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Percolation - Coursera Algorithms Part 1
Raw
Percolation.java
/* *****************************************************************************
* Name: Johanna Mesa Ramos
* Coursera User ID: c02b4bb527298de170192d644483baeb
* Last modified: 06/07/2020
* Course: Algorithms, Part I https://www.coursera.org/learn/algorithms-part1
**************************************************************************** */
import edu.princeton.cs.algs4.WeightedQuickUnionUF;
public class Percolation {
private WeightedQuickUnionUF gridBackwash;
private WeightedQuickUnionUF grid;
private boolean[] nodeStates;
private int n;
private int top;
private int bottom;
private int openSites;
/**
* Creates n-by-n nodeStates, with all sites initially blocked
* Creates n-by-n + 2 WeightedQuickUnionUF gridBackwash, the +2 is for virtual top/bottom nodes
* Creates n-by-n + 1 WeightedQuickUnionUF grid, the +1 is for only the top virtual node and to
* avoid backwash
* in the method isFull
*
* @param n Dimension of the grid
*/
public Percolation(int n) {
if (n < 1)
throw new java.lang.IllegalArgumentException(
"Stop right there, N must be greater than 0");
this.n = n;
top = get1DIndex(n, n) + 1;
bottom = get1DIndex(n, n) + 2;
openSites = 0;
gridBackwash = new WeightedQuickUnionUF(n * n + 2);
grid = new WeightedQuickUnionUF(n * n + 1); // Only add top virtual node
nodeStates = new boolean[n * n];
}
/**
* @param r row index, -1 because problem is 1 index based
* @param c col index, -1 because problem is 1 index based
* @return index from 2D array mapped to 1D array
*/
private int get1DIndex(int r, int c) {
r -= 1;
c -= 1;
return (r * n) + c;
}
private boolean outOfRange(int row, int col, boolean throwEx) {
if (row < 1 || col < 1 || row > n || col > n) {
if (throwEx)
throw new java.lang.IllegalArgumentException("Values are out of range");
return false;
}
return true;
}
public void open(int row, int col) {
outOfRange(row, col, true);
if (isOpen(row, col))
return;
int i = get1DIndex(row, col);
nodeStates[i] = true;
openSites += 1;
if (row == 1) {
gridBackwash.union(top, i);
grid.union(top, i);
}
if (row == n)
gridBackwash.union(bottom, i);
union(row - 1, col, i);
union(row, col + 1, i);
union(row + 1, col, i);
union(row, col - 1, i);
}
private void union(int r, int c, int to) {
if (!outOfRange(r, c, false) || !isOpen(r, c))
return;
gridBackwash.union(get1DIndex(r, c), to);
grid.union(get1DIndex(r, c), to);
}
public boolean isOpen(int row, int col) {
outOfRange(row, col, true);
return nodeStates[get1DIndex(row, col)];
}
/**
* A full site is an open site that can be connected to an open site in the top row
* via a chain of neighboring (left, right, up, down) open sites.
