Final answer:
Using the binary search algorithm to find the value 29 in the given list, the while loop will terminate when low is 7 and high is 6. These are the final values after the search concludes that 29 is not present in the list as the condition low <= high is no longer met.
Step-by-step explanation:
In the context of the binary search algorithm being used to find the value 29 in the given list, we start with low = 0 and high = 11. Since the list is sorted, the binary search will effectively divide the list into halves to search for the value. Here's how the search progresses:
- First, we calculate the mid index: mid = (low + high) / 2 = (0 + 11) / 2 = 5.5, which is rounded down to 5. The element at index 5 is 18.
- Since 29 is greater than 18, we set low to mid + 1, which is now 6.
- The new mid is (6 + 11) / 2 = 8.5 rounded down to 8, the element at index 8 is 45.
- As 29 is less than 45, we set high to mid - 1, which is now 7.
- Next, mid is recalculated as (6 + 7) / 2 = 6.5 rounded down to 6, and the element at index 6 is 27.
- Since 29 is greater than 27, we update low to mid + 1 again, which is now 7.
At this point, the value of low is 7 and high is also 7. The search continues, but since the next mid would also be 7, and the value at index 7 (which is 35) is not 29, in the next iteration, high will become mid - 1 which is 6. Now, low is greater than high, which will terminate the while loop of the binary search.
So, when the while loop terminates, the values of low and high will be: low = 7 and high = 6.