
Pascal Triangle
Code:
#include <stdio.h>
int main() {
int pascaltri[11][11];
int r, c;
// Initialize beginning and end of each
// row to 1.
for (r=0; r<11; r++) {
pascaltri[r][0] = 1;
pascaltri[r][r] = 1;
}
// Fill in the table.
for (r=2; r<11; r++)
for (c=1; c<r; c++)
pascaltri[r][c] = pascaltri[r1][c1]+
pascaltri[r1][c];
// Loop through each row of the table.
for (r=0; r<11; r++) {
// Loop through each value of the row.
for (c=0; c<=r; c++)
printf("%4d ", pascaltri[r][c]);
// Go to the next line.
printf("\n");
}
return 0;
}
I am trying to figure out how this works, it is the code to pascal's triangle. I understand I am making a 11x11 triangle and the reason a 1 appears upfront and at the end of each line. I don't understand the part that fills in the lines.
Code:
for (r=2; r<11; r++)
for (c=1; c<r; c++)
pascaltri[r][c] = pascaltri[r1][c1]+
pascaltri[r1][c];
For the first line this fills in , is it doing this?
r=2 c=1
[21][11]+[21][1]
[1][0]+[1][1]
Im not sure what it is doing with that information from there. Can someone explain :) Also how does this cause multiple entries? Like in row 3, there is two numbers it is entering in.

Think of pascaltri as a grid. Each box is either referencing the columns or the rows. This:
pascaltri[ rows ][ cols ]
So when you start with 11,11, you're making a grid of 11 rows by 11 columns. In C, arrays go from 0 to size 1, which in this case means you can access each column or row in ranges of:
0, 1, 2, 3, ... 8, 9, 10
So:
for( r = 2 < row = 2
And:
for( c = 1 < column = 1
And you can think of it as:
grid[ row ][ column ] = value of grid[ row something else ][ column something else ] + value of grid[ row thishere ][ column thatthere ]
The rest is just a matter of grabbing a piece of graph paper, and working through it.
Quzah.

Row 0  1
Row 1  1 1
Row 2  1 X 1
Row 3  1 _ _ 1
Okay so the first part of that is using r=2 c=1
grid[2][1] which is referring to the slot I put as a bold X. How does this come out to two?
[1][0]+[1][1] = 2 ?
Ah doh I am being slow. Is the [1][0] referring to the value at the red color and [1][1] at the blue color? That seems like it would answer my question xD
One last question:
When it continue on, does it go to [3][1] then [3][2] then [4][1]?
What I mean is, does it go back up to this code:
Code:
for (r=2; r<11; r++)
for (c=1; c<r; c++)
Add 1 to r. Followed by resetting c=1 because its indented in(?). Then it keeps adding 1 to c until it no longer satisfies c<r?
It's the only way I see that making this work. Why then wouldn't r reset to 2 every time then? (Or am I more than lost)

The first for loop runs from r=2 through r=10, and stops when r=11 (not executing its contentsthe inner loop). It never resets to r=2, because the outer loop isn't in a loop. The initializer only happens at the start of the loop, not every increment.
Quzah.