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Given an array of 1,000,000 distinct integers you are going to perform 100,000 searches, one at a time, using the linear search algorithm. Each element you are searching for is in the array. What is the expected, total number of comparisons performed by the 100,000 linear searches?

Given Ans: 5x10^10 + 5x10^4

Expected number of searches for a single linear search of $n$ elements

$$= 1.\frac{1}{n} + 2.\frac{1}{n} + \dots n.\frac{1}{n}$$

as elements are distinct and the probability of any element being equal to the searched element is $\frac{1}{n}$ as element is guaranteed to be present

$= \frac{n+1}{2}$.

Here, $n = 1,000,000$. So, expected number of comparisons $= 1,000,001/2$

Expected no. of comparisons for 100,000 such searches $= 100,000 \times 1,000,001/2 \\=5 \times 10^{10} + 5 \times 10^4$
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good question and good explaination ,thanks :)