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65 Pages

CS1114-lec9

Course: CS 100, Fall 2008
School: Cornell
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Word Count: 1776

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and Breadthfirst depthfirst traversal Prof. Noah Snavely CS1114 http://cs1114.cs.cornell.edu Administrivia Assignment 2, Part 2, due Friday Assignment 3 will be out Friday Survey: Please sign up for a Friday slot Should we move lecture closer to the lab? Prelim 1! Next Thursday, 2/26, in class There will be a review session TBA 2 Final notes on BigO Notation If algorithm A is O(n2) and algorithm B...

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and Breadthfirst depthfirst traversal Prof. Noah Snavely CS1114 http://cs1114.cs.cornell.edu Administrivia Assignment 2, Part 2, due Friday Assignment 3 will be out Friday Survey: Please sign up for a Friday slot Should we move lecture closer to the lab? Prelim 1! Next Thursday, 2/26, in class There will be a review session TBA 2 Final notes on BigO Notation If algorithm A is O(n2) and algorithm B is O(n), we know that: For large n, A will eventually run much slower than B For small n, we know very little: A could be slower B could be slower They could have similar runtimes Or difference could be very large 3 Final notes on BigO Notation B A A B 4 Finding blobs 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 Finding blobs 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 Blobs are connected components! Finding components 1. Pick a 1 to start with, where you don't know which component it is in 2. Give it a new component color 3. Assign the same component color to each pixel that is part of the same component Basic strategy: color any neighboring 1's, have them color their neighbors, and so on When there aren't any, you're done 7 Finding components For each vertex we visit, we color its neighbors and remember that we need to visit them at some point Need to keep track of the vertices we still need to visit in a todo list After we visit a vertex, we'll pick one of the vertices in the todo list to visit next This is also called graph traversal 8 Stacks and queues Two ways of representing a "todo list" Stack: Last In First Out (LIFO) (Think cafeteria trays) The newest task is the one you'll do next Queue: First In First Out (FIFO) (Think a line of people at the cafeteria) The oldest task is the one you'll do next 9 Stacks Two operations: Push: add something to the top of the stack Pop: remove the thing on top of the stack 10 Queue Two operations: Enqueue: add something to the end of the queue Dequeue: remove something from the front of the queue 11 Graph traversal Suppose you're in a maze What strategy can you use to find the exit? 12 Graph traversal London Paris Frankfurt Oslo Stockholm Hamburg Rome Naples Berlin Vienna Prague Warsaw 13 Graph traversal (stack) London 1 Paris Frankfurt Oslo Stockholm Hamburg Rome Naples Berlin Vienna Prague Warsaw Current node: London Todo list: [ ] 14 Graph traversal (stack) London 1 Paris Frankfurt Oslo Stockholm Hamburg Rome Naples Berlin Vienna Prague Warsaw Current node: London Todo list: [ Paris ] 15 Graph traversal (stack) London 1 Paris Frankfurt Oslo Stockholm 2 Hamburg Rome Naples Berlin Vienna Prague Warsaw Current node: Paris Todo list: [ ] 16 Graph traversal (stack) London 1 Paris Frankfurt Oslo Stockholm 2 Hamburg Rome Naples Berlin Vienna Prague Warsaw Current node: Paris Todo list: [ Frankfurt, Berlin, Rome ] 17 Graph traversal (stack) London 1 Paris Frankfurt Oslo Stockholm 2 Hamburg 3 Rome Naples Berlin Vienna Prague Warsaw Current node: Rome Todo list: [ Frankfurt, Berlin ] 18 Graph traversal (stack) London 1 Paris Frankfurt Oslo Stockholm 2 Hamburg 3 Rome Naples Berlin Vienna Prague Warsaw Current node: Rome Todo list: [ Frankfurt, Berlin, Naples ] 19 Graph traversal (stack) London 1 Paris Frankfurt Oslo Stockholm 2 Hamburg 3 Rome Naples Berlin Vienna Prague 4 Warsaw Current node: Naples Todo list: [ Frankfurt, Berlin ] 20 Graph traversal (stack) London 1 Paris Frankfurt Oslo Stockholm 2 Hamburg 3 Rome Naples Berlin 5 Vienna Prague 4 Warsaw Current node: Berlin Todo list: [ Frankfurt ] 21 Graph traversal (stack) London 1 Paris Frankfurt Oslo Stockholm 2 Hamburg 3 Rome Naples Berlin 5 Vienna Prague 4 Warsaw Current node: Berlin Todo list: [ Frankfurt, Hamburg, Vienna ] 22 Graph traversal (stack) London 1 Paris