Data Structures & Algorithms for Competitive Exam Prep

Data Structures & Algorithms

Q. If a stack has a maximum size of 100 and you attempt to push 101 elements onto it, what will happen?

A. The 101st element will be pushed successfully.
B. An error will occur due to stack overflow.
C. The stack will automatically resize.
D. The stack will discard the oldest element.

Solution

Attempting to push more elements than the maximum size of the stack will result in a stack overflow error.

Correct Answer: B — An error will occur due to stack overflow.

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Q. If a stack has a maximum size of 5, what will happen if we try to push a 6th element?

A. The element will be added
B. The stack will overflow
C. The stack will shrink
D. The operation will be ignored

Solution

If we try to push a 6th element onto a full stack, it will overflow.

Correct Answer: B — The stack will overflow

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Q. If a stack is implemented using a linked list, what is the time complexity of the 'pop' operation?

A. O(1)
B. O(n)
C. O(log n)
D. O(n^2)

Solution

The 'pop' operation in a stack implemented using a linked list is done in constant time, O(1), as it involves removing the head node.

Correct Answer: A — O(1)

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Q. If a stack is implemented using an array, what is the time complexity of resizing the array when it is full?

A. O(1)
B. O(n)
C. O(log n)
D. O(n^2)

Solution

Resizing the array involves creating a new array and copying all elements, which takes O(n) time.

Correct Answer: B — O(n)

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Q. If a stack is used to evaluate an expression in postfix notation, what is the time complexity of the evaluation?

A. O(1)
B. O(n)
C. O(log n)
D. O(n^2)

Solution

The time complexity of evaluating an expression in postfix notation using a stack is O(n), where n is the number of tokens in the expression.

Correct Answer: B — O(n)

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Q. If an array contains 32 elements, how many iterations will binary search take in the worst case?

A. 4
B. 5
C. 6
D. 7

Solution

For an array of 32 elements, the worst-case number of iterations is log2(32) = 5.

Correct Answer: A — 4

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Q. If an array has 16 elements, how many comparisons will binary search make in the worst case?

A. 4
B. 5
C. 16
D. 8

Solution

In the worst case, binary search will make at most log2(16) = 4 comparisons.

Correct Answer: B — 5

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Q. If an array is already sorted, what is the time complexity of Quick Sort?

A. O(n)
B. O(n log n)
C. O(n^2)
D. O(log n)

Solution

In the worst case, which occurs when the array is already sorted, Quick Sort has a time complexity of O(n^2).

Correct Answer: C — O(n^2)

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Q. If an array is sorted in descending order, can binary search still be used?

A. Yes, with modifications
B. No, it cannot be used
C. Yes, without modifications
D. Only for specific cases

Solution

Binary search can be used on a descending sorted array, but the comparison logic must be adjusted.

Correct Answer: A — Yes, with modifications

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Q. If the array has 16 elements, how many comparisons will binary search make in the worst case?

A. 4
B. 5
C. 16
D. 8

Solution

In the worst case, binary search will make log2(16) = 4 comparisons.

Correct Answer: B — 5

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Q. If the array is sorted in descending order, can binary search still be applied?

A. Yes, with modifications
B. No, it cannot be applied
C. Yes, without any changes
D. Only for specific cases

Solution

Binary search can be applied to a descending sorted array with modifications to the comparison logic.

Correct Answer: A — Yes, with modifications

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Q. If the array is [1, 2, 3, 4, 5] and the target is 3, what will be the mid index during the first iteration?

A. 0
B. 1
C. 2
D. 3

Solution

The mid index is calculated as (0 + 4) // 2 = 2, which corresponds to the value 3.

Correct Answer: C — 2

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Q. If the array is [1, 2, 3, 4, 5] and the target is 3, what will be the mid index during the first iteration of binary search?

A. 0
B. 1
C. 2
D. 3

Solution

In the first iteration, mid is calculated as (0 + 4) // 2 = 2, which corresponds to the value 3.

Correct Answer: C — 2

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Q. If the array is [1, 2, 3, 4, 5] and we search for 6, what will be the final result of binary search?

A. 0
B. -1
C. 5
D. 4

Solution

Since 6 is not in the array, binary search will return -1.

Correct Answer: B — -1

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Q. If the array is [2, 3, 4, 10, 40] and we are searching for 10, what is the first mid index calculated in binary search?

