克魯斯卡爾算法

這是用Java寫的控制臺(tái)程序感昼，我建議各位看官先運(yùn)行再看代碼荷憋。

package com.company;

public class Main {

    public static void main(String[] args) {
    // write your code here
        int[][] adjustMatrix = {
                {0,7,-1,5,-1,-1,-1},
                {-1,0,8,9,7,-1,-1},
                {-1,-1,0,-1,5,-1,-1},
                {-1,-1,-1,0,15,6,-1},
                {-1,-1,-1,-1,0,8,9},
                {-1,-1,-1,-1,-1,0,11},
                {-1,-1,-1,-1,-1,-1,0}
        };
        Kruskal.kruskal0(adjustMatrix);
    }
}

package com.company;

public class Kruskal {
    /**
     * 這是傳說中著名的克魯斯卡爾算法
     * 用于生成最小生成樹
     * 適用于無向連通圖
     * 權(quán)值必須為自然數(shù)
     * @param sourceArray
     */
    static public void kruskal0(int[][] sourceArray) {
        int arrayLength = sourceArray.length;
        //第一步對輸入的
        // 矩陣按照權(quán)值
        // 進(jìn)行從小到大
        // 排序因?yàn)殒湵?        // 的插入時(shí)間復(fù)
        // 雜度為O(1)，
        // 所以此處采用
        // 單向鏈表來構(gòu)
        // 造從小到大有
        // 序的序列阅仔。
        SingleLinkNode headPointer = new SingleLinkNode(-1,-1,-1);
        for (int counter = 0;counter < arrayLength;counter++) {
            for (int counter0 = counter + 1;counter0 < arrayLength;counter0++) {
                if (sourceArray[counter][counter0] > 0) {
                    SingleLinkNode newNode = new SingleLinkNode(counter,counter0,sourceArray[counter][counter0]);
                    SingleLinkNode currentPointer = headPointer;
                    while (currentPointer.nextPointer != null &&
                            currentPointer.nextPointer.getWeight() < newNode.getWeight())
                        currentPointer = currentPointer.nextPointer;
                    newNode.nextPointer = currentPointer.nextPointer;
                    currentPointer.nextPointer = newNode;
                }
            }
        }
        //用來創(chuàng)建連通圖結(jié)點(diǎn)的集合吹散，每個(gè)二維
        // 數(shù)組代表一個(gè)集合。初始情況下八酒，因?yàn)?        // 每個(gè)頂點(diǎn)自成一個(gè)連通圖空民，所以默認(rèn)
        // 值情況下每個(gè)二維數(shù)組的下標(biāo)為0的值
        // 是該二維數(shù)組的index。因?yàn)槊總€(gè)二維
        // 數(shù)組被當(dāng)成一個(gè)棧來使用羞迷，并且已經(jīng)有
        // 了一個(gè)元素界轩，所以棧頂指針為0.此處為
        // 判斷新邊加入到已有集合的時(shí)候是否已
        // 經(jīng)形成了環(huán)。
        //連通圖的各集合
        int[][] circleUnion = new int[arrayLength][arrayLength];
        for (int counter = 0;counter < arrayLength;counter++)
            circleUnion[counter][0] = counter;
        //這是棧頂指針衔瓮，初始狀態(tài)的時(shí)候每個(gè)棧中都有一個(gè)元素浊猾，所以棧頂指針置為0.
        int[] unionTopPointer = new int[arrayLength];
        for (int counter = 0;counter < arrayLength;counter++)
            unionTopPointer[counter] = 0;
        //此數(shù)組中代表的是每個(gè)頂點(diǎn)此時(shí)處于哪個(gè)集合之中。
        int[] vertexMarkArray = new int[arrayLength];
        //因?yàn)槟J(rèn)情況下每個(gè)頂點(diǎn)自成一個(gè)連通圖热鞍，
        // 所以該頂點(diǎn)所屬的集合編號就是它自己的編號葫慎。
        for (int counter = 0;counter < arrayLength;counter++)
            vertexMarkArray[counter] = counter;
        //逐個(gè)選擇最小的邊進(jìn)行判斷，合格的被加入到某集合中薇宠。不合格的從鏈表中摳去偷办。
        SingleLinkNode currentPointer = headPointer;
        //如果2個(gè)頂點(diǎn)對應(yīng)的編號相同代表
        // 它們屬于同一個(gè)連通分量，換句
        // 話說已經(jīng)在一個(gè)連通圖里面了澄港。
        // 不同則可以合并椒涯，不過前提是這
        // 兩個(gè)頂點(diǎn)所屬集合不為空。
        while (currentPointer.nextPointer != null) {
            System.out.println("打印調(diào)整前的各結(jié)點(diǎn)的集合歸屬狀態(tài)");
            for (int counter = 0;counter < arrayLength;counter++) {
                System.out.println(counter + "-->" + vertexMarkArray[counter]);
            }
            System.out.println("打印調(diào)整前各集合桶的狀態(tài)變化");
            for (int counter = 0;counter < arrayLength;counter++) {
                System.out.print("桶" + counter + ":");
                for (int counter0 = 0;counter0 <= unionTopPointer[counter];counter0++) {
