1. Write the recurrence relation for the binary search algorithm and explain it. Express that using Big-O notation then.
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If the target value is equal to the middle element, we have found the desired element and the search is complete. If the target value is less than the middle element, we narrow down the search to the lower half of the array. If the target value is greater than the Show more…
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Show that the worst-case time complexity for Binary Search (Algorithm 2.1) is given by $W(n)=[\lg n]+1$ When $n$ is not restricted to being a power of $2 .$ Hint. First show that the recurrence equation for $W(n)$ is given by $W(n)=1+W\left(\left\lfloor\frac{n}{2}\right\rfloor\right) \quad$ for $n>1$ $W(1)=1$ To do this, consider even and odd values of $n$ separately. Then use induction to solve the recurrence equation.
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