*
* @param row
* @param col
* @return boolean
*/
public boolean isFull(int row, int col) {
outOfRange(row, col, true);
return isOpen(row, col) && grid.connected(get1DIndex(row, col), top);
}
public int numberOfOpenSites() {
return openSites;
}
public boolean percolates() {
return gridBackwash.connected(bottom, top);
}
public static void main(String[] args) {
}
}
Raw
PercolationStats.java
/* *****************************************************************************
* Name: Johanna Mesa Ramos
* Coursera User ID: c02b4bb527298de170192d644483baeb
* Last modified: 06/07/2020
* Course: Algorithms, Part I https://www.coursera.org/learn/algorithms-part1
**************************************************************************** */
import edu.princeton.cs.algs4.StdRandom;
import edu.princeton.cs.algs4.StdStats;
public class PercolationStats {
private Percolation perc;
private int size;
private int trials;
private double[] stats;
// perform independent trials on an n-by-n grid
public PercolationStats(int n, int trials) {
if (n < 1 || trials < 1)
throw new java.lang.IllegalArgumentException(
"Halt, n and trials must be greater than 0");
this.trials = trials;
size = n;
stats = new double[trials];
generateStats();
}
private void generateStats() {
Percolation per;
for (int i = 0; i < trials; ++i) {
per = new Percolation(size);
while (!per.percolates()) {
per.open(StdRandom.uniform(1, size + 1), StdRandom.uniform(1, size + 1));
}
stats[i] = (double) per.numberOfOpenSites() / (size * size);
}
}
public double mean() {
return StdStats.mean(stats);
}
public double stddev() {
return StdStats.stddev(stats);
}
// low endpoint of 95% confidence interval
public double confidenceLo() {
return mean() - (1.96 * stddev()) / Math.sqrt(size);
}
// high endpoint of 95% confidence interval
public double confidenceHi() {
return mean() + (1.96 * stddev()) / Math.sqrt(size);
}
public static void main(String[] args) {
PercolationStats ps = new PercolationStats(Integer.parseInt(args[0]),
Integer.parseInt(args[1]));
System.out.format("mean = %.16f %n", ps.mean());
System.out.format("sttdev = %.16f %n", ps.stddev());
System.out.format("95%% confidence interval = [%.16f, %.16f] %n", ps.confidenceLo(),
ps.confidenceHi());
}
}
Raw
Z_PercolationGraderOutput.txt
See the Assessment Guide for information on how to interpret this report.
Want to receive personalized feedback on this submission?
You can pay to have a teaching assistant read and provide
personalized feedback on your submission at https://mooc.codepost.io.
ASSESSMENT SUMMARY
Compilation: FAILED (0 errors, 2 warnings)
API: PASSED
Spotbugs: PASSED
PMD: FAILED (12 warnings)
Checkstyle: FAILED (0 errors, 4 warnings)
Correctness: 36/38 tests passed
Memory: 8/8 tests passed
Timing: 20/20 tests passed
Aggregate score: 91.84%
[Compilation: 5%, API: 5%, Spotbugs: 0%, PMD: 0%, Checkstyle: 0%, Correctness: 60%, Memory: 10%, Timing: 20%]
ASSESSMENT DETAILS
The following files were submitted:
----------------------------------
3.5K Jul 2 17:07 Percolation.java
2.2K Jul 2 17:07 PercolationStats.java
********************************************************************************
* COMPILING
********************************************************************************
% javac Percolation.java
*-----------------------------------------------------------
Percolation.java:109: warning: [deprecation] connected(int,int) in WeightedQuickUnionUF has been deprecated
return isOpen(row, col) && grid.connected(get1DIndex(row, col), top);
^
Percolation.java:117: warning: [deprecation] connected(int,int) in WeightedQuickUnionUF has been deprecated
return gridBackwash.connected(bottom, top);
^
2 warnings
% javac PercolationStats.java
*-----------------------------------------------------------
================================================================
Checking the APIs of your programs.
*-----------------------------------------------------------
Percolation:
PercolationStats:
================================================================
********************************************************************************
* CHECKING STYLE AND COMMON BUG PATTERNS
********************************************************************************
% spotbugs *.class
*-----------------------------------------------------------
================================================================
% pmd .
*-----------------------------------------------------------
Percolation.java:11: The private instance (or static) variable 'gridBackwash' can be made 'final'; it is initialized only in the declaration or constructor. [ImmutableField]
Percolation.java:12: The private instance (or static) variable 'grid' can be made 'final'; it is initialized only in the declaration or constructor. [ImmutableField]
Percolation.java:14: The private instance (or static) variable 'n' can be made 'final'; it is initialized only in the declaration or constructor. [ImmutableField]
Percolation.java:15: The private instance (or static) variable 'top' can be made 'final'; it is initialized only in the declaration or constructor. [ImmutableField]
Percolation.java:16: The private instance (or static) variable 'bottom' can be made 'final'; it is initialized only in the declaration or constructor. [ImmutableField]
Percolation.java:30: Unnecessary use of fully qualified name 'java.lang.IllegalArgumentException' due to existing implicit import 'java.lang.*'. [UnnecessaryFullyQualifiedName]
Percolation.java:56: Unnecessary use of fully qualified name 'java.lang.IllegalArgumentException' due to existing implicit import 'java.lang.*'. [UnnecessaryFullyQualifiedName]
Percolation.java:120: The method body is empty. If this is your intent, document it with a comment. [UncommentedEmptyMethodBody]
PercolationStats.java:12: Avoid unused private instance (or static) variables, such as 'perc'. [UnusedPrivateField]
PercolationStats.java:13: The private instance (or static) variable 'size' can be made 'final'; it is initialized only in the declaration or constructor. [ImmutableField]
PercolationStats.java:14: The private instance (or static) variable 'trials' can be made 'final'; it is initialized only in the declaration or constructor. [ImmutableField]
PercolationStats.java:20: Unnecessary use of fully qualified name 'java.lang.IllegalArgumentException' due to existing implicit import 'java.lang.*'. [UnnecessaryFullyQualifiedName]
PMD ends with 12 warnings.
