Searching Algorithms Questions Long
Ternary search is a searching algorithm that is used to find the position of a specific value within a sorted array. It is similar to binary search, but instead of dividing the array into two parts, it divides it into three parts.
The time complexity of ternary search can be analyzed by considering the number of comparisons required to find the target value. In each iteration of the algorithm, the array is divided into three parts, and the target value is compared with the elements at two specific positions.
Let's assume that the length of the array is 'n'. In each iteration, the array is divided into three parts, so the size of each part is approximately 'n/3'. The algorithm compares the target value with the elements at two positions, which can be denoted as 'left' and 'right'. Initially, 'left' is set to 0 and 'right' is set to 'n-1'.
In the worst-case scenario, the target value is not present in the array. In this case, the algorithm will continue dividing the array until the size of the current part becomes 0. The number of iterations required to reach this point can be calculated using the formula:
n/3^k = 0
where 'k' is the number of iterations. Solving this equation for 'k', we get:
k = log3(n)
Therefore, the number of iterations required in the worst-case scenario is logarithmic with base 3 of 'n'. Since each iteration involves two comparisons, the total number of comparisons can be calculated as:
2 * log3(n)
Hence, the time complexity of ternary search is O(log3(n)).
It is important to note that the time complexity of ternary search is better than binary search, which has a time complexity of O(log2(n)). However, in practice, the difference in time complexity between these two algorithms is negligible, as the logarithmic base does not significantly affect the overall performance.