Algorithms Programming Assignment #1: Sorting solved

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In this PA, you are required to implement various sorters that we learnt in the class.
You can download the PA1.tar file from NTU COOL website. Uncompress it using
Linux command,
tar xvf PA1.tar
You can see the following directories after uncompressing it.
Name Description
bin/ Directory of binary file
doc/ Directory of document
inputs/ Directory of unsorted data
lib/ Directory of library source code
outputs/ Directory of sorted data
src/ Directory of source code
utility/ Directory of checker
Input/output Files:
In the input file (*.in), the first two lines starting with ‘#’ are just comments.
Except comments, each line contains two numbers: index followed by the unsorted
number. The range of unsorted number is between 0 and 1,000,000. Two numbers
are separated by a space. For an example, the file contains five
# 5 data points
# index number
0 16
1 13
2 0
3 6
4 7
The output file(*.out) is actually the same as the input file except that the
numbers are sorted in increasing order. For example, 5.case1.out is like:
# 5 data points
# index number
0 0
1 6
2 7
3 13
4 16
You can visualize your unsorted/sorted numbers by using the gnuplot tool by the
command gnuplot. After that, please key in the following
set xrange [0:5]
set yrange [0:20]
plot “” usi 1:2
plot “5.case1.out” usi 1:2
# if you want to save to png files
set terminal png
set output “5.case1.out.png”
You need to allow X-window display to see the window if you are login remotely. For
more gnuplot information, see
There are two example “before” and “after” sort pictures with 100 numbers benchmark.
Before sort:
After sort:
Command line parameters:
In the command line, you are required to follow this format
NTU_sort –[IS|MS|QS|HS]
where IS represents insertion sort, MS is merge sort, QS is quick sort and HS is heap
sort. The square bracket with vertical bar ‘[IS|MS|QS|HS]’ means that only one of the
four versions is chosen.
The angle bracket should be replaced by the name of the input file,
*.[case1|case2|case3].in, where case1 represents test case in random order,
case2 is test case in increasing order, and case3 is test case in reverse order. For the
best case, all the numbers are sorted in increasing order. For the worst case, all
numbers are sorted in descending order. For the average case, numbers are in random
The output file names are *.[case1|case2|case3].out. Please note that you
do NOT need to add ‘[|]’ or ‘<>’ in your command line. For example, the following
command sorts to 10000.case1.out using insertion sort.
./bin/NTU_sort -IS inputs/ outputs/10000.case1.out
Source code files:
Please notice that all of the source code files have been already finished except
sort_tool.cpp. You only need to complete the different sorting functions of class
SortTool in sort_tool.cpp. You can still modify other source code files if you think it
is necessary. The following will simply introduce the source code files.
main.cpp: main program for PA1
1. // **************************************************************************
2. // File [main.cpp]
3. // Author [Yu-Hao Ho]
4. // Synopsis [The main program of 2019 fall Algorithm PA1]
5. // Modify [2019/9/6 Cheng-Yun Hsieh]
6. // **************************************************************************
8. #include
9. #include
10. #include
11. #include “../lib/tm_usage.h”
12. #include “sort_tool.h”
14. using namespace std;
16. void help_message() {
17. cout << "usage: NTU_sort -[IS|MS|QS|HS] ” << endl; 18. cout << "options:" << endl; 19. cout << " IS - Insersion Sort" << endl; 20. cout << " MS - Merge Sort" << endl; 21. cout << " QS - Quick Sort" << endl; 22. cout << " HS - Heap Sort" << endl; 23. } 24. 25. int main(int argc, char* argv[]) 26. { 27. if(argc != 4) { 28. help_message(); 29. return 0; 30. } 31. CommonNs::TmUsage tmusg; 32. CommonNs::TmStat stat; 33. 34. //////////// read the input file ///////////// 35. 36. char buffer[200]; 37. fstream fin(argv[2]); 38. fstream fout; 39.[3],ios::out); 40. fin.getline(buffer,200); 41. fin.getline(buffer,200); 42. int junk,num; 43. vector data;
44. while (fin >> junk >> num)
45. data.push_back(num); // data[0] will be the first data.