================================================================
% checkstyle *.java
*-----------------------------------------------------------
[WARN] Percolation.java:30: Java automatically imports all classes and interfaces in the package 'java.lang'. So, there is no need to import such classes or interfaces; you can refer directly to them without the 'java.lang' prefix. [UnnecessaryJavaLang]
[WARN] Percolation.java:56: Java automatically imports all classes and interfaces in the package 'java.lang'. So, there is no need to import such classes or interfaces; you can refer directly to them without the 'java.lang' prefix. [UnnecessaryJavaLang]
[WARN] PercolationStats.java:20: Java automatically imports all classes and interfaces in the package 'java.lang'. So, there is no need to import such classes or interfaces; you can refer directly to them without the 'java.lang' prefix. [UnnecessaryJavaLang]
Checkstyle ends with 0 errors and 3 warnings.
% custom checkstyle checks for Percolation.java
*-----------------------------------------------------------
% custom checkstyle checks for PercolationStats.java
*-----------------------------------------------------------
[WARN] PercolationStats.java:7:1: The constant '1.96' appears more than once. Define a constant variable (such as 'CONFIDENCE_95') to hold the constant '1.96'. [NumericLiteralCount]
Checkstyle ends with 0 errors and 1 warning.
================================================================
********************************************************************************
* TESTING CORRECTNESS
********************************************************************************
Testing correctness of Percolation
*-----------------------------------------------------------
Running 21 total tests.
Tests 1 through 7 create a Percolation object using your code, then repeatedly
open sites by calling open(). After each call to open(), it checks the return
values of isOpen(), percolates(), numberOfOpenSites(), and isFull() in that order.
Tests 12 through 15 create a Percolation object using your code, then repeatedly
call the methods open(), isOpen(), isFull(), percolates(), and, numberOfOpenSites()
in random order with probabilities p = (p1, p2, p3, p4, p5). The tests stop
immediately after the system percolates.
Tests 18 through 21 test backwash.
Except as noted, a site is opened at most once.
Test 1: open predetermined list of sites using file inputs
* filename = input6.txt
* filename = input8.txt
* filename = input8-no.txt
* filename = input10-no.txt
* filename = greeting57.txt
* filename = heart25.txt
==> passed
Test 2: open random sites until the system percolates
* n = 3
* n = 5
* n = 10
* n = 10
* n = 20
* n = 20
* n = 50
* n = 50
==> passed
Test 3: open predetermined sites for n = 1 and n = 2 (corner case test)
* filename = input1.txt
* filename = input1-no.txt
* filename = input2.txt
* filename = input2-no.txt
==> passed
Test 4: check predetermined sites with long percolating path
* filename = snake13.txt
* filename = snake101.txt
==> passed
Test 5: open every site
* filename = input5.txt
==> passed
Test 6: open random sites until the system percolates,
allowing open() to be called on a site more than once
* n = 3
* n = 5
* n = 10
* n = 10
* n = 20
* n = 20
* n = 50
* n = 50
==> passed
Test 7: open random sites with large n
* n = 250
* n = 500
* n = 1000
* n = 2000
==> passed
Test 8: call methods with invalid arguments
* n = 10, (row, col) = (-1, 5)
* n = 10, (row, col) = (11, 5)
* n = 10, (row, col) = (0, 5)
* n = 10, (row, col) = (5, -1)
* n = 10, (row, col) = (5, 11)
* n = 10, (row, col) = (5, 0)
* n = 10, (row, col) = (-2147483648, -2147483648)