A. 0
B. 2
C. 3
D. 1

Solution

The mid index is calculated as (0 + 4) / 2 = 2, which points to the value 4.

Correct Answer: C — 3

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Q. If the binary search algorithm is implemented recursively, what is the space complexity due to recursion?

A. O(1)
B. O(log n)
C. O(n)
D. O(n log n)

Solution

The space complexity of a recursive binary search is O(log n) due to the call stack.

Correct Answer: B — O(log n)

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Q. If the size of the array is doubled, how does the time complexity of binary search change?

A. It doubles
B. It remains the same
C. It becomes O(n)
D. It becomes O(n log n)

Solution

The time complexity of binary search is O(log n), which does not change with the size of the array.

Correct Answer: B — It remains the same

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Q. If the target value is not present in a sorted array, what will binary search return?

A. The index of the closest value
B. The index of the first element
C. The index of the last element
D. -1 or a sentinel value

Solution

If the target value is not found, binary search typically returns -1 or a sentinel value indicating absence.

Correct Answer: D — -1 or a sentinel value

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Q. If the target value is not present in the array, what will binary search return?

A. The index of the closest value
B. The index of the first element
C. The index of the last element
D. -1

Solution

If the target value is not found, binary search typically returns -1 to indicate absence.

Correct Answer: D — -1

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Q. If you have a sorted array of 1000 elements, how many iterations will binary search take to find an element?

A. 10
B. 9
C. 8
D. 7

Solution

Binary search will take log2(1000) which is approximately 9.97, so it will take at most 10 iterations.

Correct Answer: B — 9

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Q. If you have a sorted array of 1000 elements, how many iterations will binary search take at most?

A. 10
B. 20
C. 30
D. 40

Solution

Binary search will take at most log2(1000) which is approximately 10 iterations.

Correct Answer: A — 10

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Q. In a binary search algorithm, if the middle element is greater than the target, what should be done next?

A. Search the left half
B. Search the right half
C. Return the middle element
D. Increase the middle index

Solution

If the middle element is greater than the target, the search continues in the left half of the array.

Correct Answer: A — Search the left half

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Q. In a binary search algorithm, if the target is less than the mid element, what should be the next step?

A. Search the right half
B. Search the left half
C. Return the mid index
D. Increase the mid index

Solution

If the target is less than the mid element, the search should continue in the left half of the array.

Correct Answer: B — Search the left half

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Q. In a binary search algorithm, if the target is less than the mid value, what should be the next step?

A. Search the left half of the array
B. Search the right half of the array
C. Return the mid index
D. Increase the mid index

Solution

If the target is less than the mid value, the next step is to search the left half of the array.

Correct Answer: A — Search the left half of the array

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Q. In a binary search algorithm, what happens if the middle element is equal to the target?

A. Search continues in the left half
B. Search continues in the right half
C. Target is found
D. Search terminates immediately

Solution

If the middle element is equal to the target, the search is successful and the target is found.

Correct Answer: C — Target is found

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Q. In a binary search algorithm, what happens if the middle element is less than the target?

A. Search the left half
B. Search the right half
C. Return the middle element
D. Terminate the search

Solution

If the middle element is less than the target, the search continues in the right half of the array.

Correct Answer: B — Search the right half

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Q. In a binary search algorithm, what happens if the target is less than the mid value?

A. Search the right half
B. Search the left half
C. Return the mid index
D. Increase the mid index

Solution

If the target is less than the mid value, the search continues in the left half of the array.

Correct Answer: B — Search the left half

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Q. In a binary search algorithm, what happens if the target is less than the middle element?

A. Search the right half
B. Search the left half
C. Return the middle element
D. End the search

Solution

If the target is less than the middle element, the search continues in the left half of the array.

Correct Answer: B — Search the left half

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Q. In a binary search algorithm, what happens to the search space after each comparison?

A. It doubles
B. It remains the same
C. It halves
D. It increases linearly

Solution

After each comparison in binary search, the search space is halved, which is why it is efficient.

Correct Answer: C — It halves

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Q. In a binary search implementation, if the target is less than the mid value, what should be the next step?

A. Search the right half
B. Search the left half
C. Return the mid index
D. Increase the mid index

Solution

If the target is less than the mid value, the search should continue in the left half of the array.

Correct Answer: B — Search the left half

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Data Structures & Algorithms

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