Sorting, Ranking & Top-N

The problem, from first principles

"Who are the top five?" is the commonest question asked of a table, and it hides three decisions. What happens when two rows tie for fifth place? Which rows go last when a value is missing? And do you want the rows reordered, or do you want each row's position in the order as a new number (its rank)? Sorting and ranking look alike and answer different questions, and the answers differ most exactly where real data is awkward: ties and gaps.

This question builds the four tools you use for it: a stable multi-key sort, ranking with a chosen tie rule, a top-N that handles ties and missing values predictably, and a percentile rank that puts every value on a 0 to 1 scale.

From theory to code

Implement sort_by_columns(df, columns, ascending), rank_scores(s, method), top_n(df, column, n) and percent_rank(s). The signatures and docstrings are already in the editor.

Constraints

• sort_by_columns(df, columns, ascending) sorts by the listed columns in order, each with its own direction (ascending is a list of bools the same length as columns). Rows that tie on every key keep their original relative order (a stable sort). Missing values go last in every key. The index labels travel with their rows.
• rank_scores(s, method) ranks so that the highest value gets rank 1. method is "min", "dense" or "average": tied values get the lowest rank of the group, the next consecutive rank, or the mean of the group's ranks. Missing values stay NaN. The result is a float Series with s's index.
• top_n(df, column, n) returns the n rows with the largest column values, largest first. Ties keep the original relative order. Rows where column is missing are never selected, so fewer than n rows can come back.
• percent_rank(s) returns (rank_min - 1) / (count - 1), where rank_min ranks ascending (smallest value gets 1, ties share the lowest rank) and count is the number of non-missing values, which is at least 2. The smallest value maps to 0.0 and the largest to 1.0. Missing stays NaN.

Hints