Add TimSort implementation and UI entries

Introduce TimSort support across the app: add TIM_SORT_WIKI to UrlConstants, implement timSort (with insertionSortRange and mergeRanges) in SortingService to produce SortSnapshot sequences (uses RUN=32, sorts runs then merges, marks comparing/unsorted/sorted states), and wire the algorithm into SortingComponent (UI entry and case branch). Also add TIMSORT_EXPLANATION translations in de.json and en.json, and add a few UI label keys (STIFFNESS, ELONGATION, RESTART_SIMULATION) to both locale files.

src/app/constants/UrlConstants.ts

@@ -7,6 +7,7 @@
   static readonly QUICK_SORT_WIKI = 'https://de.wikipedia.org/wiki/Quicksort'
   static readonly HEAP_SORT_WIKI = 'https://de.wikipedia.org/wiki/Heapsort'
   static readonly SHAKE_SORT_WIKI = 'https://de.wikipedia.org/wiki/Shakersort'
+  static readonly TIM_SORT_WIKI = 'https://de.wikipedia.org/wiki/Timsort'
   static readonly CONWAYS_WIKI = 'https://de.wikipedia.org/wiki/Conways_Spiel_des_Lebens'
   static readonly PRIMS_WIKI = 'https://de.wikipedia.org/wiki/Algorithmus_von_Prim'
   static readonly KRUSKAL_WIKI = 'https://de.wikipedia.org/wiki/Algorithmus_von_Kruskal'

src/app/pages/algorithms/sorting/service/sorting.service.ts

@@ -224,6 +224,103 @@ export class SortingService {
     }
   }
 
+  // --- TIM SORT ---
+  timSort(array: SortData[]): SortSnapshot[] {
+    const snapshots: SortSnapshot[] = [];
+    const arr = array.map(item => ({ ...item }));
+    const n = arr.length;
+    const RUN = 32;
+
+    snapshots.push(this.createSnapshot(arr));
+
+    // Step 1: Sort small runs with insertion sort
+    for (let i = 0; i < n; i += RUN) {
+      const end = Math.min(i + RUN - 1, n - 1);
+      this.insertionSortRange(arr, i, end, snapshots);
+    }
+
+    // Step 2: Merge the sorted runs
+    for (let size = RUN; size < n; size *= 2) {
+      for (let left = 0; left < n; left += 2 * size) {
+        const mid = Math.min(left + size - 1, n - 1);
+        const right = Math.min(left + 2 * size - 1, n - 1);
+        if (mid < right) {
+          this.mergeRanges(arr, left, mid, right, snapshots);
+        }
+      }
+    }
+
+    arr.forEach(item => item.state = 'sorted');
+    snapshots.push(this.createSnapshot(arr));
+
+    return snapshots;
+  }
+
+  private insertionSortRange(arr: SortData[], left: number, right: number, snapshots: SortSnapshot[]): void {
+    for (let i = left + 1; i <= right; i++) {
+      const tempValue = arr[i].value;
+      arr[i].state = 'comparing';
+      snapshots.push(this.createSnapshot(arr));
+
+      let j = i - 1;
+      while (j >= left && arr[j].value > tempValue) {
+        arr[j].state = 'comparing';
+        arr[j + 1].value = arr[j].value;
+        arr[j].state = 'unsorted';
+        snapshots.push(this.createSnapshot(arr));
+        j--;
+      }
+
+      arr[j + 1].value = tempValue;
+      arr[i].state = 'unsorted';
+      snapshots.push(this.createSnapshot(arr));
+    }
+  }
+
+  private mergeRanges(arr: SortData[], left: number, mid: number, right: number, snapshots: SortSnapshot[]): void {
+    const leftPart = arr.slice(left, mid + 1).map(item => ({ ...item }));
+    const rightPart = arr.slice(mid + 1, right + 1).map(item => ({ ...item }));
+
+    let i = 0;
+    let j = 0;
+    let k = left;
+
+    while (i < leftPart.length && j < rightPart.length) {
+      // Highlight the write target and the right-side source (arr[mid+1+j] is still
+      // untouched in the array since k never overtakes it during a merge)
+      const rightSourceIdx = mid + 1 + j;
+      arr[k].state = 'comparing';
+      arr[rightSourceIdx].state = 'comparing';
+      snapshots.push(this.createSnapshot(arr));
+
+      arr[rightSourceIdx].state = 'unsorted';
+
+      if (leftPart[i].value <= rightPart[j].value) {
+        arr[k].value = leftPart[i].value;
+        i++;
+      } else {
+        arr[k].value = rightPart[j].value;
+        j++;
+      }
+
+      arr[k].state = 'unsorted';
+      k++;
+      snapshots.push(this.createSnapshot(arr));
+    }
+
+    while (i < leftPart.length) {
+      arr[k].value = leftPart[i].value;
+      i++;
+      k++;
+    }
+
+    while (j < rightPart.length) {
+      arr[k].value = rightPart[j].value;
+      j++;
+      k++;
+    }
+  }
+
   private swap(arr: SortData[], i: number, j: number) {
     const temp = arr[i].value;
     arr[i].value = arr[j].value;

src/app/pages/algorithms/sorting/sorting.component.ts

@@ -49,6 +49,11 @@ export class SortingComponent implements OnInit {
         name: 'Heap Sort',
         description: 'SORTING.EXPLANATION.HEAP_SORT_EXPLANATION',
         link: UrlConstants.HEAP_SORT_WIKI
+      },
+      {
+        name: 'Tim Sort',
+        description: 'SORTING.EXPLANATION.TIMSORT_EXPLANATION',
+        link: UrlConstants.TIM_SORT_WIKI
       }
     ],
     disclaimer: 'SORTING.EXPLANATION.DISCLAIMER',
@@ -130,6 +135,9 @@ export class SortingComponent implements OnInit {
       case 'Cocktail Sort':
         snapshots = this.sortingService.cocktailSort(this.sortArray);
         break;
+      case 'Tim Sort':
+        snapshots = this.sortingService.timSort(this.sortArray);
+        break;
     }
 
     const endTime = performance.now();