                    System.out.print(circleUnion[counter][counter0] + " ");
                }
                System.out.println();
            }
            //鏈表中某結(jié)點(diǎn)的源頂點(diǎn)編號和目標(biāo)頂點(diǎn)編號
            int sourceIndex = currentPointer.nextPointer.getSourceNode();
            int targetIndex = currentPointer.nextPointer.getTargetNode();
            System.out.println("新頂點(diǎn)對:(" + sourceIndex + "," + targetIndex + ")");
            if (vertexMarkArray[sourceIndex] != vertexMarkArray[targetIndex]
                    && unionTopPointer[vertexMarkArray[sourceIndex]] > -1
                    && unionTopPointer[vertexMarkArray[targetIndex]] > -1) {
                System.out.println("對應(yīng)的桶編號為:(" + vertexMarkArray[sourceIndex] + "," + vertexMarkArray[targetIndex] + ")");
                //比較一個(gè)哪個(gè)集合元素多回梧，具體就是比較棧
                // 頂指針废岂。因?yàn)橐焉俚臈Ｖ械脑剞D(zhuǎn)移到多的棧中祖搓。
                if (unionTopPointer[vertexMarkArray[targetIndex]] > unionTopPointer[vertexMarkArray[sourceIndex]]) {
                    int tempIndex = sourceIndex;
                    sourceIndex = targetIndex;
                    targetIndex = tempIndex;
                }
                int moreBucket = vertexMarkArray[sourceIndex];
                int lessBucket = vertexMarkArray[targetIndex];
                while (unionTopPointer[lessBucket] > -1) {
                    int vertexId = circleUnion[lessBucket][unionTopPointer[lessBucket]--];
                    circleUnion[moreBucket][++unionTopPointer[moreBucket]] = vertexId;
                    //在轉(zhuǎn)移的同時(shí)刷新被移動(dòng)的每個(gè)頂點(diǎn)所屬的集合編號。
                    vertexMarkArray[vertexId] = moreBucket;
                }
                //只要棧中的元素個(gè)數(shù)達(dá)到了頂點(diǎn)的總數(shù)就代表算法完成了湖苞。
                if (unionTopPointer[vertexMarkArray[sourceIndex]] == arrayLength - 1) {
                    currentPointer.nextPointer.nextPointer = null;
                    System.out.println("打印調(diào)整后各集合桶的狀態(tài)變化");
                    for (int counter = 0;counter < arrayLength;counter++) {
                        System.out.print("桶" + counter + ":");
                        for (int counter0 = 0;counter0 <= unionTopPointer[counter];counter0++) {
                            System.out.print(circleUnion[counter][counter0] + " ");
                        }
                        System.out.println();
                    }
                    System.out.println("集合歸并結(jié)束");
                    break;
                }
                currentPointer = currentPointer.nextPointer;
            } else {
                System.out.println("舍去");
                currentPointer.nextPointer = currentPointer.nextPointer.nextPointer;
            }
            System.out.println("打印調(diào)整后的各結(jié)點(diǎn)的集合歸屬狀態(tài)");
            for (int counter = 0;counter < arrayLength;counter++) {
                System.out.println(counter + "-->" + vertexMarkArray[counter]);
            }
            //打印各集合桶的狀態(tài)變化
            System.out.println("打印調(diào)整后各集合桶的狀態(tài)變化");
            for (int counter = 0;counter < arrayLength;counter++) {
                System.out.print("桶" + counter + ":");
                for (int counter0 = 0;counter0 <= unionTopPointer[counter];counter0++) {
                    System.out.print(circleUnion[counter][counter0] + " ");
                }
                System.out.println();
            }
            System.out.println();
        }
        //打印剩下的摳去不合格結(jié)點(diǎn)后的鏈表
        System.out.println("\n結(jié)果集為:");
        while (headPointer.nextPointer != null) {
            System.out.println("(" + headPointer.nextPointer.getSourceNode() + "," + headPointer.nextPointer.getTargetNode() + ")-->" + headPointer.nextPointer.getWeight());
            headPointer = headPointer.nextPointer;
        }
    }

