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Unformatted text preview: Discrete Structures Sept 12 2011 Assignment 3: Due at beginning of class Mon, Sept 19 Prof. Hopcroft *******Note: this homework is subject to the style guide on the website. Points will be deducted for homeworks not following the guidelines.******** *******Please print out and staple the grade sheet to the back of your homework!****** 1 Recurrence Relations: Bottom Up For each of the characteristic equations: 1. Find the corresponding recurrence equation. 2. How many boundary conditions are necessary for a complete solution to f ( n )? 3. Show that the roots of the characteristic equations raised to the n th power are solutions of the recurrence equation. Ie f ( n ) = r n , where r is a root of the corresponding characteristic equation, satisfies the recurrence equation. The characteristic equations: x 2 = 0 x 2 + 2 x 15 = 0 8 x 3 8 x 2 + 4 x 1 = 0 2 Recurrence Relation: Top Down For each of the recurrence equations: 1. Find the characteristic equation and its roots....
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