Okay, let's carefully examine and solve this step-by-step:
1. We begin with the list of numbers: [tex]\[64, 25, 12, 22, 11\][/tex].
2. Our goal is to arrange these numbers in ascending order.
3. We will use the selection sort algorithm to sort the numbers. Here’s a detailed breakdown of each iteration:
- First iteration:
- We start by assuming the first element (64) is the minimum.
- Compare 64 with 25, 25 is smaller, so we update the minimum to 25.
- Next, compare 25 with 12. Since 12 is smaller, we update the minimum again to 12.
- Compare 12 with 22, 12 is still smaller.
- Finally, compare 12 with 11. 11 is the smallest, so we update our minimum to 11.
- Swap 64 with 11. The list becomes [tex]\[11, 25, 12, 22, 64\][/tex].
- Second iteration:
- Now we start from the second element (25) and assume it's the minimum.
- Compare 25 with 12, we find that 12 is smaller and update the minimum to 12.
- Compare 12 with 22, 12 is still smaller.
- Compare 12 with 64, 12 is still smaller.
- Swap 25 with 12. The list becomes [tex]\[11, 12, 25, 22, 64\][/tex].
- Third iteration:
- Moving to the third element (25) and assuming it's the minimum.
- Compare 25 with 22, 22 is smaller, so we update the minimum to 22.
- Compare 22 with 64, 22 is still smaller.
- Swap 25 with 22. The list becomes [tex]\[11, 12, 22, 25, 64\][/tex].
- Fourth iteration:
- Now, consider the fourth element (25) as the minimum.
- Compare 25 with 64, 25 is the minimum.
- No need to swap as it's already in its correct position. The list remains [tex]\[11, 12, 22, 25, 64\][/tex].
- Fifth iteration:
- The last element (64) is naturally the minimum since there are no elements left to compare.
- No swapping needed. The list stays [tex]\[11, 12, 22, 25, 64\][/tex].
4. Thus, the sorted list in ascending order is:
[tex]\[11, 12, 22, 25, 64\][/tex].
This is the step-by-step solution to sorting the given list of numbers.
