Brightest Squares

A heatmap with many columns has dozens of squares. An analyst wants a short list of the pairs worth a closer look: the ones that move together most strongly, whether up or down.

Task: write strongest_pairs(columns, k). columns is a dictionary mapping each column name to its list of numbers (all lists have the same length).

Return a list of up to k entries [name_a, name_b, r]:

• Each pair of different columns appears once, with name_a before name_b alphabetically. Never pair a column with itself.
• r is their correlation rounded to 2 decimal places.
• Order the pairs by the size of the rounded r, ignoring its sign, largest first. So -0.9 comes before 0.8.
• Break ties alphabetically by name_a, then by name_b.
• If there are fewer than k pairs, return them all.

There are at least two columns, no missing values, and no column holds the same value in every row.