* n = 10, (row, col) = (2147483647, 2147483647)
==> passed
Test 9: call constructor with invalid argument
* n = -10
* n = -1
* n = 0
==> passed
Test 10: create multiple Percolation objects at the same time
(to make sure you didn't store data in static variables)
==> passed
Test 11: open predetermined list of sites using file inputs,
but permute the order in which methods are called
* filename = input8.txt; order = isFull(), isOpen(), percolates()
* filename = input8.txt; order = isFull(), percolates(), isOpen()
* filename = input8.txt; order = isOpen(), isFull(), percolates()
* filename = input8.txt; order = isOpen(), percolates(), isFull()
* filename = input8.txt; order = percolates(), isOpen(), isFull()
* filename = input8.txt; order = percolates(), isFull(), isOpen()
==> passed
Test 12: call open(), isOpen(), and numberOfOpenSites()
in random order until just before system percolates
* n = 3, trials = 40, p = (0.4, 0.4, 0.0, 0.0, 0.3)
* n = 5, trials = 20, p = (0.4, 0.4, 0.0, 0.0, 0.3)
* n = 7, trials = 10, p = (0.4, 0.4, 0.0, 0.0, 0.3)
* n = 10, trials = 5, p = (0.4, 0.4, 0.0, 0.0, 0.3)
* n = 20, trials = 2, p = (0.4, 0.4, 0.0, 0.0, 0.3)
* n = 50, trials = 1, p = (0.4, 0.4, 0.0, 0.0, 0.3)
==> passed
Test 13: call open() and percolates() in random order until just before system percolates
* n = 3, trials = 40, p = (0.5, 0.0, 0.0, 0.5, 0.0)
* n = 5, trials = 20, p = (0.5, 0.0, 0.0, 0.5, 0.0)
* n = 7, trials = 10, p = (0.5, 0.0, 0.0, 0.5, 0.0)
* n = 10, trials = 5, p = (0.5, 0.0, 0.0, 0.5, 0.0)
* n = 20, trials = 2, p = (0.5, 0.0, 0.0, 0.5, 0.0)
* n = 50, trials = 1, p = (0.5, 0.0, 0.0, 0.5, 0.0)
==> passed
Test 14: call open() and isFull() in random order until just before system percolates
* n = 3, trials = 40, p = (0.5, 0.0, 0.5, 0.0, 0.0)
* n = 5, trials = 20, p = (0.5, 0.0, 0.5, 0.0, 0.0)
* n = 7, trials = 10, p = (0.5, 0.0, 0.5, 0.0, 0.0)
* n = 10, trials = 5, p = (0.5, 0.0, 0.5, 0.0, 0.0)
* n = 20, trials = 2, p = (0.5, 0.0, 0.5, 0.0, 0.0)
* n = 50, trials = 1, p = (0.5, 0.0, 0.5, 0.0, 0.0)
==> passed
Test 15: call all methods in random order until just before system percolates
* n = 3, trials = 40, p = (0.2, 0.2, 0.2, 0.2, 0.2)
* n = 5, trials = 20, p = (0.2, 0.2, 0.2, 0.2, 0.2)
* n = 7, trials = 10, p = (0.2, 0.2, 0.2, 0.2, 0.2)
* n = 10, trials = 5, p = (0.2, 0.2, 0.2, 0.2, 0.2)
* n = 20, trials = 2, p = (0.2, 0.2, 0.2, 0.2, 0.2)
* n = 50, trials = 1, p = (0.2, 0.2, 0.2, 0.2, 0.2)
==> passed
Test 16: call all methods in random order until almost all sites are open
(with inputs not prone to backwash)
* n = 3
* n = 5
* n = 7
* n = 10
* n = 20
* n = 50
==> passed
Test 17: substitute WeightedQuickUnionUF data type that sets root nondeterministically;
call all methods in random order until almost all sites are open
(with inputs not prone to backwash)
* n = 3
* n = 5
* n = 7
* n = 10
* n = 20
* n = 50
==> passed
Test 18: check for backwash with predetermined sites
* filename = input20.txt
* filename = input10.txt
* filename = input50.txt
* filename = jerry47.txt
* filename = sedgewick60.txt
* filename = wayne98.txt
==> passed
Test 19: check for backwash with predetermined sites that have
multiple percolating paths
* filename = input3.txt
* filename = input4.txt
* filename = input7.txt
==> passed
Test 20: call all methods in random order until all sites are open
(these inputs are prone to backwash)
* n = 3
* n = 5
* n = 7
* n = 10
* n = 20
* n = 50
==> passed
Test 21: substitute WeightedQuickUnionUF data type that sets root nondeterministically;
call all methods in random order until all sites are open
(these inputs are prone to backwash)
* n = 3
* n = 5
* n = 7
* n = 10
* n = 20
* n = 50
==> passed
Total: 21/21 tests passed!
