Sorting 1. Insertion Sort 3 1 4 4 5 6 2 9 5 1 3 1 4 4 5 6 2 9 5 1 1 3 4 4 5 6 2 9 5 1 1 3 4 4 5 6 2 9 5 1 1 1 3 4 5 6 2 9 5 4 1 1 3 4 5 6 2 9 5 4 1 1 3.

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Presentation transcript:

Sorting 1. Insertion Sort

Sorting 2. Selection Sort

Sorting 3. Bubble Sort

Lower Bound For Sorting Decision Tree a < b b < c a < b < c a < c < b c < a < b b < a < c b < c < a c < b < a a < b ^ a < c a < c b < a ^ c < a a < b b < a Y Y Y Y Y N N N N N

Optimal Sorting Algorithms 4. Heapsort Output:

Optimal Sorting Algorithms 4. Heapsort Output:

Optimal Sorting Algorithms 4. Heapsort Output:

Optimal Sorting Algorithms 4. Heapsort Output:

Optimal Sorting Algorithms 4. Heapsort Output:

Optimal Sorting Algorithms 4. Heapsort Output:

Optimal Sorting Algorithms 4. Heapsort Output:

Optimal Sorting Algorithms 4. Heapsort Output: 3 1 2

Optimal Sorting Algorithms 4. Heapsort Output: 2 1

Optimal Sorting Algorithms 4. Heapsort Output: Final Output:

5. Mergesort Optimal Sorting Algorithms

Quicksort. Partitioning Phase Pivot