Question: The recurrence you should solv ef or this question is only defined when n = 2 k for some inte ger k where k 3.

The recurrence you should solv ef or this question is only defined when n = 2 k for some inte ger k where k 3. The base case is T (8) = 7. When k 4t he recurrence is given by T ( n ) = n + 2 T ( n /2). Solve this recurrence relation using repeated substitution. T os howy our w ork when using repeated substitution you should number your steps so that you have: Step 0: The original recurrence for T(n). Hint: The algebra is easier if you use Step 0: T ( n ) = T (2 k ) = 2 k + 2 T (2 k 1 ). Step 1: The formula for T(n) after one substitution into the RHS. Step 2: The formula for T(n) after tw os ubstitutions into the RHS. -2- Then determine the general pattern for Step i: Step i: The formula for T(n) after i substitutions into the RHS. Ne xt determine at which step i the base case appears on the RHS of the formula, say at some step f. Then use your template for Step f to get a closed formula for the recurrence relation.

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