Programming Assignment 1: Percolation

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Programming Assignment 1: Percolation

作业网址如下：

http://coursera.cs.princeton.edu/algs4/assignments/percolation.html

正文

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第一章的作业需要制作两个类
第一个Percolation包含五个方法，主要是用来打开渗漏的格子。
第二个类PercolationStats 同样有五个方法，用来找出N*N格子中，能够产生渗漏的阈值概率的95%置信区间。
先说一下大概的想法和原理。
官网上提供有这道题目的思路，就是在创建格子的过程中首先要在顶层和底层各加一层，
这样的话在测试是否渗漏时直接测试（0，1）和（N+1,1）就好了
首先来说下第一个类：
官网的API已经写好：

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public class Percolation {
public Percolation(int N) // create N-by-N grid, with all sites blocked
public void open(int i, int j) // open site (row i, column j) if it is not open already
public boolean isOpen(int i, int j) // is site (row i, column j) open?
public boolean isFull(int i, int j) // is site (row i, column j) full?
public boolean percolates() // does the system percolate?
public static void main(String[] args // test client (optional)
}

public class Percolation {   public Percolation(int N)               // create N-by-N grid, with all sites blocked   public void open(int i, int j)          // open site (row i, column j) if it is not open already   public boolean isOpen(int i, int j)     // is site (row i, column j) open?   public boolean isFull(int i, int j)     // is site (row i, column j) full?   public boolean percolates()             // does the system percolate?   public static void main(String[] args   // test client (optional)}

1.构造函数 public Percolation(int N)
运用了虚拟节点的方法，把坐标（i,j）转化为（i*N+J），这样能更直观的找到坐标点的位置。
可以直接使用quick-find 和quick-union。
为了实现这个目标，调用WeightedQuickUnionUF创建了一个((N+1)*(N)+N+1)的一位数组。
第零排和第N+1排用来判断是否渗漏，而第零列被整体抛弃。
这样的做法是浪费了一定的存储空间，若非为了查找坐标方便，采用N*N+2个格子也是足够用的。
2.public void open(int i, int j)
判断该点是否打开，如果打开则结束。未打开则与上下左右四个点连接。
3.public boolean isOpen(int i, int j)
只需要返回该点的开闭状态值；
4.public boolean isFull(int i, int j)
判断该点是否与顶部联通。
5.public boolean percolates()
判断是否渗漏
也就是检查（0，1）和（N+1,1）；
注意：题目中提到了一个回流问题（如图）

由于底部的一排是联通的，那么所有与底部相连的点将会出现“灌水”。
为了解决这个问题，就要再建立一个不包含最底层的格子。在isFull（）中使用该数组进行检查
如果底部的格子确实没有与顶部的虚拟点连通，是不会“灌满”的。

全部代码如下：

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public class Percolation {
private WeightedQuickUnionUF uf;
private WeightedQuickUnionUF uf_backwash;
private int N;
//private int count_n=0;//record the number of open site;
private boolean[] ifopen;//an array record if the site is open;
public Percolation(int N) {
if (N<=0) throw new IllegalArgumentException(“N is<=0”);
this.N = N;
int i;
uf=new WeightedQuickUnionUF((N+1)*(N)+N+1);
uf_backwash=new WeightedQuickUnionUF(N*N+N+1);
ifopen=new boolean[(N+1)*(N)+N+1];
for(i=1;i<=N;i++){
uf.union(0*N+1, 0*N+i);
uf_backwash.union(0*N+1, 0*N+i);
ifopen[0*N+i]=true;
uf.union((N+1)*N+1, (N+1)*N+i);
ifopen[(N+1)*N+i] = true;
}
}// create N-by-N grid, with all sites blocked
public void open(int i, int j){
if (i<1||i>N) throw new IndexOutOfBoundsException(“row index i out of bounds”);
if(j<1||j>N) throw new IndexOutOfBoundsException(“column index j out of bounds”);
if(ifopen[i*N+j]) return;
ifopen[i*N+j]=true;
//count_n++;
if (ifopen[(i-1)*N+j]){
uf.union(i*N+j, (i-1)*N+j);
uf_backwash.union(i*N+j, (i-1)*N+j);
}
if (ifopen[(i+1)*N+j]){
uf.union(i*N+j, (i+1)*N+j);
if (i!=N){
uf_backwash.union(i*N+j, (i+1)*N+j);
}
}
if (j!=1 && ifopen[i*N+j-1]){
uf.union(i*N+j, i*N+j-1);
uf_backwash.union(i*N+j, i*N+j-1);
}
if (j!=N && ifopen[i*N+j+1]){
uf.union(i*N+j, i*N+j+1);
uf_backwash.union(i*N+j, i*N+j+1);
}
}// open site (row i, column j) if it is not already
public boolean isOpen(int i, int j){
if (i<1||i>N) throw new IndexOutOfBoundsException(“row index i out of bounds”);
if(j<1||j>N) throw new IndexOutOfBoundsException(“column index j out of bounds”);
return ifopen[i*N+j];
}// is site (row i, column j) open?
public boolean isFull(int i, int j){
if (i<1||i>N) throw new IndexOutOfBoundsException(“row index i out of bounds”);
if(j<1||j>N) throw new IndexOutOfBoundsException(“column index j out of bounds”);
return uf_backwash.connected(i*N+j, 0*N+1) && ifopen[i*N+j];
} // is site (row i, column j) full?
public boolean percolates() {
return uf.connected(0*N+1, (N+1)*N+1);
}// does the system percolate?
public static void main(String[] args){
int N = StdIn.readInt();
Percolation pe=new Percolation(N);
pe.open(1, 1);
pe.open(2, 1);
System.out.println(pe.percolates());
}// test client, optional
}

