Draft zigzag traversal post

Author: mmore500

blog_professional/_posts/2023-12-16-zigzag-traversal.md

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+---
+layout: post
+title:  "Nice Zigzag Traversal with Itertools"
+date:   2023-12-16
+no_toc: true
+---
+
+Just a cute Python snippet I put together today and thought worth sharing.
+Needed to fill in a matrix in from the corner outwards, iterating down successive diagonals.
+You might also run into this problem doing a zigzag traversal of a nested list-of-lists.
+
+![zig-zag traversal over a 3x4 grid](/resources/2023-12-16-zigzag-traversal.png){:style="width: 40%;display:block; margin-left:auto; margin-right:auto;"}
+
+Itertools comes to the rescue with a nice one liner to generate the `(row, col)` coordinate sequence.
+
+## Ctrl-C Ctrl-V
+
+For a `dim`x`dim` square matrix,
+```python
+sorted(itertools.product(range(dim), repeat=2), key=sum)
+```
+
+In the arbitrary `nrow`x`ncol`case,
+```python
+sorted(itertools.product(range(nrow), range(ncol)), key=sum)
+```
+
+## How does this work?
+
+In iterating over the matrix, we want to see all combinations of row and column indices --- this is a product.
+Sort by `(row, col)` coordinate sums to get ascending diagonals.
+For example, `(0, 0)` has sum `0` so will be ordered first.
+The coordinates, `(0, 1)` and `(1, 0)` both have sum `1` so will be ordered next.
+
+The stability of `sort` and the iteration order of `product` gets us the correct ordering along same-sum diagonals.
+
+## Examples
+
+For a square matrix with `dim = 3`,
+```python
+>>> import itertools as it
+>>> sorted(it.product(range(3), repeat=2), key=sum)
+[(0, 0), (0, 1), (1, 0), (0, 2), (1, 1), (2, 0), (1, 2), (2, 1), (2, 2)]
+```
+
+For a matrix with `nrow=2` and `ncol=3`,
+```python
+>>> sorted(it.product(range(2), range(3)), key=sum)
+[(0, 0), (0, 1), (1, 0), (0, 2), (1, 1), (1, 2)]
+```
+
+## Bonus: Chunked Diagonals
+
+To take successive diagonal coordinate sequences as separate chunks, just group by coordinates' sums.
+
+```python
+>>> import itertools as it
+>>> for diagonal, coords in it.groupby(
+...     sorted(it.product(range(3), repeat=2), key=sum),
+...     key=sum,
+...):
+...     print(f"{diagonal=}")
+...     print("coords=", [*coords], "\n")
+...
+diagonal=0
+coords= [(0, 0)]
+
+diagonal=1
+coords= [(0, 1), (1, 0)]
+
+diagonal=2
+coords= [(0, 2), (1, 1), (2, 0)]
+
+diagonal=3
+coords= [(1, 2), (2, 1)]
+
+diagonal=4
+coords= [(2, 2)]
+```