Use Tokuda's gap sequence in shell sort

Author: mszula

src/lib/sort-algorithms/shell-sort.ts

@@ -3,7 +3,17 @@ import type { SortingGenerator } from './types';
 export const shellSort = function* (arr: number[]): SortingGenerator {
   const n = arr.length;
 
-  for (let gap = Math.floor(n / 2); gap > 0; gap = Math.floor(gap / 2)) {
+  // Tokuda's gap sequence: 1, 4, 9, 20, 46, 103, 233, 525, ...
+  // Much better worst case than Shell's original n/2, n/4, ... split.
+  const gaps: number[] = [];
+  for (let k = 0; ; k++) {
+    const gap = Math.ceil((9 * Math.pow(9 / 4, k) - 4) / 5);
+    if (gap >= n) break;
+    gaps.push(gap);
+  }
+
+  for (let g = gaps.length - 1; g >= 0; g--) {
+    const gap = gaps[g];
     for (let i = gap; i < n; i++) {
       const temp = arr[i]; // 1 read
       let j = i;