public class Percolation {    private WeightedQuickUnionUF uf;    private WeightedQuickUnionUF uf_backwash;    private int N;    //private int count_n=0;//record the number of open site;    private boolean[] ifopen;//an array record if the site is open;            public Percolation(int N) {               if (N<=0) throw new IllegalArgumentException("N is<=0");               this.N = N;               int i;               uf=new WeightedQuickUnionUF((N+1)*(N)+N+1);               uf_backwash=new WeightedQuickUnionUF(N*N+N+1);               ifopen=new boolean[(N+1)*(N)+N+1];               for(i=1;i<=N;i++){                   uf.union(0*N+1, 0*N+i);                   uf_backwash.union(0*N+1, 0*N+i);                   ifopen[0*N+i]=true;                   uf.union((N+1)*N+1, (N+1)*N+i);                      ifopen[(N+1)*N+i] = true;                 }              }// create N-by-N grid, with all sites blocked           public void open(int i, int j){               if (i<1||i>N) throw new IndexOutOfBoundsException("row index i out of bounds");               if(j<1||j>N)  throw new IndexOutOfBoundsException("column index j out of bounds");                   if(ifopen[i*N+j]) return;                   ifopen[i*N+j]=true;                   //count_n++;                   if (ifopen[(i-1)*N+j]){                         uf.union(i*N+j, (i-1)*N+j);                         uf_backwash.union(i*N+j, (i-1)*N+j);                     }                     if (ifopen[(i+1)*N+j]){                         uf.union(i*N+j, (i+1)*N+j);                         if (i!=N){                             uf_backwash.union(i*N+j, (i+1)*N+j);                         }                     }                     if (j!=1 && ifopen[i*N+j-1]){                         uf.union(i*N+j, i*N+j-1);                         uf_backwash.union(i*N+j, i*N+j-1);                     }                     if (j!=N && ifopen[i*N+j+1]){                         uf.union(i*N+j, i*N+j+1);                         uf_backwash.union(i*N+j, i*N+j+1);                     }             }// open site (row i, column j) if it is not already           public boolean isOpen(int i, int j){               if (i<1||i>N) throw new IndexOutOfBoundsException("row index i out of bounds");               if(j<1||j>N)  throw new IndexOutOfBoundsException("column index j out of bounds");               return ifopen[i*N+j];           }// is site (row i, column j) open?           public boolean isFull(int i, int j){               if (i<1||i>N) throw new IndexOutOfBoundsException("row index i out of bounds");               if(j<1||j>N)  throw new IndexOutOfBoundsException("column index j out of bounds");                return uf_backwash.connected(i*N+j, 0*N+1) && ifopen[i*N+j];            } // is site (row i, column j) full?           public boolean percolates() {               return uf.connected(0*N+1, (N+1)*N+1);           }// does the system percolate?           public static void main(String[] args){               int N = StdIn.readInt();               Percolation pe=new Percolation(N);               pe.open(1, 1);               pe.open(2, 1);               System.out.println(pe.percolates());           }// test client, optional}

第二个类：

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public class PercolationStats {
public PercolationStats(int N, int T) // perform T independent experiments on an N-by-N grid
public double mean() // sample mean of percolation threshold
public double stddev() // sample standard deviation of percolation threshold
public double confidenceLo() // low endpoint of 95% confidence interval
public double confidenceHi() // high endpoint of 95% confidence interval
public static void main(String[] args) // test client (described below)
}

public class PercolationStats {   public PercolationStats(int N, int T)     // perform T independent experiments on an N-by-N grid   public double mean()                      // sample mean of percolation threshold   public double stddev()                    // sample standard deviation of percolation threshold   public double confidenceLo()              // low  endpoint of 95% confidence interval   public double confidenceHi()              // high endpoint of 95% confidence interval   public static void main(String[] args)    // test client (described below)}

