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ECE220: Computer Systems & Programming
Machine Problem 10 due: Saturday
Mieber: Walk Me There, Part II
Your task this week is to extend last week’s program to make
use of dynamic allocation in several ways and to attempt to pair
up requests from a list of many requests. For this purpose, you
must also implement and use structures designed to help
improve performance.
In particular, you must write C subroutines that manage
dynamic allocation of vertex sets and paths, subroutines that
enable, calculate, and use “mini maps” based on a high level of
a pyramid tree, and a subroutine that attempts to find a partner
for a request among a linked list of unpaired requests.
Successful pairings must then be moved into a list of paired
requests.
The objective for this week is for you to gain experience with
dynamic allocation and singly-linked lists in C.
Background
The screenshot shown here was again generated automatically based on the results of the program. As
before, the input data are taken from OpenStreetMap data for the ZJUI campus area, and the image
generation is provided by your MP5 code. In the image, the yellow and orange circles represent the starting
and ending locales for two different people. Light grey lines represent roads, and blue dots represent nodes
not in the intersection of the yellow and orange circles. Green dots represent nodes in the intersection of
the yellow and orange circles (either the starting locales or the ending locales). Green dots are thus possible
starting and ending points for the shared walk. The black line is then the chosen shortest path between any
pair of green dots, assuming that the path must follow the roads.
This week’s program reads a file consisting of many requests. For each request, your code must attempt to
find a matching request from among those requests that have not already been matched. If a match is found,
your code must find a path as before and record the trip information in a list of matched requests. If no
match is found, your code must add the request to the list of unmatched requests.
In order to speed up comparisons, you must make use of a “minimap” bit vector based on a high level of
the pyramid tree—the level with 64 nodes. For vertex sets and paths, each vertex is associated with an
ancestor node at that level of the pyramid tree, and the minimap is the 64-bit value in which each of the 64
pyramid tree nodes is represented with a 1 if any of its children nodes appear in the vertex set (or path) and
a 0 if none of them appear. By checking to see whether the minimaps overlap (with AND), one can quickly
rule out overlap between distant locales and thus skip over any requests that cannot possibly match.
Pieces
Your program will consist of a total of five files:
mp10.h This header file provides type definitions, function declarations, and brief
descriptions of the subroutines that you must write for this assignment. You
should read through the file before you begin coding. Changes from mp9.h
are marked as such.
mp10.c The source file for your implementation of minimap and vertex set merging
functions. A version has been provided to you with placeholders for the
subroutines described in this document.
mp10alloc.c The source file for your implementation of some dynamic allocation subroutines.
mp10match.c The source file for your implementation of the handle_request function.
mp9.c Your solution to MP9, which requires some modifications for MP10.
Six other files are also provided to you:
graph The map data. Feel free to test with your own graphs as well.
Makefile A file that simplifies the building and visualization process. See the section below
on Compiling and Executing Your Program.
mp10main.c The main program for MP10: reads the graph and requests files, builds the
pyramid tree, allocates a heap for your code, and creates a file to illustrate the
results of your code. You need not read this file, although you are welcome to do
so.
mp10graph.c A source file that contain functions for reading a graph file and freeing a graph.
This file is used both by mp10 and by the request generation tool. You need not
read this file, although you are welcome to do so.
genreq.c The main program for a tool used to generate requests. You need not read this
file, although you are welcome to do so.
requests A file of requests to be matched one at a time against all unmatched requests. As
before, each request consists of a starting locale and an ending locale, and each
locale consists of an X position, a Y position, and an acceptable range (distance)
from that center point. The version given to you was generated with the genreq
tool (again, see Compiling and Executing Your Program) with parameters 100
12345 1055000 480000 1225000 650000 4000 8000 on Cygwin. My
implementation matches 6 pairs among the 100 requests.
As in MP9, we have included slightly modified copies of mp5.h and mp5main.c for visualization
purposes. In order to visualize your results, you must first add your own mp5.c solution file to your mp10
directory. Only draw_line and draw_circle are used from your code, so as long as those functions are
reasonably correct, the visualization should work.
The Task
The total amount of code needed in my version of this assignment was under 250 extra lines.
You should first copy your mp9.c solution into your mp10 directory, then add it to your repository. If
you forget to do so, we cannot grade your modifications, and you will lose many points. Edit the file and
change the mp9.h include at the top to include mp10.h instead. At the same time, add an include line for
stdlib.h, which you need for dynamic allocation calls.
You need to modify two of the subroutines that your developed in MP9: find_nodes and dijkstra.
These routines must now use dynamic allocation for the id fields (the array of graph vertex ids) of the
vertex set and the path, respectively.
For find_nodes, you must modify your code in two ways. First, the id array is no longer defined as a
fixed-size array. Instead, you should use dynamic resizing to grow the array as necessary. If malloc or
realloc fails, simply skip insertion of that vertex’ id (as did the earlier version when it ran out of space in
the array). The second modification needed is to build the array of vertex ids in increasing order (in other
words, sorted from smallest to largest). Sorting the arrays makes intersecting two such arrays faster.
