Given two runtime for algorithm A and algorithms B for solvi

Given two runtime for algorithm A and algorithms B, for solving the same problem. If the runtime for: algorithm A and B are given as below: T_A(N) - O(N lg N) and T_B(N) = O(N^2). Which algorithm will you prefer and why?

Solution

So if we have 2 algorithms having Runtime

T_A(N)=O(NlogN)

T_B(N)=O(N²)

So we will prefer the first Algorithm that is Algorithm \'A\', because in Algorithm A, for all very lage Values of N,the Value of NlogN has a very small value as compared to N².

As NlogN is Smaller in Value as Compared to N², so NlogN will take Smaller time as Compared to N²

So,Algorithm having runtime O(NlogN) will take less time as compared to the algorithm having runtime O(N²).

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