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Official PYQ · 1999

GATE CS 1999 Q2.21 — Asymptotic Worst Case Time and Space Complexity

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If T1=O(1)T_1 = O(1), give the correct matching for the following pairs:
(M) Tn=Tn−1+n(U) T_n=O(n)(N) Tn=Tn/2+n(V) T_n=O(nlog⁡n)(O) Tn=Tn/2+nlog⁡n(W) T_n=O(n2)(P) Tn=Tn−1+log⁡n(X) T_n=O(log⁡2n)\begin{array}{|ll|ll|}\hline & \text{(M) $T_n = T_{n-1} + n$} & \text{(U) $T\_n = O(n)$} \\ \hline & \text{(N) $T_n = T_{n/2} + n$} & \text{(V) $T\_n = O(n \log n)$} \\ \hline & \text{(O) $T_n = T_{n/2} + n \log n$} & \text{(W) $T\_n = O(n^2)$} \\ \hline & \text{(P) $T_n = T_{n-1} + \log n$} & \text{(X) $T\_n = O(\log^2 n)$} \\ \hline \end{array}

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