Programming Assignment 1: Percolation

问题描述可以详见：http://coursera.cs.princeton.edu/algs4/assignments/percolation.html

关于QuickFindUF的javadoc:http://algs4.cs.princeton.edu/15uf/QuickFindUF.java.html

关于WeightedQuickUnionUF的javadoc:http://algs4.cs.princeton.edu/15uf/WeightedQuickUnionUF.java.html

附言：（引用于http://blog.csdn.net/revilwang/article/details/10823467）

关于这个模型，其实存在一个问题，在算法课程的论坛上，讨论的热度很高。问题是这样的：

由于引入虚拟的顶层区域和虚拟的底层区域，那么当模型渗透的时候，可能会出现下图的情况

如右边图所示，由于所有的底层区域都和虚拟底层区域相连，所以一旦当区域渗透，则和其他的底层开启区域相连的区域也显示为区域满状态。而实际的情况应该是按照左图所示。这个问题称为 backwash，个人把这个翻译成“回流”。引入虚拟底层区域，很难避免这个问题。讨论的结果，有两种方式可以改进：

1. 不使用虚拟底层区域，只保留顶层，判断是否渗透的时候用虚拟顶层和一个for循环来判断。

2. 保留虚拟底层区域，另外加一个不使用虚拟底层的模型，将两个模型结合在一起来判断是否渗透，通过浪费一些内存来保证效率。

backwash的情况导致Percolation.java在测试时public void isfull(int i, int j) 方法出现错误，这一点从上面两张图也可以明显的看出来。（而解决的办法通过上面两种方法实现)

下面两段代码是从http://www.cnblogs.com/tiny656/p/3820653.html 复制来的，因为自己写的没有考虑到backwash的情况，所以有一些错误，就不挂上来误人子弟了。

Percolation.java

public class Percolation {

    private boolean[] matrix;
    private int row, col;
    private WeightedQuickUnionUF wquUF;
    private WeightedQuickUnionUF wquUFTop;
    private boolean alreadyPercolates;

    public Percolation(int N) {
        if (N < 1) throw new IllegalArgumentException("Illeagal Argument");
        wquUF = new WeightedQuickUnionUF(N*N+2);
        wquUFTop = new WeightedQuickUnionUF(N*N+1);
        alreadyPercolates = false;
        row = N;
        col = N;
        matrix = new boolean[N*N+1];
    }

    private void validate(int i, int j) {
        if (i < 1 || i > row)
            throw new IndexOutOfBoundsException("row index i out of bounds");
        if (j < 1 || j > col)
            throw new IndexOutOfBoundsException("col index j out of bounds");
    }

    public void open(int i, int j) {
        validate(i, j);
        int curIdx = (i-1)*col + j;
        matrix[curIdx] = true;
        if (i == 1) {
            wquUF.union(curIdx, 0);
            wquUFTop.union(curIdx, 0);
        }
        if (i == row) {
            wquUF.union(curIdx, row*col+1);
        }

        int[] dx = {1, -1, 0, 0};
        int[] dy = {0, 0, 1, -1};
        for (int dir = 0; dir < 4; dir++) {
            int posX = i + dx[dir];
            int posY = j + dy[dir];
            if (posX <= row && posX >= 1
                    && posY <= row && posY >= 1
                    && isOpen(posX, posY)) {
                wquUF.union(curIdx, (posX-1)*col+posY);
                wquUFTop.union(curIdx, (posX-1)*col+posY);
            }
        }
    }

    public boolean isOpen(int i, int j) {
        validate(i, j);
        return matrix[(i-1)*col + j];
    }

    public boolean isFull(int i, int j) {
        validate(i, j);
        int curIdx = (i-1)*col+j;
        if (wquUFTop.find(curIdx) == wquUFTop.find(0)) return true;
        return false;
    }

    public boolean percolates() {
        if (alreadyPercolates) return true;
        if (wquUF.find(0) == wquUF.find(row*col+1)) {
            alreadyPercolates = true;
            return true;
        }
        return false;
    }

    public static void main(String[] args) {
        Percolation perc = new Percolation(2);
        perc.open(1, 1);
        perc.open(1, 2);
        perc.open(2, 1);
        System.out.println(perc.percolates());
    }

}

PercolationStats.java

public class PercolationStats {
    private double[] x;
    private int expTime;
   public PercolationStats(int N, int T) {    // perform T independent experiments on an N-by-N grid

       if (N <= 0 || T <= 0)
           throw new IllegalArgumentException("Illeagal Argument");
       x = new double[T+1];
       expTime = T;
       for (int i = 1; i <= T; i++) {
           Percolation perc = new Percolation(N);
           while (true) {
               int posX, posY;
               do {
                   posX = StdRandom.uniform(N) + 1;
                   posY = StdRandom.uniform(N) + 1;
               } while(perc.isOpen(posX, posY));
               perc.open(posX, posY);
               x[i] += 1;
                  if (perc.percolates())
                          break;
           }
           x[i] = x[i]/(double) (N * N);
       }
   }
   public double mean() {                     // sample mean of percolation threshold

       double u = 0.0;
       for (int i = 1; i <= expTime; i++) {

           u += x[i];
       }
       return u / (double)expTime;
   }
   public double stddev() {                   // sample standard deviation of percolation threshold

       double q = 0.0;
       double u = mean();
       for (int i = 1; i <= expTime; i++) {

           q += (x[i]-u)*(x[i]-u);
       }
       return Math.sqrt(q / (double)(expTime - 1));
   }
   public double confidenceLo() {            // low  endpoint of 95% confidence interval

       double mu = mean();
       double sigma = stddev();
       return mu - 1.96*sigma / Math.sqrt(expTime);
   }
   public double confidenceHi() {           // high endpoint of 95% confidence interval

       double mu = mean();
       double sigma = stddev();
       return mu + 1.96*sigma / Math.sqrt(expTime);
   }

   public static void main(String[] args) {   // test client (described below)

       int N = Integer.parseInt(args[0]);
       int T = Integer.parseInt(args[1]);
       PercolationStats percStats = new PercolationStats(N, T);
       StdOut.printf("mean = %f\n", percStats.mean());
       StdOut.printf("stddev = %f\n", percStats.stddev());
       StdOut.printf("95%% confidence interval = %f, %f\n",
                      percStats.confidenceLo(), percStats.confidenceHi());

   }
}