data structure

Question

describe in details

Comments

Option D, it returns 0

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nope answer given b

Answer 1

ANSWER: B

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EXPLANATION

The for loop (line 4-5) calculates the sum of numbers in the array and store it in a variable called value.

Sum of k natural numbers is given by

$x = \frac{k(k-1)}{2}$

Validity of this formula can be checked with the help of Principle of Mathematical Induction. On line 7 in the code, the same is being calculated and stored in variable called last.

So if we have an array with no repetition of numbers, then calculating the sum of numbers in array iteratively will be same as that of result produced from the above formula. However, the results will not be same if there is a repetition of numbers in the array. In fact, the difference between the two is the number which was repeated in the array.

Let us assume an array $(k = 5)$

$arr = [1,2,3,2,4]$

As we can see that $2$ is repeatd in the assumed array above. 

Let's calculate the sum of numbers in the array iteratively; we get 

$value = 12$. 

Now calculate the sum using the formula; we get

$last = \frac{5*4}{2} = 10$

If we subtract the two values calculated above we get the repeated number in the array.

$value-last = 2$

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P.S You might find this blogpost helpful.

Comments

is it works only for one repitition,cause i choosed  array as 1224335 then this program fails.

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@Sayantan Ganguly~ Yes, you are right. This technique works only in case of one repetition. However, the technique can be generalized for more than one repetition. Please refer to the link in P.S of my answer. It included a detailed explanation of this problem and its solution.