Understanding Space Complexity in Algorithms
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Questions and Answers

What is the time complexity of Linear Search?

O(n)

When does the Linear Search algorithm yield 'No match found'?

If no element is found equal to the key.

In the context of Linear Search, what does 'Auxiliary space' refer to?

Extra space used by the algorithm to perform the search.

What are the ideal applications of Linear Search?

<p>Searching operations in smaller arrays.</p> Signup and view all the answers

How does the Linear Search algorithm determine a successful match?

<p>When the key matches an element in the array.</p> Signup and view all the answers

Define space complexity.

<p>Space complexity includes both Auxiliary space and space used by input.</p> Signup and view all the answers

What factors are used to compute space complexity?

<p>Constant and instance characteristics.</p> Signup and view all the answers

Explain the space requirement formula S(p) = C + Sp.

<p>S(p) = C + Sp where C is a constant fixed part and Sp denotes the space of inputs and outputs.</p> Signup and view all the answers

Provide an example algorithm and calculate its space complexity.

<p>Algorithm add(a,b,c) { return a+b+c; } If a, b, c occupy one word size, the total size is 3.</p> Signup and view all the answers

Explain how Linear Search algorithm works.

<p>Linear Search is a sequential search algorithm that checks each element of a list until the desired element is found or the end of the data set is reached.</p> Signup and view all the answers

What happens if the key is not found during a Linear Search?

<p>The search continues till the end of the data set.</p> Signup and view all the answers

What is the time complexity of an algorithm that has a running time proportional to the square of the input size?

<p>O(n^2)</p> Signup and view all the answers

Give an example of an algorithm associated with O(n^2) time complexity.

<p>Selection sort</p> Signup and view all the answers

In the Selection Sort algorithm, what does the number of comparisons and swaps grow with as the size of the array increases?

<p>Square of the input size</p> Signup and view all the answers

What is the time complexity of an algorithm that has a running time proportional to the cube of the input size?

<p>O(n^3)</p> Signup and view all the answers

Give an example of an algorithm associated with O(n^3) time complexity.

<p>Naive matrix multiplication</p> Signup and view all the answers

What type of algorithms often have triple nested loops and O(n^3) time complexity?

<p>Less efficient algorithms</p> Signup and view all the answers

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