What will be the number of passes to sort the elements using insertion sort?14, 12,16, 6, 3, 106571

1. ### Break Down the Problem

To determine the number of passes in insertion sort for the given array, we'll analyze how insertion sort works. Each pass refers to one complete iteration through the list where at least one element is inserted into its correct position.

2. ### Relevant Concepts

Insertion sort iteratively builds a sorted portion of the list. In each pass (or iteration), one element is taken from the unsorted section and inserted into the sorted portion.

3. ### Analysis and Detail

Given the array to sort: $[14, 12, 16, 6, 3, 106571]$:

• Pass 1: Insert 12. Array becomes: $[12, 14, 16, 6, 3, 106571]$
• Pass 2: Insert 16. Array remains the same: $[12, 14, 16, 6, 3, 106571]$
• Pass 3: Insert 6. Array becomes: $[6, 12, 14, 16, 3, 106571]$
• Pass 4: Insert 3. Array becomes: $[3, 6, 12, 14, 16, 106571]$
• Pass 5: Insert 106571. Array remains the same: $[3, 6, 12, 14, 16, 106571]$

4. ### Verify and Summarize

After analyzing each step, we see that even though some elements stayed in the same relative positions, each of the six elements resulted in their own individual attempt to get into the right location within the sorted portion. Hence, we have a total of 5 significant passes for 6 elements.

Final Answer

The number of passes required to sort the elements using insertion sort is 5.