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Nested loops are here presented using for loops. See Nested loops using while loops for the same loop discussion using while loops.

Most people start counting at 1.

• 1 is the first number
• 2 is the second number
• 3 is the third number
• ... and so on ...

Most computer people start counting at 0.

• 0 is the first number
• 1 is the second number
• 2 is the third number
• ... and so on ...

Nested loops are loops within loops. A nice way to think about nested loops is with a rectangular set of blocks arranged into rows and columns.

Let X represent one block. Here is a depiction of 12 blocks arranged into 3 rows and 4 columns.

We can process these blocks in row-major order or column-major order. (Or some other order).

Most people think of the block orderings as follows.

Computer people

Row-major order processes the rows in the outer loop and columns in the inner loop.

Here is the C code.
#include <stdio.h> int main() { int rlen1 = 3; int clen1 = 4; for (int rpos1=0; rpos1 < rlen1; rpos1++) { for (int cpos1=0; cpos1 < clen1; cpos1++) { printf("r=%d c=%d\n",rpos1,cpos1); } } return 0; }

Here is the output of the C code.
r=0 c=0 r=0 c=1 r=0 c=2 r=0 c=3 r=1 c=0 r=1 c=1 r=1 c=2 r=1 c=3 r=2 c=0 r=2 c=1 r=2 c=2 r=2 c=3

Here as a while loop for comparison.

Here is the C code.
#include <stdio.h> int main() { int rlen1 = 3; int clen1 = 4; int rpos1 = 0; while (rpos1 != rlen1) { int cpos1 = 0; while (cpos1 != clen1) { printf("r=%d c=%d\n",rpos1,cpos1); cpos1 = cpos1+1; } rpos1 = rpos1+1; } return 0; }

Here is the output of the C code.
r=0 c=0 r=0 c=1 r=0 c=2 r=0 c=3 r=1 c=0 r=1 c=1 r=1 c=2 r=1 c=3 r=2 c=0 r=2 c=1 r=2 c=2 r=2 c=3

Column-major order processes the columns in the outer loop and rows in the inner loop.

Here is the C code.
#include <stdio.h> int main() { int rlen1 = 3; int clen1 = 4; for (int cpos1=0; cpos1 < clen1; cpos1++) { for (int rpos1=0; rpos1 < rlen1; rpos1++) { printf("r=%d c=%d\n",rpos1,cpos1); } } return 0; }

Here is the output of the C code.
r=0 c=0 r=1 c=0 r=2 c=0 r=0 c=1 r=1 c=1 r=2 c=1 r=0 c=2 r=1 c=2 r=2 c=2 r=0 c=3 r=1 c=3 r=2 c=3

Here is the C code.
#include <stdio.h> int main() { int rlen1 = 3; int clen1 = 4; int cpos1 = 0; while (cpos1 != clen1) { int rpos1 = 0; while (rpos1 != rlen1) { printf("r=%d c=%d\n",rpos1,cpos1); rpos1 = rpos1+1; } cpos1 = cpos1+1; } return 0; }

Here is the output of the C code.
r=0 c=0 r=1 c=0 r=2 c=0 r=0 c=1 r=1 c=1 r=2 c=1 r=0 c=2 r=1 c=2 r=2 c=2 r=0 c=3 r=1 c=3 r=2 c=3