1. Comments from last time
Purpose of Master theorem?
What does a, b, and d represent
Finding a, b, d from pseudocode 1

2. Div-Conquer Multiplication
n: lenth of numbers,
input size: 2n
1234 × 5678
12 × 56
12 × 78
34 × 56
34 × 78
1×5
1×6
2×5
2×6 2

3. O(n) time operations n: lenth of numbers
Shift  multiply by 10: take array, move all elements
Addition / subtraction: add/subtract digits, then carry 3

4. Comment cards 4

5. = Faster Div-Conquer Multiplication 1234 × 5678 12 × 56 34 × 78
( ) × ( ) =
68 × 112 5

6. = Faster Div-Conquer Multiplication 12345678 × 87654321×
( ) × ( )
1234 × 8765
5678 × 4321 =
6912 × 13086 6

7. Recursion Tree: T(n) = 3T(n / 2) + O(n)
n: lenth of numbers,
input size: 2n n
n/2
n/2
n/2
n/4
n/4
n/4
n/4
n/4
n/4
n/4
n/4
n/4 7

8. Recursion Tree: T(n) = 2T(n / 3) + O(n)8

9. Recursion Tree: T(n) = 3T(n / 3) + O(n)9