For dijkstra, you should allocate an array of appropriate size after you have determined the length of the
path (including the starting and ending nodes, just as before), but before writing the graph vertex ids into
the array. If allocation fails, the function should also fail by returning 0.
You may next want to implement dynamic allocation calls for vertex sets and paths in mp10alloc.c.
These routines should be used to create and free vertex sets and paths. Allocation calls should return
pointers to the new objects, or NULL on failure. Be sure to initialize at least the count and id fields for
vertex sets, and at least the id field for paths. Note that the id field of either type may be NULL when either
type is freed, so be careful not to free a NULL pointer. The signatures for the four routines are:
vertex_set_t* new_vertex_set ();
void free_vertex_set (vertex_set_t* vs);
path_t* new_path ();
void free_path (path_t* path);
After the allocation routines, we suggest implementing the minimap functionality in mp10.c. Begin by
writing a function to mark each vertex in a graph with a bit indicating which node in the fourth level of a
pyramid tree is the ancestor of the pyramid tree node corresponding to the vertex. The vertex_t structure
has been extended with an mm_bit field to hold this information, but the field for each vertex must be
filled in by your function. These bit numbers will be used to implement the new 64-bit minimap fields of
the vertex sets and the paths. Note that the fourth level of a pyramid tree has 64 nodes. The signature for
the function is:
int32_t mark_vertex_minimap (graph_t* g, pyr_tree_t* p);
If the graph has 64 vertices or fewer, simply use each vertex’ array index for the vertex’ mm_bit field.
Otherwise, for each graph vertex, your function must identify the pyramid tree node corresponding to each
vertex, then find the ancestor node with index from 21 to 84 (these are the nodes at the fourth level of the
pyramid tree). Finally, set the vertex’ mm_bit to the ancestor’s node index minus 21. Note that the
description here is chosen for clarity in the definition; you may want to use a more efficient approach to
finding the necessary information.

Once you have the vertices marked, you can implement the following two functions to build minimaps for
the vertex sets and paths:
void build_vertex_set_minimap (graph_t* g, vertex_set_t* vs);
void build_path_minimap (graph_t* g, path_t* vs);
Note that the graph contains the minimap bit information for each vertex, so you can calculate the vertex
set (or path’s) minimap field by ORing together the bits for all ids in the vertex set (or the path). Use 1ULL
to obtain a 64-bit constant before shifting; if your code shifts a 32-bit constant by more than 31 bits, the
results are undefined.
The last function in mp10.c merges two vertex sets into a third set. This function is used to check for
overlap between the vertex sets of two requests. The function has the following signature:
int32_t merge_vertex_sets (const vertex_set_t* v1, const vertex_set_t* v2,
vertex_set_t* vint);
This function finds the intersection of two vertex sets v1 and v2 and writes the results into vint. The
function should assume that the id array in vint has enough space to hold the intersection of the sets (as
mentioned below, your handle_request function must guarantee this property). If the resulting intersection
is non-empty, the function returns 1. Otherwise, it returns 0.
The primary function for this MP appears in mp10match.c and has the following signature:
int32_t handle_request (graph_t* g, pyr_tree_t* p, heap_t* h, request_t* r);
This function processes a single request, allocating structures as necessary, then comparing it with all
unpaired requests handled previously. If a match is found, the function moves the new request and the
matching request into a separate list.
Two file-scope lists are used for recording requests: available is the singly-linked list of unpaired
requests. Any unmatched request is added to this list. The shared list is the list of paired requests. Initially,
of course, both lists are empty.
The available list is a singly-linked list connected by the next field of the request_t structure. The
partner field of all requests in this list should be NULL. The source and destination vertex sets should be
dynamically allocated vertex sets that correspond to the request. The path field should be NULL.
The shared list is also a singly-linked list connected by the next field of the request_t structure. When
a request is matched to a second request in the available list, the second request should be removed from
the available list and referenced through the partner field of the first request. The partner and next
fields of the second request should then be set to NULL, and the first request should be added to the shared
list (using the first request’s next field). For pairs of requests in the shared list, both requests should
point to the same two vertex sets and to the same path structure. These vertex sets should correspond to
the intersection of the two requests, and the path should be that found by the dijkstra routine.
Here’s a little more detail on what your handle_request routine must do:
 Allocate vertex sets for the request and for use with matching.
 Allocate a path for use with matching.
 If any allocation fails, clean up (free any successful allocations) and return 0.
 Fill in the vertex sets for the request. If either is empty, the function should return 0. Be sure to
free any vertex sets and path allocated by the function before returning.
 Create minimaps for the request’s source and destination vertex sets.
 Allocate id arrays for the vertex sets to be used for matching. Make these large enough that they
can hold any intersection with the request’s corresponding vertex set. Note that you must clean up
and return 0 if allocation fails.
 Try to find a matching request in the available list. Skip any requests that have no overlap in
the source vertex set minimaps or no overlap in the destination vertex set minimaps. For those with
overlap, use merge_vertex_sets to check for non-empty intersections, then call dijkstra to
find a path (if both are non-empty). If everything succeeds, pair the two requests.
