All orderings to execute a basket of trades

Question

Given a basket of distinct child orders, list every ordering in which they could be executed. For a small basket you might want to simulate all execution sequences.

orders = ["X", "Y", "Z"]
-> 6 orderings: XYZ, XZY, YXZ, YZX, ZXY, ZYX

Return all n! permutations of the input.

Accepted Answer

Backttrack by building the sequence one slot at a time. Keep a used flag per order so each appears exactly once per permutation. When the current sequence is full, record a copy. After each recursive branch, unmark the order so it becomes available again for other positions. Tracing ["X","Y","Z"]: fixing X first yields XYZ and XZY; fixing Y and Z first give two each, for six in total. Time O(n n!) to produce and copy every permutation, space O(n) recursion depth. Edge cases: an empty input returns [[]] (one empty ordering); duplicate orders would produce duplicate permutations, sort and skip …

All orderings to execute a basket of trades

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