46. // data[1] will be the second data and so on.
48. //////////// the sorting part ////////////////
49. tmusg.periodStart();
50. SortTool NTUSortTool;
52. if(!strcmp(argv[1],”-QS”)) {
53. NTUSortTool.QuickSort(data);
54. }
55. else if(!strcmp(argv[1],”-IS”)) {
56. NTUSortTool.InsertionSort(data);
57. }
58. else if(!strcmp(argv[1],”-MS”)) {
59. NTUSortTool.MergeSort(data);
60. }
61. else if(!strcmp(argv[1],”-HS”)) {
62. NTUSortTool.HeapSort(data);
63. }
64. else {
65. help_message();
66. return 0;
67. }
69. tmusg.getPeriodUsage(stat);
70. cout <<"The total CPU time: " << (stat.uTime + stat.sTime) / 1000.0 << "ms" << endl; 71. cout <<"memory: " << stat.vmPeak << "KB" << endl; // print peak memory 72. 73. //////////// write the output file /////////// 74. fout << "# " << data.size() << " data points" <
12. using namespace std;
14. class SortTool {
15. public:
16. SortTool(); // constructor
17. void InsertionSort(vector&); // sort data using insertion sort
18. void MergeSort(vector&); // sort data using merge sort
19. void QuickSort(vector&); // sort data using quick sort
20. void HeapSort(vector&); // sort data using heap sort
21. private:
22. void QuickSortSubVector(vector&, int, int); // quick sort subvector
23. int Partition(vector&, int, int); // partition the subvector
24. void MergeSortSubVector(vector&, int, int); // merge sort subvector
25. void Merge(vector&, int, int, int, int); // merge two sorted subvector
26. void MaxHeapify(vector&, int); // make tree with given root be a max-heap
27. //if both right and left sub-tree are max-heap
28. void BuildMaxHeap(vector&); // make data become a max-heap
29. int heapSize; // heap size used in heap sort
31. };
33. #endif
Line 17-20: sort function which will be called in main.cpp.
Line 22: This function will be used in quick sort. It will sort sub vector with given lower and
upper bound. This function should be implemented to partition the sub vector and
recursively call itself.
Line 23: This function will be used in quick sort and should be implemented to partition the sub
Line 24: This function will be used in merge sort. It will sort sub vector with given lower and
upper bound. This function should be implemented to call itself for splitting and
merging the sub vector.
Line 25: This function will be used in merge sort and should be implemented to merge two
sorted sub vector.
Line 26: This function will be used in heap sort and should be implemented to make the tree
with given root be a max-heap if both of its right subtree and left subtree are
Line 28: This function will be used in heap sort and should be implemented to make input data
be a max-heap.
sort_tool.cpp: the implementation of the SortTool Class
1. // **************************************************************************
2. // File [sort_tool.cpp]
3. // Author [Yu-Hao Ho]
4. // Synopsis [The implementation of the SortTool Class]
5. // Modify [2019/9/6 Cheng-Yun Hsieh]
6. // **************************************************************************
8. #include “sort_tool.h”
9. #include
11. // Constructor
12. SortTool::SortTool() {}
14. // Insertsion sort method
15. void SortTool::InsertionSort(vector& data) {
16. // Function : Insertion sort
17. // TODO : Please complete insertion sort code here
18. }
20. // Quick sort method
21. void SortTool::QuickSort(vector& data){
22. QuickSortSubVector(data, 0, data.size() – 1);
23. }
24. // Sort subvector (Quick sort)
25. void SortTool::QuickSortSubVector(vector& data, int low, int high) {
26. // Function : Quick sort subvector
27. // TODO : Please complete QuickSortSubVector code here
28. // Hint : recursively call itself
29. // Partition function is needed
30. }
32. int SortTool::Partition(vector& data, int low, int high) {
33. // Function : Partition the vector
34. // TODO : Please complete the function
