Computer Science study slides on Recursion
- 1. Comments from last time • Purpose of Master theorem? • What does a, b, and d represent • Finding a, b, d from pseudocode
- 2. Div-Conquer Multiplication 1234 × 5678 n: lenth of numbers, input size: 2n 12 × 78 1×5 34 × 56 34 × 78 12 × 56 1×6 2×5 2×6
- 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
- 5. Faster Div-Conquer Multiplication 1234 × 5678 34 × 78 (12 + 56) × (34 + 78) 12 × 56 = 68 × 112
- 6. Faster Div-Conquer Multiplication 12345678 × 87654321 5678 × 4321 (1234 + 5678) × (8765 + 4321) 1234 × 8765 = 6912 × 13086
- 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/ n/4 /4 n/4
- 8. Recursion Tree: T(n) = 2T(n / 3) + O(n) n n/3 n/9 n/9 n/9 n/9 n/3
- 9. Recursion Tree: T(n) = 3T(n / 3) + O(n) n/3 n/9 n/9 n/9 n/9 n/9 n/9 n/3 n n/9 n/9 n/9 n/3