================================================================
********************************************************************************
* TESTING CORRECTNESS (substituting reference Percolation)
********************************************************************************
Testing correctness of PercolationStats
*-----------------------------------------------------------
Running 17 total tests.
Test 1: check formatting of output of main()
% java-algs4 PercolationStats 20 10
mean = 0.5747500000000001
sttdev = 0.0456503924773198
95% confidence interval = [0.5547428333673490, 0.5947571666326512]
- line 1 of output in student solution:
'sttdev = 0.0456503924773198 '
- the required format is:
'stddev() = <double>'
% java-algs4 PercolationStats 200 100
mean = 0.5923817499999999
sttdev = 0.0081723317201977
95% confidence interval = [0.5912491226092182, 0.5935143773907816]
- line 1 of output in student solution:
'sttdev = 0.0081723317201977 '
- the required format is:
'stddev() = <double>'
==> FAILED
Test 2: check that methods in PercolationStats do not print to standard output
* n = 20, trials = 10
* n = 50, trials = 20
* n = 100, trials = 50
* n = 64, trials = 150
==> passed
Test 3: check that mean() returns value in expected range
* n = 2, trials = 10000
* n = 5, trials = 10000
* n = 10, trials = 10000
* n = 25, trials = 10000
==> passed
Test 4: check that stddev() returns value in expected range
* n = 2, trials = 10000
* n = 5, trials = 10000
* n = 10, trials = 10000
* n = 25, trials = 10000
==> passed
Test 5: check that PercolationStats constructor creates
trials Percolation objects, each of size n-by-n
* n = 15, trials = 15
* n = 20, trials = 10
* n = 50, trials = 20
* n = 100, trials = 50
* n = 64, trials = 150
==> passed
Test 6: check that PercolationStats.main() creates
trials Percolation objects, each of size n-by-n
* n = 15, trials = 15
* n = 20, trials = 10
* n = 50, trials = 20
* n = 100, trials = 50
* n = 64, trials = 150
==> passed
Test 7: check that PercolationStats calls open() until system percolates
* n = 20, trials = 10
* n = 50, trials = 20
* n = 100, trials = 50
* n = 64, trials = 150
==> passed
Test 8: check that PercolationStats does not call open() after system percolates
* n = 20, trials = 10
* n = 50, trials = 20
* n = 100, trials = 50
* n = 64, trials = 150
==> passed
Test 9: check that mean() is consistent with the number of intercepted calls to open()
on blocked sites
* n = 20, trials = 10
* n = 50, trials = 20
* n = 100, trials = 50
* n = 64, trials = 150
==> passed
Test 10: check that stddev() is consistent with the number of intercepted calls to open()
on blocked sites
* n = 20, trials = 10
* n = 50, trials = 20
* n = 100, trials = 50
* n = 64, trials = 150
==> passed
Test 11: check that confidenceLo() and confidenceHigh() are consistent with mean() and stddev()
* n = 20, trials = 10
- PercolationStats confidence low = 0.5621864738891835
- PercolationStats confidence high = 0.6003135261108163
- PercolationStats mean = 0.5812499999999999
- PercolationStats stddev = 0.04349728599451797
- T = 10
- student T = 10
- mean - 1.96 * stddev / sqrt(T) = 0.5542901028274297
- mean + 1.96 * stddev / sqrt(T) = 0.6082098971725701
* n = 50, trials = 20
- PercolationStats confidence low = 0.5707660802429328
- PercolationStats confidence high = 0.5866339197570669
- PercolationStats mean = 0.5786999999999999
- PercolationStats stddev = 0.028623104395979794
- T = 20
- student T = 20
- mean - 1.96 * stddev / sqrt(T) = 0.5661553713973291
- mean + 1.96 * stddev / sqrt(T) = 0.5912446286026707
* n = 100, trials = 50
- PercolationStats confidence low = 0.5908420611695019