这个类是用来求取统计概率，想法如下：
初始化一个N*N格子，并处于关闭状态。
每次随机选择一个格子进行开启操作，直到渗漏为止。
记录此时打开格子数与总格子数的比例P
重复N此得到最后的样本平均值。
1.public PercolationStats(int N, int T)
进行T次关于N*N格子的独立重复试验。

进行一次循环，通过Percolation类构造函数，用到了书中给出的类库
StdRandom.uniform（int N）生成随机数
StdStats.mean(double); 求均值
StdStats.stddev(double);求方差

全部代码如下：

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public class PercolationStats {
private double staT[];
private double sta_mean;
private double sta_stddev;
private int N;
public PercolationStats(int N, int T){
staT=new double[T];
this.N=N;
int times=0;
if(N<=0) throw new IllegalArgumentException();
if(T<=0) throw new IllegalArgumentException();
while(times<T){
Percolation pe=new Percolation(N);
int count=0;
while(true){
count++;
while(true){
int x = StdRandom.uniform(N) + 1;
int y = StdRandom.uniform(N) + 1;
if(pe.isOpen(x, y)){
continue;
}else{
pe.open(x, y);
break;
}
}
if(pe.percolates()){
staT[times]=(double)count/((double)N*(double)N);
break;
}
}
times++;
}
this.sta_mean = StdStats.mean(staT);
this.sta_stddev = StdStats.stddev(staT);
}// perform T independent computational experiments on an N-by-N grid
public double mean(){
return this.sta_mean;
}// sample mean of percolation threshold
public double stddev(){
return this.sta_stddev;
} // sample standard deviation of percolation threshold
public double confidenceLo(){
return this.sta_mean-1.96*this.sta_stddev/Math.sqrt(N);
}// returns lower bound of the 95% confidence interval
public double confidenceHi(){
return this.sta_mean+1.96*this.sta_stddev/Math.sqrt(N);
} // returns upper bound of the 95% confidence interval
public static void main(String[] args){
int N = StdIn.readInt();
int T = StdIn.readInt();
PercolationStats percolationStats = new PercolationStats(N, T);
StdOut.println(”mean = ” + percolationStats.mean());
StdOut.println(”stddev = ” + percolationStats.stddev());
StdOut.println(”95% confidence interval ” + percolationStats.confidenceLo() + “, ” + percolationStats.confidenceHi());
} // test client, described below
}

public class PercolationStats {    private double staT[];      private double sta_mean;      private double sta_stddev;      private int N;   public PercolationStats(int N, int T){      staT=new double[T];      this.N=N;      int times=0;      if(N<=0) throw new IllegalArgumentException();      if(T<=0) throw new IllegalArgumentException();      while(times<T){          Percolation pe=new Percolation(N);          int count=0;          while(true){              count++;              while(true){                  int x = StdRandom.uniform(N) + 1;                    int y = StdRandom.uniform(N) + 1;                  if(pe.isOpen(x, y)){                      continue;                  }else{                      pe.open(x, y);                      break;                  }              }              if(pe.percolates()){                  staT[times]=(double)count/((double)N*(double)N);                  break;              }             }          times++;     }      this.sta_mean = StdStats.mean(staT);        this.sta_stddev = StdStats.stddev(staT);   }// perform T independent computational experiments on an N-by-N grid   public double mean(){       return this.sta_mean;   }// sample mean of percolation threshold   public double stddev(){       return this.sta_stddev;   } // sample standard deviation of percolation threshold   public double confidenceLo(){       return this.sta_mean-1.96*this.sta_stddev/Math.sqrt(N);   }// returns lower bound of the 95% confidence interval   public double confidenceHi(){       return this.sta_mean+1.96*this.sta_stddev/Math.sqrt(N);   }             // returns upper bound of the 95% confidence interval   public static void main(String[] args){            int N = StdIn.readInt();              int T = StdIn.readInt();              PercolationStats percolationStats = new PercolationStats(N, T);              StdOut.println("mean = " + percolationStats.mean());              StdOut.println("stddev = " + percolationStats.stddev());              StdOut.println("95% confidence interval " + percolationStats.confidenceLo() + ", " + percolationStats.confidenceHi());     } // test client, described below}

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