Frankfurt Oslo Stockholm 2 Hamburg 3 Rome Naples Berlin 5 Vienna 6 Prague 4 Warsaw Current node: Vienna Todo list: [ Frankfurt, Hamburg ] 23 Graph traversal (stack) London 1 Paris Frankfurt Oslo Stockholm 2 Hamburg 3 Rome Naples Berlin 5 Vienna 6 Prague 4 Warsaw Current node: Vienna Todo list: [ Frankfurt, Hamburg, Prague, Warsaw ] 24 Graph traversal (stack) London 1 Paris Frankfurt Oslo Stockholm 2 Hamburg 3 Rome Naples Berlin 5 Vienna 6 Prague 4 Warsaw Current node: Vienna Todo list: [ Frankfurt, Hamburg, Prague, Warsaw ] 25 Graph traversal (stack) London 1 Paris Frankfurt Oslo Stockholm 2 Hamburg 3 Rome Naples Berlin 5 Vienna 6 Prague 4 7 Warsaw Current node: Warsaw Todo list: [ Frankfurt, Hamburg, Prague ] 26 Graph traversal (stack) London 1 Paris Frankfurt Oslo Stockholm 2 Hamburg 3 Rome Naples Berlin 5 Vienna 6 Prague 8 7 Warsaw 4 Current node: Prague Todo list: [ Frankfurt, Hamburg ] 27 Graph traversal (stack) London 1 Paris Frankfurt Oslo Stockholm 2 9 Hamburg 5 Vienna Prague 3 Rome Naples Berlin 6 8 7 Warsaw 4 Current node: Hamburg Todo list: [ Frankfurt ] 28 Graph traversal (stack) London 1 Paris Frankfurt Oslo 2 10 Stockholm 9 Hamburg 5 Vienna Prague 3 Rome Naples Berlin 6 8 7 Warsaw 4 Current node: Frankfurt Todo list: [ ] 29 Depthfirst search (DFS) 1 2 10 9 5 6 7 8 3 4 Call the starting node the root We traverse paths all the way until we get to a deadend, then backtrack (until we find an unexplored path) 30 Another strategy 1. Explore all the cities that are one hop away from the root 2. Explore all cities that are two hops away from the root 3. Explore all cities that are three hops away from the root ... This corresponds to using a queue 31 Graph traversal (queue) London 1 Paris Frankfurt Oslo Stockholm Hamburg Rome Naples Berlin Vienna Prague Warsaw Current node: London Todo list: [ ] 32 Graph traversal (queue) London 1 Paris Frankfurt Oslo Stockholm Hamburg Rome Naples Berlin Vienna Prague Warsaw Current node: London Todo list: [ Paris ] 33 Graph traversal Naples Berlin Vienna Prague Warsaw Current (queue) London 1 Paris Frankfurt Oslo Stockholm 2 Hamburg Rome node: Paris Todo list: [ ] 34 Graph traversal (queue) London 1 Paris Frankfurt Oslo Stockholm 2 Hamburg Rome Naples Berlin Vienna Prague Warsaw Current node: Paris Todo list: [ Frankfurt, Berlin, Rome ] 35 Graph traversal (queue) London 1 Paris Frankfurt Oslo 2 3 Stockholm Hamburg Rome Naples Berlin Vienna Prague Warsaw Current node: Frankfurt Todo list: [ Berlin, Rome ] 36 Graph traversal (queue) London 1 Paris Frankfurt Oslo 2 3 Stockholm Hamburg Rome Naples Berlin Vienna Prague Warsaw Current node: Frankfurt Todo list: [ Berlin, Rome, Hamburg ] 37 Graph traversal (queue) London 1 Paris Frankfurt Oslo 2 3 Stockholm Hamburg Rome Naples Berlin 4 Vienna Prague Warsaw Current node: Berlin Todo list: [ Rome, Hamburg ] 38 Graph traversal (queue) London 1 Paris Frankfurt Oslo 2 3 Stockholm Hamburg Rome Naples Berlin 4 Vienna Prague Warsaw Current node: Berlin Todo list: [ Rome, Hamburg, Vienna ] 39 Graph traversal (queue) London 1 Paris Frankfurt Oslo 2 3 Stockholm Hamburg 5 Rome Naples Berlin 4 Vienna Prague Warsaw Current node: Rome Todo list: [ Hamburg, Vienna ] 40 Graph traversal (queue) London 1 Paris Frankfurt Oslo 2 3 Stockholm Hamburg 5 Rome Naples Berlin 4 Vienna Prague Warsaw Current node: Rome Todo list: [ Hamburg, Vienna, Naples ] 41 Graph traversal (queue) London 1 Paris Frankfurt Oslo 2 3 Stockholm 6 Hamburg 4 Vienna Prague 5 Rome Naples Berlin Warsaw Current node: Hamburg Todo list: [ Vienna, Naples ] 42 Graph traversal (queue) London 1 Paris Frankfurt Oslo 2 3 Stockholm 6 Hamburg 4 Vienna Prague 5 Rome Naples Berlin 7 Warsaw Current node: Vienna Todo list: [ Naples ] 43 Graph traversal (queue) London 1 Paris Frankfurt Oslo 2 3 Stockholm 6 Hamburg 4 Vienna Prague 5 Rome Naples Berlin 7 Warsaw Current node: Vienna Todo list: [ Naples, Prague, Warsaw ] 44 Graph traversal (queue) London 1 Paris Frankfurt Oslo 2 3 Stockholm 6 Hamburg 4 Vienna Prague 5 Rome Naples Berlin 7 8 Warsaw Current node: Naples Todo list: [ Prague, Warsaw ] 45 Graph traversal (queue) London 1 Paris Frankfurt Oslo 2 3 Stockholm 6 Hamburg 4 Vienna Prague 5 Rome Naples Berlin 7 9 Warsaw 8 Current node: Prague Todo list: [ Warsaw ] 46 Graph traversal (queue) London 1 Paris Frankfurt Oslo 2 3 Stockholm 6 Hamburg 4 Vienna Prague 5 Rome Naples Berlin 7 9 10 Warsaw 8 Current node: Warsaw Todo list: [ ] 47 