35. // Hint : Textbook page 171
36. }
38. // Merge sort method
39. void SortTool::MergeSort(vector& data){
40. MergeSortSubVector(data, 0, data.size() – 1);
41. }
43. // Sort subvector (Merge sort)
44. void SortTool::MergeSortSubVector(vector& data, int low, int high) {
45. // Function : Merge sort subvector
46. // TODO : Please complete MergeSortSubVector code here
47. // Hint : recursively call itself
48. // Merge function is needed
49. }
51. // Merge
52. void SortTool::Merge(vector& data, int low, int middle1, int middle2, int high) {
53. // Function : Merge two sorted subvector
54. // TODO : Please complete the function
55. }
57. // Heap sort method
58. void SortTool::HeapSort(vector& data) {
59. // Build Max-Heap
60. BuildMaxHeap(data);
61. // 1. Swap data[0] which is max value and data[i] so that the max value will be in correct location
62. // 2. Do max-heapify for data[0]
63. for (int i = data.size() – 1; i >= 1; i–) {
64. swap(data[0],data[i]);
65. heapSize–;
66. MaxHeapify(data,0);
67. }
68. }
70. //Max heapify
71. void SortTool::MaxHeapify(vector& data, int root) {
72. // Function : Make tree with given root be a max-heap if both right and left sub-tree are max-heap
73. // TODO : Please complete max-heapify code here
74. }
76. //Build max heap
77. void SortTool::BuildMaxHeap(vector& data) {
78. heapSize = data.size(); // initialize heap size
79. // Function : Make input data become a max-heap
80. // TODO : Please complete BuildMaxHeap code here
81. }
Line 15-18: please complete the function of insertion sort here.
Line 21-23: the function of quick sort will call function of Sorting sub-vector and give initial
lower/upper bound.
Line 25-30: please complete the function of sorting sub-vector using quick sort algorithm here.
Line 32-36: please complete the function of partition here.
Line 39-41: the function of merge sort will call function of Sorting sub-vector and give initial
lower/upper bound.
Line 44-49: please complete the function of sorting sub-vector using merge sort algorithm here.
Line 52-55: please complete the function of merging two sorted sub-vector here.
Line 58-68: the function of heap sort will build max-heap first. And then, exchange data
Line 71-74: please complete the function of max-heapify which makes the tree with given root
be a max-heap if its right and left sub-tree are both max-heap.
Line 77-81: please complete the function of building max-heap with given input data.
1. Please check the source code files under the src directory. You may need to
complete the functions of class SortTool in sort_tool.cpp. You can also modify
main.cpp and sort_tool.h if you think it is necessary.
2. Your source code must be written in C or C++. The code must be executable on
EDA union lab machines.
3. In your report, compare the running time of four versions of different input sizes.
Please fill in the following table. Please use –O2 optimization and turn off all
debugging message.
Input size IS MS QS HS
CPU time
CPU time
CPU time
CPU time
4. Draw figures to show the growth of running time as a function of input size and try to
analyze the curve (as the following example, where each curve represents an algorithm.)
You can skip the test case if the run time is more than 10 minutes.
5. Notice: You are not allowed to include the header or in STL!
We expected your code can compile and run in this way.
Type the following commands under _pa1 directory,
cd bin
./NTU_sort –[IS|MS|QS|HS]
We provide the sample makefile, please modify into yours if needed.
Control the stack size
To prevent stack overflow cause by the recursion function calls, please set the stack size to
256MB using the following Linux comment:
ulimit -s 262144
1. # CC and CFLAGS are varilables
2. CC = g++
3. CFLAGS = -c
4. AR = ar
5. ARFLAGS = rcv
6. # -c option ask g++ to compile the source files, but do not link.
