Two pointers from opposite ends, left skips past evens, right skips past odds, and when both land on violations you swap and count it.
First, clarify that the goal is to partition the array into evens followed by odds, and that any two elements can be swapped. Then, use a two-pointer technique to count the number of misplaced elements (odds in the even section and evens in the odd section) and determine the minimum swaps as the maximum of these two counts. Explain that each swap can fix at most two misplaced elements, so the minimum swaps equals the number of misplaced evens (or odds) in the wrong section.
Pro tip: Mention that the minimum swaps equals the number of misplaced elements of one type, and that this is optimal because each swap can correct at most one misplaced element of each type. Also, note that if the array is already partitioned, the answer is 0.
Confirm that the partition requires all even numbers before all odd numbers, and that we can swap any two elements. Ask if the order within evens or odds matters (usually not).
Scan the array to find the number of odd numbers in the even section (left part) and even numbers in the odd section (right part). These are the elements that need to be swapped.
The minimum number of swaps is the maximum of the two counts, because each swap can fix one misplaced even and one misplaced odd simultaneously. If counts are unequal, extra swaps will involve swapping two misplaced elements of the same type, but that still counts as one swap per pair.
Walk through a small example, such as [2,1,4,3], to illustrate the counting and swapping process, showing that the minimum swaps is 1.
State that the algorithm runs in O(n) time and O(1) space. Mention edge cases: all evens, all odds, already partitioned, and empty array.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by clarifying the original approach (likely a two-pointer swap that is unstable) and explain why it fails to preserve relative order. Then propose a stable alternative such as using an auxiliary array to collect evens and odds in order, or a stable in-place algorithm like stable partitioning via rotation. Discuss trade-offs between time/space complexity and stability.
Pro tip: Mention that stability often requires extra space or more complex in-place algorithms, and that in production code, clarity and maintainability may outweigh the cost of O(n) extra space. Also, relate to real-world scenarios like sorting records by multiple keys where stability matters.
Briefly describe the typical two-pointer swap method for partitioning even/odd numbers, and point out that swapping elements can change the relative order of elements within each group.
State that a stable partition preserves the original relative order of elements within each partition (evens and odds). Emphasize that this is a key property when the elements have associated data or when multiple sorting criteria are applied.
Present one or more stable algorithms: e.g., using an auxiliary array to collect evens then odds in a single pass, or an in-place stable partition using rotations (like the block swap algorithm). Explain the steps clearly.
Compare the auxiliary array method (O(n) time, O(n) space) with in-place stable methods (O(n log n) time, O(1) space for some algorithms). Discuss the trade-offs and when each might be appropriate.
Summarize that the choice depends on constraints like memory availability, performance requirements, and code simplicity. Mention that in many cases, the auxiliary array approach is preferred for its simplicity and linear time.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Easy pivot off the previous answer, just replace the even/odd check with a function parameter.
Start by defining the generalized partitioning problem: given an array and a predicate function, rearrange elements so that those satisfying the predicate come before those that don't. Then describe a two-pointer or single-pass algorithm that uses the predicate to decide placement, and discuss how this abstraction improves code reusability and testability.
Pro tip: Mention that using a predicate function allows the partitioning logic to be decoupled from specific conditions, making it easier to unit test and adapt to new requirements without modifying the core algorithm.
Restate the goal: partition an array into two groups based on whether elements satisfy a given predicate, preserving or not preserving order as required.
Explain that the predicate is a function that takes an element and returns a boolean, e.g., `bool pred(T element)`. This allows any condition to be plugged in.
Describe a two-pointer approach (like Hoare's partition) or a stable single-pass approach (like Lomuto's) that uses the predicate to decide swaps or placements.
Discuss time complexity (typically O(n)) and space complexity (O(1) for in-place). Mention whether the algorithm is stable and how that affects the choice.
Walk through a concrete example, such as partitioning numbers by `x -> x % 2 == 0`, to illustrate how the predicate drives the logic.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.