project euler 81

Problem 81

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Path sum: two ways

In the 5 by 5 matrix below, the minimal path sum from the top left to the bottom right, by only moving to the right and down, is indicated in bold red and is equal to 2427.

     131673234103182019634296515063080374642211153769949712195680573252437331

Find the minimal path sum, in matrix.txt (right click and “Save Link/Target As…”), a 31K text file containing a 80 by 80 matrix, from the top left to the bottom right by only moving right and down.

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路径和：两个方向

在如下的5乘5矩阵中，从左上方到右下方始终只向右或向下移动的最小路径和为2427，由标注红色的路径给出。

     131673234103182019634296515063080374642211153769949712195680573252437331

在这个31K的文本文件matrix.txt（右击并选择“目标另存为……”）中包含了一个80乘80的矩阵，求出从该矩阵的左上方到右下方始终只向右和向下移动的最小路径和。

package projecteuler;import java.io.BufferedReader;import java.io.FileInputStream;import java.io.InputStreamReader;import java.util.Stack;import junit.framework.TestCase;public class Prj81 extends TestCase {public static final String PATH = "E:\\whua\\mathWorkspace\\test_jgraph\\src\\projecteuler\\Prj81.txt";public static final int ROW_COUNT = 80;public static int[][] DATA;public void testPathSumTwoWays() {DijkStraShortPath shortPath = new DijkStraShortPath() {class Vertex implements IVertex {private int m;@Overridepublic String toString() {return "Vertex [m=" + m + ", n=" + n + "]";}private int n;private int rowCount;public Vertex(int m, int n, int Col) {this.m = m;this.n = n;this.rowCount = Col;}@Overridepublic int getVertexId() {return m * rowCount + n;}@Overridepublic Object getDescrp() {return "(" + m + "," + n + ")";}}@Overridepublic IVertex id2Vertex(int id) {return new Vertex(id / ROW_COUNT, id % ROW_COUNT, ROW_COUNT);}@Overridepublic void createEdge() {int[][] data = readStr();int rowCount = data[0].length;int numOfVertex = rowCount * rowCount;this.flag = new boolean[numOfVertex];this.edge = new int[numOfVertex][numOfVertex];for (int i = 0; i < numOfVertex; i++) {for (int j = 0; j < numOfVertex; j++) {edge[i][j] = MAX_MASK;}}for (int i = 0; i < rowCount - 1; i++) {for (int j = 0; j < rowCount; j++) {edge[i * rowCount + j][(i + 1) * rowCount + j] = data[i][j]+ data[i + 1][j];}}for (int i = 0; i < rowCount; i++) {for (int j = 0; j < rowCount - 1; j++) {edge[i * rowCount + j][i * rowCount + j + 1] = data[i][j]+ data[i][j + 1];}}}@Overridepublic Object trace(int startId, int findId) {System.out.println("START++++");int sum = 0;sum += DATA[findId / ROW_COUNT][findId % ROW_COUNT];IVertex vt = path[findId];Stack<IVertex> stack = new Stack<IVertex>();while (vt.getVertexId() != startId) {stack.push(vt);int id = vt.getVertexId();sum += DATA[id / ROW_COUNT][id % ROW_COUNT];vt = path[vt.getVertexId()];}sum += DATA[startId / ROW_COUNT][startId % ROW_COUNT];System.out.println( id2Vertex(findId));Object[] objArr = stack.toArray();for (Object o : objArr) {System.out.println(o);}System.out.println(path[startId]);System.out.println("END++++");System.out.println("sum=" + sum);return objArr;}};shortPath.findPath(0);shortPath.trace(0, ROW_COUNT * ROW_COUNT - 1);}static int[][] readStr() {try {BufferedReader reader = new BufferedReader(new InputStreamReader(new FileInputStream(PATH), "utf8"));int[][] ret = new int[ROW_COUNT][ROW_COUNT];int count = 0;String str = "";while ((str = reader.readLine()) != null) {String[] strs = str.split(",");for (int i = 0; i < strs.length; i++) {ret[count][i] = Integer.parseInt(strs[i]);}count++;}reader.close();DATA = ret;return ret;// int[][] ret = new int[][] { { 131, 673, 234, 103, 18 },// { 201, 96, 342, 965, 150 }, { 630, 803, 746, 422, 111 },// { 537, 699, 497, 121, 956 }, { 805, 732, 524, 37, 331 } };//// DATA = ret;// return ret;} catch (Exception ex) {ex.printStackTrace();}return null;}public interface IVertex {int getVertexId();Object getDescrp();}public static abstract class DijkStraShortPath {public static final int MAX_MASK = Integer.MAX_VALUE;protected int[][] edge;protected boolean[] flag;protected IVertex[] path;public abstract void createEdge();public abstract IVertex id2Vertex(int id);public abstract Object trace(int startId, int endId);public int[] findPath(int startId) {createEdge();path = new IVertex[flag.length];IVertex start = id2Vertex(startId);path[startId] = start;int numOfVertex = flag.length;int[] dist = new int[numOfVertex];for (int i = 0; i < dist.length; i++) {dist[i] = edge[start.getVertexId()][i];}for (int i = 0; i < dist.length; i++) {if (i != startId && edge[startId][i] != MAX_MASK) {path[i] = id2Vertex(startId);}}dist[startId] = 0;flag[startId] = true;for (;;) {int minId = -1;int minVal = MAX_MASK;for (int i = 0; i < flag.length; i++) {if (!flag[i]) {if (dist[i] < minVal) {minVal = dist[i];minId = i;}}}if (minId == -1) {break;}for (int j = 0; j < flag.length; j++) {if (j != minId && !flag[j] && edge[minId][j] != MAX_MASK&& edge[minId][j] + dist[minId] < dist[j]) {dist[j] = edge[minId][j] + dist[minId];path[j] = id2Vertex(minId);}}flag[minId] = true;}return dist;}}}