ACM HDOJ 1151 (Air Raid)

题目链接 http://acm.hdu.edu.cn/showproblem.php?pid=1151

思路 DAG图（无回路有向图）的最小路径覆盖数 = 节点数 - 最大匹配数

程序一 匈牙利算法 DFS

import java.util.Arrays;
import java.util.Scanner;

public class Main {

public static void main(String[] args) {
Scanner scn = new Scanner(System.in);
int casesNumber = Integer.parseInt(scn.next());
while (0 <= --casesNumber) {
int leftSetNumber = Integer.parseInt(scn.next());
int rightSetNumber = leftSetNumber;
int edgesNumber = Integer.parseInt(scn.next());
Hungary hungary = new Hungary(leftSetNumber, rightSetNumber);
for (int i = 0; i < edgesNumber; ++i) {
int left = Integer.parseInt(scn.next()) - 1;
int right = Integer.parseInt(scn.next()) - 1;
hungary.addEdge(left, right);
}
System.out.println(leftSetNumber - hungary.maxMatch());
}
scn.close();
}

}

class Hungary {

private int leftSetNumber;
private int rightSetNumber;
private boolean[][] matrix;
private int[] leftResult;
private int[] rightResult;
private boolean[] rightUsed;

private boolean searchPath(int left) {
for (int right = 0; right < rightSetNumber; ++right) {
if (matrix[left][right] && !rightUsed[right]) {
rightUsed[right] = true;
if (-1 == rightResult[right] || searchPath(rightResult[right])) {
rightResult[right] = left;
leftResult[left] = right;
return true;
}
}
}
return false;
}

public Hungary(int leftSetNumber, int rightSetNumber) {
this.leftSetNumber = leftSetNumber;
this.rightSetNumber = rightSetNumber;
matrix = new boolean[leftSetNumber][rightSetNumber];
leftResult = new int[leftSetNumber];
rightResult = new int[rightSetNumber];
rightUsed = new boolean[rightSetNumber];
}

public void addEdge(int left, int right) {
matrix[left][right] = true;
}

public int maxMatch() {
Arrays.fill(leftResult, -1);
Arrays.fill(rightResult, -1);
Arrays.fill(rightUsed, false);
int count = 0;
for (int left = 0; left < leftSetNumber; ++left) {
if (-1 == leftResult[left]) {
Arrays.fill(rightUsed, false);
if (searchPath(left)) {
++count;
}
}
}
return count;
}

}

程序二 匈牙利算法 BFS

import java.util.Arrays;
import java.util.LinkedList;
import java.util.Queue;
import java.util.Scanner;

public class Main {

public static void main(String[] args) {
Scanner scn = new Scanner(System.in);
int casesNumber = Integer.parseInt(scn.next());
while (0 <= --casesNumber) {
int leftSetNumber = Integer.parseInt(scn.next());
int rightSetNumber = leftSetNumber;
int edgesNumber = Integer.parseInt(scn.next());
Hungary hungary = new Hungary(leftSetNumber, rightSetNumber);
for (int i = 0; i < edgesNumber; ++i) {
int left = Integer.parseInt(scn.next()) - 1;
int right = Integer.parseInt(scn.next()) - 1;
hungary.addEdge(left, right);
}
System.out.println(leftSetNumber - hungary.maxMatch());
}
scn.close();
}

}

class Hungary {

private int leftSetNumber;
private int rightSetNumber;
private boolean[][] matrix;
private int[] leftResult;
private int[] rightResult;
private boolean[] rightUsed;
private int[] preLeft;

public Hungary(int leftSetNumber, int rightSetNumber) {
this.leftSetNumber = leftSetNumber;
this.rightSetNumber = rightSetNumber;
matrix = new boolean[leftSetNumber][rightSetNumber];
leftResult = new int[leftSetNumber];
rightResult = new int[rightSetNumber];
rightUsed = new boolean[rightSetNumber];
preLeft = new int[leftSetNumber];
}

