Assertion (A): Ternary search is asymptotically faster than binary search because . Reason (R): Asymptotic notation ignores constant multiplicative factors, and making their asymptotic growth rate identical: .

(A) is false, but (R) is true. Explanation: Analysis of Assertion (A): Asymptotic time complexity ignores constant factors. Although ternary search reduces the search space to per iteration requiring iterations, each iteration requires 2 comparisons instead of 1. Total comparisons for ternary search . Asymptotically, both Binary Search and Ternary Search have the same growth rate of . Ternary search is not asymptotically faster. Therefore, Assertion (A) is False. Analysis of Reason (R): By the change of base formula for logarithms: Since is a constant multiplicative factor, asymptotic notations ( , , ) ignore it. Hence, both algorithms have an identical asymptotic growth rate of . Therefore, Reason (R) is True.

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CUET PG 2026 — DSA PYQ

CUET PG | DSA | 2026

Assertion (A): Ternary search is asymptotically faster than binary search because $\log_3 n < \log_2 n$ .

Reason (R): Asymptotic notation ignores constant multiplicative factors, and $lo g_{3} n = \frac{1}{l o g _{2} 3} lo g_{2} n$ making their asymptotic growth rate identical: $Θ (lo g n)$ .

Choose the correct answer: