Time complexities of three algorithms are given. Which should execute the slowest for largevalues of N?(A) O(N^0.5)#(B) O(n)(C) O(logN)(D) O(log2n)(E)O(NlogN

The time complexity of an algorithm gives us an idea of how the runtime increases as the size of the input increases. The larger the time complexity, the slower the algorithm will be for large inputs.

Here are the given time complexities in order from fastest to slowest:

1. O(logN) and O(log2n): These are the fastest because logarithmic time complexity increases very slowly as N increases. Note that O(logN) and O(log2n) are equivalent because the base of the logarithm is not significant in big O notation.

2. O(N^0.5): This is the square root function, which grows faster than the logarithm but slower than a linear function.

3. O(N): This is a linear time complexity, which means the runtime increases proportionally with N.

4. O(NlogN): This is slower than linear time but faster than quadratic time. It's commonly seen in efficient sorting algorithms like quicksort and mergesort.

So, for large values of N, the algorithm with time complexity O(NlogN) should execute the slowest. Therefore, the answer is (E) O(NlogN).

The time complexity of an algorithm gives us an idea of how the runtime increases as the size of the input increases. The larger the time complexity, the slower the algorithm will be for large inputs.

Here are the given time complexities in order from fastest to slowest:

1. O(logN) and O(log2n): These are the fastest because logarithmic time complexity increases very slowly as N increases. Note that O(logN) and O(log2n) are equivalent because the base of the logarithm is not significant in big O notation.

2. O(N^0.5): This is the square root function, which grows faster than logarithmic time but slower than linear time.

3. O(N): This is linear time complexity, which means the runtime increases proportionally with N.

4. O(NlogN): This is linearithmic time complexity, which grows faster than linear time but slower than quadratic time.

So, the algorithm with time complexity O(NlogN) should execute the slowest for large values of N.