Algorithms - Lab 1, Problem 2

Introduction

This is a hand-in written by Group 7 (FIRE) for the Algorithms course (TIN092) at Chalmers University of Technology.

Group 7 consists of:

  • Mazdak Farrokhzad

    • 901011-0279

    • twingoow@gmail.com

    • Program: IT

  • Niclas Alexandersson

    • 920203-0111

    • nicale@student.chalmers.se

    • Program: IT

This problem deals with complexity analysis of a recursive algorithm to rotate the pixels of a bitmap. The algorithm uses a low level operation called a blit, which copies one rectangular chunk of pixels from one location to another. The algorithm works by splitting the bitmap into four sections of equal size, using a sequence of five blits to move the sections into their right place, then recursively rotating each section in the same manner.

function rotate(s) begin if side length of s > 1 then split s into 4 sections blit sections into place for each section loop rotate(section) end loop end if end

Laws and forumulas of summation

These summation laws/formulas are used. They are very common and thus we won’t prove any of them. Most of them can be found here.

  1. \(\displaystyle\sum_{n=s}^t C\cdot f(n) = C\cdot \sum_{n=s}^t f(n)\)

  2. \(\displaystyle\sum_{i = 0}^{n-1} a^i = \frac{1 - a^n}{1 - a}\)

</