Largest Number

Problem

A financial reporting tool needs to display account balances as the largest possible combined value by reordering the figures. Given a list of non-negative integers, arrange them to form the largest possible number and return it as a string.

Input: [10, 2]          -> "210"
Input: [3, 30, 34, 5, 9] -> "9534330"
Input: [0, 0]           -> "0"

Solution

Approach: Custom comparator sort via functools.cmp_to_key.

The largest concatenation is built by sorting the numbers under a pairwise rule rather than by their numeric value. For any two numbers a and b, a should come before b exactly when the string str(a) + str(b) is lexicographically larger than str(b) + str(a) - that is, when putting a first yields the bigger combined number. The compare(a, b) function returns -1 in that case (a precedes b) and 1 otherwise, and cmp_to_key wraps it so sorted can apply it. Once every adjacent pair satisfies this relation, joining the numbers left to right produces the maximum possible number. Trace [3, 30, 34, 5, 9]: comparing 3 and 30 gives "330" > "303", so 3 precedes 30; comparing 9 against everything wins, so 9 leads. The sort settles to [9, 5, 34, 3, 30], which joins to "9534330".

Why a comparator and not a key= function: the decision depends on both elements at once (a+b vs b+a), a relation no per-element key can capture. The comparator is transitive, so the global sort is well defined. String comparison naturally handles different lengths - "9" > "30" because '9' > '3' at position 0 - which is exactly the ordering this problem needs.

Edge cases: All zeros - [0, 0] joins to "00", so the leading-zero check "0" if result[0] == "0" else result collapses it to "0". A single element returns its own digits.

Complexity: O(nk log n) time, O(n) space - n log n comparisons, each comparing two k-digit strings; the output and decorated list are O(n).