Binary Search Algorithm

Binary Search Algorithm:

Divide the search space into two equal halves.Compare the target element with the middle element.If the target element is equal to the middle element, return its index.If the target element is less than the middle element, search in the left half.If the target element is greater than the middle element, search in the right half....

Ternary Search Algorithm:

Divide the search space into three equal parts.Compare the target element with the two middle elements.If the target element is equal to one of the middle elements, return its index.If the target element is less than the left middle element, search in the left third.If the target element is between the left and right middle elements, search in the middle third.If the target element is greater than the right middle element, search in the right third....

Time Complexity of Binary Search:

Each iteration divides the search space in half.Therefore, the number of iterations required is log2(n)....

Time Complexity of Ternary Search:

Each iteration divides the search space into three parts.Therefore, the number of iterations required is log3(n)....

Complexity Comparison between Ternary Search and Binary Search:

Ternary search requires 4 comparisons, while binary search only needs a maximum of 2 comparisons per iteration....

Proof of why Binary search is faster than Ternary Search:

For Binary Search, [Tex]T_{b}(N) = C_{b} \cdot \log_{2}(N)[/Tex] …1...

Conclusion

Binary search algorithm is preferred over the Ternary search because Ternary search needs more comparisons, even though it reduces the number of steps. Hence, Binary search is better than Ternary search....