Breadthfirst search (BFS) 1 2 3 6 4 7 10 9 5 8 We visit all the vertices at the same level (same distance to the root) before moving on to the next level 48 BFS vs. DFS 1 2 3 6 4 7 10 9 4 1 2 10 9 5 6 7 8 5 8 3 Breadthfirst (queue) Depthfirst (stack) 49 BFS vs. DFS (tree = graph with no cycles) 50 Basic algorithms BREADTHFIRST SEARCH (Graph G) While there is an uncolored node r Choose a new color Create an empty queue Q Let r be the root node, color it, and add it to Q While Q is not empty Dequeue a node v from Q For each of v's neighbors u - If u is not colored, color it and add it to Q 51 Basic algorithms DEPTHFIRST SEARCH (Graph G) While there is an uncolored node r Choose a new color Create an empty stack S Let r be the root node, color it, and push it on S While S is not empty Pop a node v from S For each of v's neighbors u - If u is not colored, color it and push it onto S 52 Queues and Stacks Examples of Abstract Data Types (ADTs) ADTs fulfill a contract: The contract tells you what the ADT can do, and what the behavior is For instance, with a stack: We can push and pop If we push X onto S and then pop S, we get back X, and S is as befor...

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Cornell - CS - 100
Breadth-first and depth-first traversalProf. Noah Snavely CS1114 http:/cs1114.cs.cornell.eduAdministriviaAssignment 2, Part 2, due Friday Please sign up for a Friday slotAssignment 3 will be out Friday Survey: Should we move lecture closer t
Cornell - CS - 100
Linked listsProf. Noah Snavely CS1114 http:/cs1114.cs.cornell.eduAdministrivia Assignment 2, Part 2 due tomorrow Please don't wait until the last minute to finish (the last two problems are challenging) Assignment 3 will be posted tomorrow
Cornell - CS - 100
Linked listsProf. Noah Snavely CS1114 http:/cs1114.cs.cornell.eduAdministriviaAssignment 2, Part 2 due tomorrow Please don't wait until the last minute to finish (the last two problems are challenging)Assignment 3 will be posted tomorrow Due
Cornell - CS - 100
Linked lists and memory allocationProf. Noah Snavely CS1114 http:/cs1114.cs.cornell.eduAdministrivia Assignment 3 has been posted Due next Friday, March 6 Prelim 1 Thursday in class Review session this evening at 7:15pm, Upson 315 Review
Cornell - CS - 100
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CS1114: Study Guide 1In the first part of this course, we have covered the topics in this document. Please refer to the class slides for more details.1Finding the center of things: Bounding boxes, centroids, trimmed means, and medians(x1, y1),
Cornell - CS - 100
PolygonsandtheconvexhullProf.NoahSnavely CS1114 http:/cs1114.cs.cornell.eduAdministrivium Assignment3duethisFridayby5pm PleasesignupforslotsonCMS Thelastproblemhasyoucontrollingtherobots withthecamera;youllneedtousethe robotGetFrame function
Cornell - CS - 100
Polygons and the convex hullProf. Noah Snavely CS1114 http:/cs1114.cs.cornell.eduAdministriviumAssignment 3 due this Friday by 5pm Please sign up for slots on CMS The last problem has you controlling the robots with the camera; you'll need to
Cornell - CS - 100
InterpolationProf. Noah Snavely CS1114 http:/cs1114.cs.cornell.eduAdministrivia Assignment 3 due tomorrow by 5pm Please sign up for a demo slot Assignment 4 will be posted tomorrow Quiz 3 next Thursday2Last time Convex hull the smalles
Cornell - CS - 100
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Cornell - CS - 100
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Cornell - CS - 100
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Cornell - CS - 100
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Cornell - CS - 100
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Cornell - CS - 100
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Cornell - CS - 100
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Cornell - CS - 100
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Cornell - CS - 100
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Cornell - CS - 100
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Cornell - CS - 100
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Cornell - CS - 100
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Cornell - CS - 100
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Cornell - CS - 100
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Cornell - CS - 100
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Cornell - CS - 100
