4. (20 Points) Provide best-case and worst-case running time and space complexit

Question

4. (20 Points) Provide best-case and worst-case running time and space complexity analysis in Big-Oh notation forthe following pow 2 method. Foreach case, provide an example input pair and brief explanation Big-0 Notation Example InputExplanation Best-Case Running Time Worst-Case Running Time Best-Case Space Complexi Worst-Case Space Complexi public static long pow_2(long x, int n) { if (n 0) if (n1) if (n % 2- 0) { return 1 return x; return pow2( x, n/ 2 ) * pow 2( x, n / 2); return pow 2(x * x, n /2) * x; else {

Explanation / Answer

Solution:

If we write down the recurrence relation for the above given pow_2 metho, then the recurrence relation will be

T(n)= 3T(n/2) + n

The given table will be filled as:

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Big-O notation Example Input Explanation Best-Case Running Time O(1) for n= 0 and 1 since this condition will directly terminate the recursive function Worst-Case Running Time O(n^1.585) at n After solving the above recurrence relation with the help of recursive tree method we will get this r Best-Case Space Complexity O(1) for n= 0 and 1 Worst-Case Space Complexity O(n) at n

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