rovide best-case and worst-case running time and space complexity analysis in Bi
ID: 3746708 • Letter: R
Question
rovide best-case and worst-case running time and space complexity analysis in Big-Oh notation for the following pow_2 method. For each case, provide an example input pair and brief explanation. Big-O Notation Example Input Explanation Best-Case Running Time Worst-Case Running Time Best-Case Space Complexity Worst-Case Space Complexit public static long pow_2(long x, int n) { if (n-8) if (n1) if(n % 2-0) { return 1; return x; return pow 2X, n / 2) pow2x, n/ 2 ); return pow 2(x * x, n / 2) * x; elseExplanation / Answer
Big-O Notation
Example Input
Explanation
Best-Case Running Time
O(1) i.e. Constant
X = any number ; n=1
Since n==1 it will return from the function returning the value X
Worst-Case Running Time
O(n) i.e. Linear
X = any number ; n=a number which is a power of 2
Here the function will keep calling itself until n becomes equal to 1 which will lead to
(2*n-1) iterations
Best-Case Space Complexity
O(1) i.e. Constant
X = any number ; n=1
It will just return X without using any extra space i.e. will only use constant space
Worst-Case Space Complexity
O(n) i.e. Linear
X = any number ; n=a number which is a power of 2
This will use stack for recursive calls and 2*n-1 space will be occupied
Big-O Notation
Example Input
Explanation
Best-Case Running Time
O(1) i.e. Constant
X = any number ; n=1
Since n==1 it will return from the function returning the value X
Worst-Case Running Time
O(n) i.e. Linear
X = any number ; n=a number which is a power of 2
Here the function will keep calling itself until n becomes equal to 1 which will lead to
(2*n-1) iterations
Best-Case Space Complexity
O(1) i.e. Constant
X = any number ; n=1
It will just return X without using any extra space i.e. will only use constant space
Worst-Case Space Complexity
O(n) i.e. Linear
X = any number ; n=a number which is a power of 2
This will use stack for recursive calls and 2*n-1 space will be occupied
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