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Cornell - CS - 100
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Cornell - CS - 100
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Cornell - CS - 100
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Cornell - CS - 100
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Cornell - CS - 100
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Cornell - CS - 100
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Cornell - CS - 100
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Cornell - CS - 100
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Uni. Westminster - RRG - 1024
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Uni. Westminster - RRG - 1024
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Uni. Westminster - RRG - 1024
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Iowa State - CPRE - 211
Assigned: 2/6/04Due: 2/17/04CprE 211 Spring 2004 Homework 2Last Name First Name Section_ __Grading Procedure for Homework: The number of points of each question is given in brackets. You shall turn in your homework in the class when it is
Iowa State - CPRE - 211
Assigned: 2/6/04Due: 2/17/04CprE 211 Spring 2004 Homework 2 SolutionLast Name First Name Section_ __Grading Procedure for Homework: The number of points of each question is given in brackets. You shall turn in your homework in the class wh
Iowa State - CPRE - 211
Assigned: 3/9/04Due: 3/25/04CprE 211 Spring 2004 Homework 4 SolutionLast Name First Name Section _ _ _Grading Procedure for Homework: The number of points of each question is given in brackets. You shall turn in your homework in the class whe
Iowa State - CPRE - 211
Assigned: 4/20/03Completed by: 4/27/03CprE 211 Spring 2004 Homework 6Last Name First Name Section_ __Grading Procedure for Homework: This homework will not be collected and not be graded. The solution will be distributed on-line one week l
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Washington - FACULTY - 122
Physics 122 Solutions Ch 2727.1. Visualize:As discussed in Section 27.1, the symmetry of the electric field must match the symmetry of the charge distribution. In particular, the electric field of a cylindrically symmetric charge distribution cann
Washington - FACULTY - 122
Physics 122 Solutions to Chapter 2525.1.Model:Use the charge model.Solve:(a) In the process of charging by rubbing, electrons are removed from one material and transferred to the other because they are relatively free to move. Protons, on the other
Washington - FACULTY - 122
Physics 122 Solutions Ch 2626.31. Model: The electric field is that of three point charges q1, q2 and q3.Visualize: Please refer to Figure P26.31. Assume the charges are in the x-y plane. The 5 nC charge is q1, the 10 nC charge is q3, and the -
Washington - FACULTY - 122
30.1. Solve: The potential difference V between two points in space isV = V ( xf ) - V ( xi ) = - Ex dxxi xfwhere x is the position along a line from point i to point f. When the electric field is uniform, V = - Ex dx = - Ex x = - ( 1000 V/m )
Washington - FACULTY - 122
31.1. Solve: From Table 30.1, the resistivity of carbon is = 3.5 10-5 m. From Equation 31.3, the resistanceof lead from a mechanical pencil is R= 3.5 10 -5 m ( 0.06 m ) L L = 2 = = 5.5 2 A r 0.35 10 -3 m(())31.6. Solve: The slope o
Washington - FACULTY - 122
32.7. Model: The magnetic field is that of a moving charged particle.Visualize: Please refer to Figure Ex32.7. Solve: Using the Biot-Savart law, B= 10 -7 T m/A 1.60 10 -19 C 2.0 107 m/s sin135 0 qv sin = = 1.13 10 -15 T 2 2 -2 -2 4 r 2 1.0 10 m
Washington - FACULTY - 122
33.1. Model: Assume the magnetic field is uniform.Visualize: Please refer to Figure Ex33.1. Since a motional emf was developed the field must be perpendicular to v . The positive charges experienced a magnetic force to the left. By the right-hand r
Washington - FACULTY - 122
34.21. Model: The electric and magnetic field amplitudes of an electromagnetic wave are related.Solve: Using Equation 34.40, E0 = cB0 = 3.0 108 m/s 2.0 10 -3 T = 6.0 10 5 V/m()()34.23. Model: Electromagnetic waves are sinusoidal.Solve:
Washington - FACULTY - 122
35.6.Model:Current and voltage phasors are vectors that rotate counterclockwise around the origin at angularfrequency . Visualize:Please refer to Figure 35.6. Solve:(a) From the figure we note that VR = 10 V and IR = 0.50 A. Using Ohm's law, R= (b)