- The user specifies the number of rows
n
they want to generate for Pascal's Triangle. - The value of
n
determines how many levels of the triangle will be printed.
- The user specifies the number of rows
-
Triangle Structure:
- The first row is always
[1]
. - The second row is
[1, 1]
, and every subsequent row starts and ends with1
. - Each intermediate element in a row is computed by adding the two numbers directly above it from the previous row.
- The first row is always
-
Computation of Elements:
- If
i
is the current row index andj
is the column index within that row, the value of the element at position(i, j)
is:triangle[i][j] = triangle[i-1][j-1] + triangle[i-1][j]
, wherei
is the row number, andj
is the position in that row.- For
j = 0
andj = i
,triangle[i][j] = 1
, as the edges of each row are always1
.
- If
If the user inputs n = 5
, the program generates Pascal's Triangle with 5 rows as follows:
- Row 1:
[1]
- There is only one element in this row.
- Row 2:
[1, 1]
- Starts and ends with
1
.
- Starts and ends with
- Row 3:
[1, 2, 1]
- Starts with
1
. 2
is obtained by adding the two1
s from Row 2.- Ends with
1
.
- Starts with
- Row 4:
[1, 3, 3, 1]
- Starts with
1
. 3
is obtained by adding the1
and2
above it.- The next
3
is obtained by adding the2
and1
above it. - Ends with
1
.
- Starts with
- Row 5:
[1, 4, 6, 4, 1]
- Starts with
1
. 4
is obtained by adding1
and3
above it.6
is obtained by adding3
and3
above it.- The next
4
is obtained by adding3
and1
above it. - Ends with
1
.
- Starts with
1 1 1 1 2 1 1 3 3 1 1 4 6 4 1