From b6aea74c10047ce11583c22982cf8afad6fe29d1 Mon Sep 17 00:00:00 2001 From: "Brady J. Garvin" <bgarvin@cse.unl.edu> Date: Mon, 24 Oct 2022 10:49:22 -0500 Subject: [PATCH] Designed and implemented merge sort. --- divide-and-conquer/notes.md | 18 +++++++-------- .../src/features/sorting/sorting.js | 22 +++++++++++++++++-- 2 files changed, 29 insertions(+), 11 deletions(-) diff --git a/divide-and-conquer/notes.md b/divide-and-conquer/notes.md index de61696..f4a53c4 100644 --- a/divide-and-conquer/notes.md +++ b/divide-and-conquer/notes.md @@ -21,19 +21,19 @@ 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 @@ -42,14 +42,14 @@ 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) -------------------------------------------------------------------------------- diff --git a/divide-and-conquer/src/features/sorting/sorting.js b/divide-and-conquer/src/features/sorting/sorting.js index bca3d88..10eb765 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 results = []; + let i = 0; + let j = 0; + while (i < left.length || j < right.length) { + if (j >= right.length || (i < left.length && left[i] < right[j])) { + results.push(left[i]); + ++i; + } else { + results.push(right[j]); + ++j; + } + } + return results; } export function sort(list) { - return list; // TODO: stub + if (list.length < 2) { + 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); } -- GitLab