- PercolationStats confidence high = 0.5973819388304983
- PercolationStats mean = 0.5941120000000001
- PercolationStats stddev = 0.016683361380092902
- T = 50
- student T = 50
- mean - 1.96 * stddev / sqrt(T) = 0.5894876081577791
- mean + 1.96 * stddev / sqrt(T) = 0.598736391842221
* n = 64, trials = 150
- PercolationStats confidence low = 0.5868394247987333
- PercolationStats confidence high = 0.5965915647846
- PercolationStats mean = 0.5917154947916666
- PercolationStats stddev = 0.019902326501768482
- T = 150
- student T = 150
- mean - 1.96 * stddev / sqrt(T) = 0.5885304592095912
- mean + 1.96 * stddev / sqrt(T) = 0.594900530373742
==> FAILED
Test 12: check that exception is thrown if either n or trials is out of bounds
* n = -23, trials = 42
* n = 23, trials = 0
* n = -42, trials = 0
* n = 42, trials = -1
* n = -2147483648, trials = -2147483648
==> passed
Test 13: create two PercolationStats objects at the same time and check mean()
(to make sure you didn't store data in static variables)
* n1 = 50, trials1 = 10, n2 = 50, trials2 = 5
* n1 = 50, trials1 = 5, n2 = 50, trials2 = 10
* n1 = 50, trials1 = 10, n2 = 25, trials2 = 10
* n1 = 25, trials1 = 10, n2 = 50, trials2 = 10
* n1 = 50, trials1 = 10, n2 = 15, trials2 = 100
* n1 = 15, trials1 = 100, n2 = 50, trials2 = 10
==> passed
Test 14: check that the methods return the same value, regardless of
the order in which they are called
* n = 20, trials = 10
* n = 50, trials = 20
* n = 100, trials = 50
* n = 64, trials = 150
==> passed
Test 15: check that no calls to StdRandom.setSeed()
* n = 20, trials = 10
* n = 20, trials = 10
* n = 40, trials = 10
* n = 80, trials = 10
==> passed
Test 16: check distribution of number of sites opened until percolation
* n = 2, trials = 100000
* n = 3, trials = 100000
* n = 4, trials = 100000
==> passed
Test 17: check that each site is opened the expected number of times
* n = 2, trials = 100000
* n = 3, trials = 100000
* n = 4, trials = 100000
==> passed
Total: 15/17 tests passed!
================================================================
********************************************************************************
* MEMORY (substituting reference Percolation)
********************************************************************************
Analyzing memory of PercolationStats
*-----------------------------------------------------------
Running 4 total tests.
Test 1a-1d: check memory usage as a function of T trials for n = 100
(max allowed: 8*T + 128 bytes)
T bytes
--------------------------------------------
=> passed 16 192
=> passed 32 320
=> passed 64 576
=> passed 128 1088
==> 4/4 tests passed
Estimated student memory = 8.00 T + 64.00 (R^2 = 1.000)
Total: 4/4 tests passed!
================================================================
********************************************************************************
* TIMING (substituting reference Percolation)
********************************************************************************
Timing PercolationStats
*-----------------------------------------------------------
Running 4 total tests.
Test 1: Call PercolationStats constructor and instance methods and
count calls to StdStats.mean() and StdStats.stddev().
* n = 20, trials = 10
* n = 50, trials = 20
* n = 100, trials = 50
* n = 64, trials = 150
==> passed
Test 2: Call PercolationStats constructor and instance methods and
count calls to methods in StdRandom.
* n = 20, trials = 10
* n = 20, trials = 10
* n = 40, trials = 10
* n = 80, trials = 10
==> passed
Test 3: Call PercolationStats constructor and instance methods and
count calls to methods in Percolation.
