1 Assume the addition of the two functions public void recur

1. Assume the addition of the two functions:

public void recursiveDelete(int ky) {

// calls the private version

}

private Node recursiveDelete(int ky, Node n);

Write both functions.

2. Algorithm A has running time T_A(n) = 10⁶ + 10⁴ × n + 10⁵ × n² and algorithm B has running time TB(n) = 3 × n³ , where n is the number of values the algorithms processes. Give the “big O” equations for the running times and state which algorithm is fastest for large n.

3. Algorithm C has running time T_C(n) = O(n), algorithm D has running time T_D(n) = O(log n), and algorithm E has running time T_E(n) = O(sqrt(n)). Which algorithm is the fastest and which is the slowest for large n?

Solution

Q1.) Given question is not clear

Q2.) t(A(n)) = 105n²+104n+106 = O(n²)

t(B(n)) = 3n³ = O(n³)

It is clear, algo. A will be fastest for large value of n as algo. A has time complexity O(n²) while algo B has time complexity O(n³).

Q3.)

We know, O(logn)>O(sqrt(n)) > O(n) will be the order for fast execution.

Therefore, out of three algo. , D will be fastest as time complexity of D is O(logn) and C will be slowest as time complexity of C is O(n).

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