8/10/2019 Lab1 - 4 Slides Per Page

1/9

Programming TechniquesLab 1

Lecture Overview

Note on invariants

The Dutch national flag problem

Star proximity

Profiling

Debugging

nvariants

The assert! " function can be #isable# #uringcompiling so you shoul# never put comman#s thatare part of the algorithm in the assertion$$$

Programmers can eliminate the assertions withoutchanging the source co#e% if the macro ND&'()is#efine# before the inclusion of *assert+h,- or thesource co#e is compile# with the .DND&'()flag theassert!" macro is #efine# simply as%

/#efine assert!ignore"!!voi#" 0"

e+g+ assert! myPointer malloc!si2eof3myPointer "4 55bro6enco#e

Problem Statement

7ssume we have an unor#ere# array withre#an# blueelements

8ow #o we separate the re# from the blueelements

9emember re#,* blue

8/10/2019 Lab1 - 4 Slides Per Page

2/9

The #utch national flag problem

The #utch national flag problem !1st attempt":ount an# reconstruct

/of%9e#%'lue%

The #utch national flag problem !1st attempt":ount an# reconstruct

/of%9e#% ;'lue% ;

The #utch national flag problem !1st attempt"

:reate a new array with the number of re# an#blue elements counte# before

8/10/2019 Lab1 - 4 Slides Per Page

3/9

The #utch national flag problem !

8/10/2019 Lab1 - 4 Slides Per Page

4/9

The #utch national flag problem !

8/10/2019 Lab1 - 4 Slides Per Page

5/9

The #utch national flag problem

=hich approach ren#ers better results> =hat is the complexity of this problem> n what #irections can we exam the problem>

Optimi2ations might complicate things

Same experiment run with optimi2ation #isable# !left" an# with optimi2ation !.O?flag" enable# !right"+ The re# @ blue is represente# by 0 an# 1- respectively- in anarray of integers+

10

8/10/2019 Lab1 - 4 Slides Per Page

6/9

The #utch national flag problem !original"

Problem invariants%7ll the cells to the left of re# mar6er are re#$7ll the cells to the right of blue mar6er are blue$

9ules of the game

Start transparent mar6er+

f re#element is foun#- swap the element pointe# by the transparentmar6er with the one pointe# by the re#one an# increment bothmar6ers+

f a white element is foun#- increment only the transparent mar6er+ f a blueelement is foun#- swap the element pointe# by the transparent

mar6er with the one pointe# by the blueone an# #ecrement the bluemar6er only+

The #utch national flag problem !original"

The #utch national flag problem is cre#ite# to DiG6stra+ t is the i#ea behin# the ?.way partitioning in quic6.sort Huic6sort goes qua#raticunless partitioning stops on equal 6eys+

Star proximity

Task: Find all the pairs ofpoints that are closer thana given distance d, (d

8/10/2019 Lab1 - 4 Slides Per Page

7/9

Star proximity !brute force"

We could compare the distanceof every pair of points i, j usingthe knon formula:

!ut, e ill end up ith a vastamount of comparisons" #incee have Ndots and e compareeach one of them ith theremaining N-1 dots, e end upith N*(N-1)/2 ~ O(N2)calculations. $his pro%lem%ecomes infeasi%lefor large N.

d i, j=(xix j)2+(yiyj)

2

Star proximity !

8/10/2019 Lab1 - 4 Slides Per Page

8/9

A+0

8/10/2019 Lab1 - 4 Slides Per Page

9/9

Star proximity

intmain(intargc, charargv23)4 inti, j, 0 atoi(argv213)5 d atof(argv23)5

6 17d5 grid mallocd(68, 68)5 for(i 5 i < 685 i88) for(j 5 j < 685 j88) grid2i32j3 095 for(i 5 i < 05 i88) gridinsert(randFloat(), randFloat())5 printf(;dedges shorter than f=n;, cnt, d)5 return5>

?include