public void addEdge(int left, int right) {
matrix[left][right] = true;
}

public int maxMatch() {
Arrays.fill(leftResult, -1);
Arrays.fill(rightResult, -1);
Arrays.fill(preLeft, -1);
int count = 0;
for (int i = 0; i < leftSetNumber; ++i) {
if (-1 == leftResult[i]) {
Queue<Integer> queue = new LinkedList<Integer>();
queue.offer(i);
boolean hasAP = false;
Arrays.fill(rightUsed, false);
while (!queue.isEmpty() && !hasAP) {
int left = queue.poll();
for (int right = 0; right < rightSetNumber && !hasAP; ++right) {
if (matrix[left][right] && !rightUsed[right]) {
rightUsed[right] = true;
queue.offer(rightResult[right]);
if (0 <= rightResult[right]) {
preLeft[rightResult[right]] = left;
} else {
hasAP = true;
int currentLeft = left;
int currentRight = right;
while (-1 != currentLeft) {
int lastRight = leftResult[currentLeft];
leftResult[currentLeft] = currentRight;
rightResult[currentRight] = currentLeft;
currentLeft = preLeft[currentLeft];
currentRight = lastRight;
}
}
}
}
}
if (-1 != leftResult[i]) {
++count;
}
}
}
return count;
}

}

程序三 Hopcroft-Carp 算法

import java.util.Arrays;
import java.util.LinkedList;
import java.util.Queue;
import java.util.Scanner;

public class Main {

public static void main(String[] args) {
Scanner scn = new Scanner(System.in);
int casesNumber = Integer.parseInt(scn.next());
while (0 <= --casesNumber) {
int leftSetNumber = Integer.parseInt(scn.next());
int rightSetNumber = leftSetNumber;
int edgesNumber = Integer.parseInt(scn.next());
HopcroftCarp hopcroftCarp = new HopcroftCarp(leftSetNumber,
rightSetNumber);
for (int i = 0; i < edgesNumber; ++i) {
int left = Integer.parseInt(scn.next()) - 1;
int right = Integer.parseInt(scn.next()) - 1;
hopcroftCarp.addEdge(left, right);
}
System.out.println(leftSetNumber - hopcroftCarp.maxMatch());
}
scn.close();
}

}

class HopcroftCarp {

private final int INF = Integer.MAX_VALUE / 2;
private int leftSetNumber;
private int rightSetNumber;
private boolean[][] matrix;
private int[] leftResult;
private int[] rightResult;
private boolean[] rightUsed;
private int[] leftGradation;
private int[] rightGradation;
private int gradation;

private boolean searchPath() {
Arrays.fill(leftGradation, -1);
Arrays.fill(rightGradation, -1);
gradation = INF;
Queue<Integer> queue = new LinkedList<Integer>();
for (int left = 0; left < leftSetNumber; ++left) {
if (-1 == leftResult[left]) {
queue.offer(left);
++leftGradation[left];
}
}
while (!queue.isEmpty()) {
int left = queue.poll();
if (leftGradation[left] > gradation) {
break;
}
for (int right = 0; right < rightSetNumber; ++right) {
if (matrix[left][right] && -1 == rightGradation[right]) {
rightGradation[right] = leftGradation[left] + 1;
if (-1 == rightResult[right]) {
gradation = rightGradation[right];
} else {
leftGradation[rightResult[right]] = rightGradation[right] + 1;
queue.offer(rightResult[right]);
}
}
}
}
return INF != gradation;
}

private boolean dfs(int left) {
for (int right = 0; right < rightSetNumber; right++) {
if (!rightUsed[right] && matrix[left][right]
&& rightGradation[right] == leftGradation[left] + 1) {
rightUsed[right] = true;
if (-1 != rightResult[right]
&& rightGradation[right] == gradation) {
continue;
}
if (-1 == rightResult[right] || dfs(rightResult[right])) {
rightResult[right] = left;
leftResult[left] = right;
return true;
}
}
}
return false;
}

public HopcroftCarp(int leftSetNumber, int rightSetNumber) {
this.leftSetNumber = leftSetNumber;
this.rightSetNumber = rightSetNumber;
matrix = new boolean[leftSetNumber][rightSetNumber];
leftResult = new int[leftSetNumber];
rightResult = new int[rightSetNumber];
rightUsed = new boolean[rightSetNumber];
leftGradation = new int[leftSetNumber];
rightGradation = new int[rightSetNumber];
gradation = INF;
}

public void addEdge(int left, int right) {
matrix[left][right] = true;
}

public int maxMatch() {
Arrays.f
4000
ill(leftResult, -1);
Arrays.fill(rightResult, -1);
int count = 0;
while (searchPath()) {
Arrays.fill(rightUsed, false);
for (int left = 0; left < leftSetNumber; ++left) {
if (-1 == leftResult[left] && dfs(left)) {
++count;
}
}
}
return count;
}

}