* n = 20, trials = 10
* n = 50, trials = 20
* n = 100, trials = 50
* n = 64, trials = 150
==> passed
Test 4: Call PercolationStats constructor and instance methods with trials = 3
and values of n that go up by a multiplicative factor of sqrt(2).
The test passes when n reaches 2,896.
The approximate order-of-growth is n ^ (log ratio)
n seconds log ratio
------------------------
724 0.14 2.3
1024 0.32 2.4
1448 0.81 2.7
2048 1.99 2.6
2896 4.56 2.4
==> passed
Total: 4/4 tests passed!
================================================================
********************************************************************************
* MEMORY
********************************************************************************
Analyzing memory of Percolation
*-----------------------------------------------------------
Running 4 total tests.
Test 1a-1d: check that total memory <= 17 n^2 + 128 n + 1024 bytes
n bytes
--------------------------------------------
=> passed 64 69936
=> passed 256 1114416
=> passed 512 4456752
=> passed 1024 17826096
==> 4/4 tests passed
Estimated student memory = 17.00 n^2 + 0.00 n + 304.00 (R^2 = 1.000)
Test 2 (bonus): check that total memory <= 11 n^2 + 128 n + 1024 bytes
- failed memory test for n = 64
==> FAILED
Total: 4/4 tests passed!
================================================================
********************************************************************************
* TIMING
********************************************************************************
Timing Percolation
*-----------------------------------------------------------
Running 16 total tests.
Test 1a-1e: Creates an n-by-n percolation system; open sites at random until
the system percolates, interleaving calls to percolates() and open().
Count calls to connected(), union() and find().
2 * connected()
n union() + find() constructor
-----------------------------------------------------------------------------------
=> passed 16 282 272 2
=> passed 32 1305 1158 2
=> passed 64 5690 4800 2
=> passed 128 23513 19592 2
=> passed 256 92736 77982 2
=> passed 512 369855 311216 2
=> passed 1024 1467816 1240582 2
==> 7/7 tests passed
If one of the values in the table violates the performance limits
the factor by which you failed the test appears in parentheses.
For example, (9.6x) in the union() column indicates that it uses
9.6x too many calls.
Tests 2a-2f: Check whether the number of calls to union(), connected(), and find()
is a constant per call to open(), isOpen(), isFull(), and percolates().
The table shows the maximum number of union() and find() calls made
during a single call to open(), isOpen(), isFull(), and percolates().
One call to connected() counts as two calls to find().
n per open() per isOpen() per isFull() per percolates()
---------------------------------------------------------------------------------------------
=> passed 16 8 0 2 2
=> passed 32 8 0 2 2
=> passed 64 8 0 2 2
=> passed 128 8 0 2 2
=> passed 256 8 0 2 2
=> passed 512 8 0 2 2
=> passed 1024 8 0 2 2
==> 7/7 tests passed
Running time (in seconds) depends on the machine on which the script runs.
Test 3: Create an n-by-n percolation system; interleave calls to percolates()
and open() until the system percolates. The values of n go up by a
factor of sqrt(2). The test is passed if n >= 4096 in under 10 seconds.
The approximate order-of-growth is n ^ (log ratio)
log union-find log
n seconds ratio operations ratio
-------------------------------------------
1024 0.11 2.4 4190934 2.0
1448 0.28 2.6 8388256 2.0
2048 0.68 2.6 16751688 2.0
2896 1.79 2.8 33529654 2.0
4096 3.78 2.2 67001568 2.0
==> passed
Test 4: Create an n-by-n percolation system; interleave calls to open(),
percolates(), isOpen(), isFull(), and numberOfOpenSites() until.
the system percolates. The values of n go up by a factor of sqrt(2).
The test is passed if n >= 4096 in under 10 seconds.
log union-find log
n seconds ratio operations ratio
-------------------------------------------
1024 0.11 1.9 4180368 2.0
1448 0.29 2.9 8351516 2.0
2048 0.87 3.2 16767330 2.0
2896 1.92 2.3 33624770 2.0
4096 4.15 2.2 67553946 2.0
==> passed
Total: 16/16 tests passed!
================================================================
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