CPS 130 Quiz 1 Recurrences

Write your answers on this sheet in the space provided.^{1}

1. Prove using the substitution method that the recurrence T (n) = 2T (n/2) + n has solution T (n) = O(n log n). Assume, as usual, that n is a power of 2 and T (1) = 1.

1Collaboration is NOT allowed and is severly penalized.

2. Using the iteration method find an asymptotic tight bound for the recurrence T (n) = 7T (n/2) + n^{3}. Assume, as usual, that n is a power of 2 and T (1) = 1.