7. # -g option is for debugging version
8. # -O2 option is for optimized version
10. OPTFLAGS = -O2
11. # make all
12. all: bin/NTU_sort
13. @echo -n “”
15. # optimized version
16. bin/NTU_sort: sort_tool_opt.o main_opt.o lib
17. $(CC) $(OPTFLAGS) sort_tool_opt.o main_opt.o -ltm_usage -Llib -o bin/NTU_sort
18. main_opt.o: src/main.cpp lib/tm_usage.h
19. $(CC) $(CFLAGS) $< -Ilib -o $@ 20. sort_tool_opt.o: src/sort_tool.cpp src/sort_tool.h 21. $(CC) $(CFLAGS) $(OPTFLAGS) $< -o $@ 22. 23. # DEBUG Version 24. dbg: bin/NTU_sort_dbg 25. @echo -n "" 26. 27. bin/NTU_sort_dbg: sort_tool_dbg.o main_dbg.o lib 28. $(CC) $(DBGFLAGS) sort_tool_dbg.o main_dbg.o -ltm_usage -Llib -o bin/NTU_sort_dbg 29. main_dbg.o: src/main.cpp lib/tm_usage.h 30. $(CC) $(CFLAGS) $< -Ilib -o $@ 31. sort_tool_dbg.o: src/sort_tool.cpp src/sort_tool.h 32. $(CC) $(CFLAGS) $(DBGFLAGS) $< -o $@ 33. 34. lib: lib/libtm_usage.a 35. 36. lib/libtm_usage.a: tm_usage.o 37. $(AR) $(ARFLAGS) $@ $< 38. tm_usage.o: lib/tm_usage.cpp lib/tm_usage.h 39. $(CC) $(CFLAGS) $< 40. 41. # clean all the .o and executable files 42. clean: 43. rm -rf *.o lib/*.a bin/* makefile Line 38-39: compile the object file tm_usage.o from tm_usage.cpp and tm_usage.h Line 36-37: archive tm_usage.o into a static library file libtm_usage.a. Please note that library must start with lib and ends with .a. Line 37: this small library has only one objet file. In a big library, more than one objective files can be archived into a single lib*.a file like this ar rcv libx.a file1.o [file2.o …] Lines 12-21: When we type ‘make’ without any option the makefile will do the first command (line.12 in this sample). Thus, we can compile the optimization version when we type ‘make’. This version invokes options ‘-O2’ for speed improvement. Also ‘_DEBUG_ON_’ is not defined to disable the printing of arrays in sort_tool.cpp. Lines 23-32: Compile the debug version when we type ‘make dbg’. This version invokes options ‘-g’ (for DDD debugger) and also ‘-D_DEBUG_ON_’ to enable the printing of arrays in sort_tool.cpp. Lines 13,25: @echo –n “” will print out the message in “”. In this sample we print nothing. Notice: $< represent the first dependency. $@ represent the target itself. Example: a.o : b.cpp b.h $(CC) $(CFLAGS) $(DBGFLAGS) $< -o $@ $< = b.cpp $@ = a.o You can find some useful information here. Validation: You can verify your answer very easily by comparing your output with case2 which is the sorted input. Or you can see the gnuplot and see if there is any dot that is not sorted in order. Also, you can use our result checker which is under utility directory to check whether your result is correct or not. To use this checker, simply type ./PA1_Result_Checker
Please notice that it will not check whether the format of result file is correct or not.
You have to check the format by yourself if you modify the part of writing output file in
Please submit a single *.tgz file to NTU COOL system before 10/13(Su) 13:00.
Your submission must contain:
1. _pa1 directory contains your source code in src directory. By simply
typing “make” can compile.
2. A report in the doc directory. _pa1_report.doc or pdf.
3. A README file that explains your files.
4. We will use our own test cases so do NOT include the input files.
5 In summary, you should at least have the following item in your *.tgz file.
lib/ bin/NTU_sort
The submission filename should be compressed in a single file
_pa1.tgz. (e.g. b90901000_pa1.tgz). You can use the following command
to compress a whole directory:
tar zcvf .tgz

For example, goto the same level as PA1 directory, and type
tar zcvf b99901000_pa1.tgz PA1
6. You are required to run the checksubmitPA1 script to check if your .tgz submission
file is correct. Suppose you are in the same level as PA1 directory
./PA1/utility/ b99901000_pa1.tgz
Please note the path must be correct. If you are located in the ~/ directory, then
‘./PA1/utility/’ means the path ~/PA1/utility/
and b99901000_pa.tgz means the path ~/b99901000_pa1.tgz
We have so many students in the class so we need automatic grading. Any mistake in
the submission will result in cost 20% off your score. Please be very careful in your
60% correctness (including submission correctness)
20% file format and location
20% report

TA will check your source code carefully. Copying other source code can result in
zero grade for all students involved.