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CUET PG 2026 — DSA PYQ

CUET PG | DSA | 2026

What is the expected time complexity of Interpolation Search on a uniformly distributed sorted array of size N?

Choose the correct answer:

Explanation

Working Principle:
Interpolation Search estimates the likely position of the target element using linear interpolation:
$pos = low + [\frac{target - arr [ low ]}{arr [ high ] - arr [ low ]}] \times (high - low)$
Expected Time Complexity:
When elements are uniformly distributed, the probe position divides the search space such that the size of the remaining array is reduced roughly to $N$ at each step.
Solving the recurrence relation $T (N) = T (N) + O (1)$ yields:
$Expected Time Complexity = O (lo g lo g N)$
Other Cases:
- Best Case: $O (1)$ (when the target is at the calculated position on the first try).
- Worst Case: $O (N)$ (when elements are exponentially distributed rather than uniform).

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