1. [5 pts]: What is the worst-case big-O asymptotic running time of the following method mthd, assuming that the parameter n is a positive integer? Assume that the time complexity of addition is logarithmic in the magnitude of the number. Justify your answer.

void mthd ( int n ) {

int answer = 0;

for ( int i = 1; i <= n; i++ ) {

for ( int k = 1; k <= n; k++ ) {

answer += i + k;

}

}

for ( int m = 1; m < n; m++ ) {

answer += m;

}

}

Solution:

2. [5 pts]: Consider that f(n) = n + n lg n is Q(n lg n) by applying the definition of Q-complexity from Chapter 3 of Cormen (reproduced below).

Definition: (g(n)) = { f(n) : there exists positive constants c₁, c₂, n₀ such that 0 c₁g(n) f(n) c₂g(n) , for n n₀}. Find a (c₁, c₂, n₀) triple that meets the criteria. Show some work.