普林斯顿算法（第一周作业Percolation 100分)

什么是backwash?

如上图，使用一个WeightedQuickUnionUF对象，带有virtual top site和virtual bottom site。当渗透时，bottom row上可能存在连通virtual bottom site，但是没有连通virtual top site的site。比如上图红色圈内的site，调用isFull()时返回true，因为会通过红色箭头连通到virtual top site，这就产生了backwash问题。
可以使用两个WeightedQuickUnionUF对象避免backwash问题，其中一个只带有virtual top site。

存在的问题：使用两个WeightedQuickUnionUF对象，存在内存占用问题。

********************************************************************************
*  MEMORY
********************************************************************************Analyzing memory of Percolation
*-----------------------------------------------------------
Running 4 total tests.Test 1a-1d: check that total memory <= 17 n^2 + 128 n + 1024 bytesn        bytes
--------------------------------------------
=> passed       64        69944
=> passed      256      1114424
=> passed      512      4456760
=> passed     1024     17826104
==> 4/4 tests passedEstimated student memory = 17.00 n^2 + 0.00 n + 312.00   (R^2 = 1.000)Test 2 (bonus): check that total memory <= 11 n^2 + 128 n + 1024 bytes-  failed memory test for n = 64
==> FAILEDTotal: 4/4 tests passed!

Percolation.java


import edu.princeton.cs.algs4.WeightedQuickUnionUF;/*** $ClassName Percolation* $Description TODO* $Author Freedom Wen* $Date 2022/8/7 22:47*/
public class Percolation {private final int n; // n阶private int openSiteNum; // 已经open的数量private final boolean[] site;private final WeightedQuickUnionUF wquWithTopAndBottom; // 带两个虚拟结点的modelprivate final WeightedQuickUnionUF wquWithTop; // 带两个虚拟结点的modelprivate final int virtualTop; // 虚拟头部结点private final int virtualBottom; // 虚拟底部结点// creates n-by-n grid, with all sites initially blockedpublic Percolation(int n) {if (n < 1) {throw new IllegalArgumentException("param is not valid!");}this.n = n;openSiteNum = 0;virtualTop = 0; //virtualBottom = n * n + 1;site = new boolean[n * n + 2];site[virtualTop] = true;site[virtualBottom] = true;for (int i = 1; i < n*n; i++) {site[i] = false;}wquWithTopAndBottom = new WeightedQuickUnionUF(n * n + 2); // with top and bottomwquWithTop = new WeightedQuickUnionUF(n * n + 1); // only with top}private void checkParams(int row, int col) {if (row < 1 || row > n || col < 1 || col > n) {throw new IllegalArgumentException("params are not valid!");}}private int getSitePos(int row, int col) {return (row - 1) * n + col;}// opens the site (row, col) if it is not open alreadypublic void open(int row, int col) {checkParams(row, col);if (isOpen(row, col)) {return;}int sitePos = getSitePos(row, col);site[sitePos] = true;openSiteNum++; // 每打开一个结点，openSiteNum+1// 连通周围已经打开的结点connectSite(row, col, sitePos);}private void connectSite(int row, int col, int sitePos) {// 当row==1时，连接结点到virtualTopif (row == 1) {wquWithTopAndBottom.union(sitePos, virtualTop);wquWithTop.union(sitePos, virtualTop);}// 当row==n时，连接结点到virtualBottomif (row == n) {wquWithTopAndBottom.union(sitePos, virtualBottom);}if (row > 1 && isOpen(row - 1, col)) {wquWithTopAndBottom.union(sitePos, getSitePos(row - 1, col));wquWithTop.union(sitePos, getSitePos(row - 1, col));}if (row < n && isOpen(row + 1, col)) {wquWithTopAndBottom.union(sitePos, getSitePos(row + 1, col));wquWithTop.union(sitePos, getSitePos(row + 1, col));}if (col > 1 && isOpen(row, col - 1)) {wquWithTopAndBottom.union(sitePos, getSitePos(row, col - 1));wquWithTop.union(sitePos, getSitePos(row, col - 1));}if (col < n && isOpen(row, col + 1)) {wquWithTopAndBottom.union(sitePos, getSitePos(row, col + 1));wquWithTop.union(sitePos, getSitePos(row, col + 1));}}// is the site (row, col) open?public boolean isOpen(int row, int col) {checkParams(row, col);int sitePos = getSitePos(row, col);return site[sitePos];}// is the site (row, col) full?public boolean isFull(int row, int col) {checkParams(row, col);return wquWithTop.find(getSitePos(row, col)) == wquWithTop.find(virtualTop);}// returns the number of open sitespublic int numberOfOpenSites() {return openSiteNum;}// does the system percolate?public boolean percolates() {return wquWithTopAndBottom.find(virtualTop) == wquWithTopAndBottom.find(virtualBottom);}// test client (optional)// public static void main(String[] args) {// }
}

PercolationStats.java

import edu.princeton.cs.algs4.StdOut;
import edu.princeton.cs.algs4.StdRandom;
import edu.princeton.cs.algs4.StdStats;/*** $ClassName PercolationStats* $Description TODO* $Author Freedom Wen* $Date 2022/8/7 22:47*/
public class PercolationStats {private static final double CONFIDENCE_95 = 1.96;private final double[] threshold;private final int trials;// perform independent trials on an n-by-n gridpublic PercolationStats(int n, int trials) {if (n <= 0 || trials <= 0) {throw new IllegalArgumentException("illegal args exception!");}this.trials = trials;threshold = new double[trials];for (int i = 0; i < trials; i++) {Percolation percolation = new Percolation(n);while (!percolation.percolates()) {int row = StdRandom.uniform(1, n + 1);int col = StdRandom.uniform(1, n + 1);percolation.open(row, col);}int openSites = percolation.numberOfOpenSites();threshold[i] = (double) openSites / (n * n);}}// sample mean of percolation thresholdpublic double mean() {return StdStats.mean(threshold);}// sample standard deviation of percolation thresholdpublic double stddev() {return StdStats.stddev(threshold);}// low endpoint of 95% confidence intervalpublic double confidenceLo() {return mean() - CONFIDENCE_95 * stddev() / Math.sqrt(trials);}// high endpoint of 95% confidence intervalpublic double confidenceHi() {return mean() + CONFIDENCE_95 * stddev() / Math.sqrt(trials);}// test client (see below)public static void main(String[] args) {PercolationStats percolationStats = new PercolationStats(Integer.parseInt(args[0]), Integer.parseInt(args[1]));StdOut.println("mean                    = " + percolationStats.mean());StdOut.println("stddev                  = " + percolationStats.stddev());StdOut.println("95% confidence interval = [" + percolationStats.confidenceLo() + ","+ percolationStats.confidenceHi() + "]");}
}

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