Trace the quick sort for data A = {6,5,3,11,10,4,7,9}

Sure, I can help you trace the quick sort algorithm for the given data A = {6, 5, 3, 11, 10, 4, 7, 9}. Here are the step-by-step instructions:

Step 1: Choose a pivot element. Let's choose the first element of the array as the pivot, which is 6. Step 2: Partition the array around the pivot. Rearrange the elements such that all elements smaller than the pivot are placed to the left, and all elements greater than the pivot are placed to the right. The pivot element should be in its final sorted position. After partitioning, the array may look like this: {4, 5, 3, 6, 10, 11, 7, 9}. Step 3: Now, recursively apply the quick sort algorithm to the subarrays on the left and right of the pivot.

• For the left subarray {4, 5, 3}, repeat steps 1 and 2.
  • Choose the first element, 4, as the pivot.
  • Partition the array around the pivot. The array becomes {3, 4, 5}.
• For the right subarray {10, 11, 7, 9}, repeat steps 1 and 2.
  • Choose the first element, 10, as the pivot.
  • Partition the array around the pivot. The array becomes {7, 9, 10, 11}. Step 4: Continue recursively applying the quick sort algorithm to the remaining subarrays until all subarrays are sorted.
• For the left subarray {3, 4, 5}, no further partitioning is needed as it is already sorted.
• For the right subarray {7, 9, 10, 11}, repeat steps 1 and 2.
  • Choose the first element, 7, as the pivot.
  • Partition the array around the pivot. The array becomes {7, 9, 10, 11}.
• Now, the right subarray {7, 9, 10, 11} is also sorted. Step 5: Finally, combine all the sorted subarrays to get the final sorted array. In this case, the final sorted array is {3, 4, 5, 6, 7, 9, 10, 11}.

So, the quick sort algorithm for the given data A = {6, 5, 3, 11, 10, 4, 7, 9} results in the sorted array {3, 4, 5, 6, 7, 9, 10, 11}.