diff --git a/divide-and-conquer/notes.md b/divide-and-conquer/notes.md index cdbfed9a5ce2ecb0d224119eb6b8cc75f3d2cea3..ce6f8325de0c4c73cf63097f18048efca9de0a50 100644 --- a/divide-and-conquer/notes.md +++ b/divide-and-conquer/notes.md @@ -48,19 +48,19 @@ Problem: Sort a list in Θ(n log n) time. ``` In: [8, 7, 6, 9, 5] - Out: […, …, …, …, …] + Out: [5, 6, 7, 8, 9] / \ / \ - In: […] In: […] - Out: […] Out: […] + In: [8, 7] In: [6, 9, 5] + Out: [7, 8] Out: [5, 6, 9] / \ / \ / \ / \ -In: […] In: […] In: […] In: […] -Out: […] Out: […] Out: […] Out: […] +In: [8] In: [7] In: [6] In: [9, 5] +Out: [8] Out: [7] Out: [6] Out: [5, 9] / \ / \ - In: […] In: […] - Out: […] Out: […] + In: [9] In: [5] + Out: [9] Out: [5] ``` ## Analysis @@ -69,14 +69,14 @@ Out: […] Out: […] Out: […] Out: […] T(n) = T(⌊n/2⌋) + T(⌈n/2⌉) + Θ(n) for n ≫ 0 T(n) ≈ 2T(n/2) + Θ(n) for n ≫ 0 - T(n) = Θ(⋯) + T(n) = Θ(n log n) * Uneven split: T(n) = T(n - 1) + T(1) + Θ(n) for n ≫ 0 T(n) = T(n - 1) + Θ(1) + Θ(n) for n ≫ 0 T(n) = T(n - 1) + Θ(n) for n ≫ 0 - T(n) = Θ(⋯) + T(n) = Θ(n²) -------------------------------------------------------------------------------- @@ -96,11 +96,11 @@ Problem: Find the median of an odd-length list in average-case Θ(n) time. Use ``` In: [8, 7, 6, 9, 5] - Out: … + Out: 7 (but how?) / \ / \ - In: […] In: […] - Out: … Out: … + In: [8, 7] In: [6, 9, 5] + Out: 7.5 Out: 6 ``` * Option A: We are missing information from the recursive calls. Add output(s) so that they can return that information. @@ -108,15 +108,15 @@ Problem: Find the median of an odd-length list in average-case Θ(n) time. Use ## Design (second attempt) -* More generally, we want …, so we add an input `k`: +* More generally, we want `k`th element if the list were sorted, so we add an input `k`: ``` In: [8, 7, 6, 9, 5], k = 2 - Out: … + Out: 7 / \ / \ - In: […], k = 2 In: […], k = 0 - Out: … Out: … + In: [8, 7], k = 2 In: [6, 9, 5], k = 0 + Out: ??? Out: 5 ``` ## Partitioning diff --git a/divide-and-conquer/src/features/sorting/sorting.js b/divide-and-conquer/src/features/sorting/sorting.js index bca3d88bf5b65b3bddba99daeff360e4205312d0..2a295023d99b692abe242661ba9d1819c4390acf 100644 --- a/divide-and-conquer/src/features/sorting/sorting.js +++ b/divide-and-conquer/src/features/sorting/sorting.js @@ -1,7 +1,25 @@ function merge(left, right) { - return []; // TODO: stub + const merged = []; + let i = 0; + let j = 0; + while (i < left.length || j < right.length) { + if (i < left.length && (j === right.length || left[i] < right[j])) { + merged.push(left[i]); + ++i; + } else { + merged.push(right[j]); + ++j; + } + } + return merged; } export function sort(list) { - return list; // TODO: stub + if (list.length <= 1) { + return list; + } + const middleIndex = Math.floor(list.length / 2); + const left = sort(list.slice(0, middleIndex)); + const right = sort(list.slice(middleIndex, list.length)); + return merge(left, right); }