 If no match is found, add the request to the available list and return 1 for success. Again, be
sure to free any dynamically allocated structures (specifically, those used for testing matches).
 If a matching request is found, remove the matching request from the available list, free both
requests vertex sets (these should be replaced with the intersected vertex sets), and make both
requests point to the intersected vertex sets and the path filled in by dijkstra. Be sure to build
minimaps for both intersected vertex sets and for the path. Link the two requests as described
previously into the shared list and return 1 for success.
Specifics
Be sure that you have read the type definitions and other information in the code and header file before you
begin coding.
 Your code must be written in C and must be contained in files named mp9.c, mp10.c,
mp10alloc.c, and mp10match.c files in the mp/mp10 subdirectory of your repository. We will
NOT grade files with any other names. If you added fields to vertex_t for MP9, you must
merge them into mp10.h yourself. As with MP9, you may not make other changes to other
files except for debugging purposes. Track any such changes with care, and make sure to test
without them. If your code does not work properly without such changes, you are likely to receive
0 credit.
 You must modify the find_nodes and dijkstra functions correctly.
 You must write the new_vertex_set, free_vertex_set, new_path, free_path,
mark_vertex_minimap, build_vertex_set_minimap, build_path_minimap,
merge_vertex_sets, and handle_request functions correctly.
 You may assume that the parameter values passed into your handle_request function are valid.
You must ensure that your routines are then passed valid parameters. We may test the individual
routines mentioned with parameters other than those provided to you as examples. You may,
however, also assume that both vertex sets passed into dijkstra contain at least one vertex.
 You may assume that only dynamically allocated vertex sets are passed into free_vertex_set,
and that only dynamically allocated paths are passed into free_path, provided that your code
does not violate these assumptions.
 You may assume that the pyramid tree passed with the graph was built from that graph.
 Note that you should assume that the vertex sets passed into merge_vertex_sets are sorted, but
you are responsible for guaranteeing that property by modifying find_nodes.
 Your routine’s return values and outputs must be correct.
 Your code must be well-commented. Follow the commenting style of the code examples provided
in class and in the textbook, and be sure to add function headers containing the information that
has been provided for you in previous assignments (inputs, outputs, return value, and any side
effects, as well as a brief description).
Compiling and Executing Your Program
When you are ready to compile, type:
make
Warnings and debugging information are turned on in the Makefile, so you can use gdb to find your bugs
(you will have some).
If compilation succeeds, you can then execute the program by typing, “./mp10 graph requests” (no
quotes). You can also specify other graph files or other requests files, but you will have to create such files
yourself (you may share them with other students for testing purposes). The program will print a list of
matched and unmatched requests (their identifiers are the line numbers in the requests file, starting with 0
instead of 1).
If you want to visualize a particular matched pair or unmatched request, execute with an extra argument:
the id of the desired request (either for a matched pair). The program will then also create the result.c
file. After creating the file, you can visualize the given result by typing:
make image
which will produce the file image.png. Be sure to put a copy of your mp5.c implementation into the
mp10 directory before trying to make an image. If you make the image without executing mp10, the
Makefile will execute mp10 for you with the default arguments (the graph file and the requests file
and id 2).
To clean up, type “make clean” (no quotes), or to really clean up, type “make clear” (as usual, no
quotes).
To make the request generation tool, type:
make genreq
You can then run the tool to generate new requests files at random. Run the tool without arguments for
instructions. Feel free to identify the (x,y) coordinates of points of interest (such as the residential college)
yourselves and to share such findings with others. The units are 10 millionths of degrees of
latitude/longitude (about 1.11 meters / unit), so you should be able to make calculations, too…roughly. The
aspect ratios aren’t quite right.
Grading Rubric
Functionality (65%)
 8% – find_nodes function works correctly
 3% – dijkstra function works correctly
 4% – new_vertex_set function works correctly
 3% – free_vertex_set function works correctly
 4% – new_path function works correctly
 3% – free_path function works correctly
 10% – mark_vertex_minimap function works correctly
 3% – build_vertex_set_minimap function works correctly
 3% – build_path_minimap function works correctly
 6% – merge_vertex_sets function works correctly
 18% – handle_request function works correctly
Style (15%)
 5% – mark_vertex_minimap avoids searching pyramid tree for each graph vertex
 5% – merge_vertex_sets uses fact that id arrays are sorted to avoid quadratic running time
 5% – handle_request uses minimaps to avoid checking matches when possible
Comments, Clarity, and Write-up (20%)
 5% – introductory paragraph explaining what you did (even if it’s just the required work)
 5% – function headers are complete for all implemented functions (including those for any support
functions that you create)
 10% – code is clear and well-commented, and compilation generates no warnings (note: any
warning means 0 points here)
Note that some categories in the rubric may depend on other categories and/or criteria. For example, if you
code does not compile, you will receive no functionality points. As always, your functions must be able to
be called many times and produce the correct results, so we suggest that you avoid using any static storage
(or you may lose most/all of your functionality points).

Mieber: Walk Me There, Part II
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