    /**
     * 本實(shí)現(xiàn)是對kruskal0的改進(jìn)
     * @param sourceArray
     */
    static public void kruskal1(int[][] sourceArray) {
        int arrayLength = sourceArray.length;
        SingleLinkNode headPointer = new SingleLinkNode(-1,-1,-1);
        for (int counter = 0;counter < arrayLength;counter++) {
            for (int counter0 = counter + 1;counter0 < arrayLength;counter0++) {
                if (sourceArray[counter][counter0] > 0) {
                    SingleLinkNode newNode = new SingleLinkNode(counter,counter0,sourceArray[counter][counter0]);
                    SingleLinkNode currentPointer = headPointer;
                    while (currentPointer.nextPointer != null &&
                            currentPointer.nextPointer.getWeight() < newNode.getWeight())
                        currentPointer = currentPointer.nextPointer;
                    newNode.nextPointer = currentPointer.nextPointer;
                    currentPointer.nextPointer = newNode;
                }
            }
        }
        //此處原本采用了n×n的二維數(shù)組拯欧，
        // 但是實(shí)際元素?cái)?shù)量只有n，所以
        // 利用率只有1/n袒啼，太低了哈扮，于是
        // 考慮用鏈表來實(shí)現(xiàn)。而且這樣做
        // 也不用再使用棧頂指針了蚓再。
        DoubleLinkNode[] circleUnion = new DoubleLinkNode[arrayLength];
        //在這里姑且用結(jié)點(diǎn)的vertexId屬性
        // 來標(biāo)識連通集的ID吧滑肉，用counter屬性來記錄當(dāng)前桶的頂點(diǎn)個(gè)數(shù)。
        for (int counter = 0;counter < arrayLength;counter++)
            circleUnion[counter] = new DoubleLinkNode(1,counter);
        int[] vertexMarkArray = new int[arrayLength];
        for (int counter = 0;counter < arrayLength;counter++)
            vertexMarkArray[counter] = counter;
        SingleLinkNode currentPointer = headPointer;
        while (currentPointer.nextPointer != null) {
            System.out.println("打印調(diào)整前的各結(jié)點(diǎn)的集合歸屬狀態(tài)");
            for (int counter = 0;counter < arrayLength;counter++) {
                System.out.println(counter + "-->" + vertexMarkArray[counter]);
            }
            System.out.println("打印調(diào)整前各集合桶的狀態(tài)變化");
            for (int counter = 0;counter < arrayLength;counter++) {
                System.out.print("桶" + counter + ":");
                DoubleLinkNode bucketHeadPointer = circleUnion[counter];
                while (bucketHeadPointer != null) {
                    System.out.print(bucketHeadPointer.getVertexId() + " ");
                    bucketHeadPointer = bucketHeadPointer.prePointer;
                }
                System.out.println();
            }
            int sourceIndex = currentPointer.nextPointer.getSourceNode();
            int targetIndex = currentPointer.nextPointer.getTargetNode();
            System.out.println("新頂點(diǎn)對:(" + sourceIndex + "," + targetIndex + ")");
            if (vertexMarkArray[sourceIndex] != vertexMarkArray[targetIndex]
                    && circleUnion[vertexMarkArray[sourceIndex]] != null
                    && circleUnion[vertexMarkArray[targetIndex]] != null) {
                System.out.println("對應(yīng)的桶編號為:(" + vertexMarkArray[sourceIndex] + "," + vertexMarkArray[targetIndex] + ")");
                if (circleUnion[vertexMarkArray[targetIndex]].getCounter() >
                        circleUnion[vertexMarkArray[sourceIndex]].getCounter()) {
                    int tempIndex = sourceIndex;
                    sourceIndex = targetIndex;
                    targetIndex = tempIndex;
                }
                int moreBucket = vertexMarkArray[sourceIndex];
                int lessBucket = vertexMarkArray[targetIndex];
                while (circleUnion[lessBucket] != null) {
                    DoubleLinkNode moreHeadPointer = circleUnion[moreBucket];
                    DoubleLinkNode lessHeadPointer = circleUnion[lessBucket];
                    DoubleLinkNode movedPointer = lessHeadPointer;
                    lessHeadPointer = lessHeadPointer.prePointer;
                    movedPointer.nextPointer = null;
                    movedPointer.prePointer = null;
                    vertexMarkArray[movedPointer.getVertexId()] = moreBucket;
                    moreHeadPointer.nextPointer = movedPointer;
                    movedPointer.prePointer = moreHeadPointer;
                    movedPointer.setCounter(moreHeadPointer.getCounter() + 1);
                    moreHeadPointer = movedPointer;
                    circleUnion[moreBucket] = moreHeadPointer;
                    circleUnion[lessBucket] = lessHeadPointer;
                }
                if (circleUnion[moreBucket].getCounter() == arrayLength) {
                    currentPointer.nextPointer.nextPointer = null;
                    System.out.println("打印調(diào)整后各集合桶的狀態(tài)變化");
                    for (int counter = 0;counter < arrayLength;counter++) {
                        System.out.print("桶" + counter + ":");
                        DoubleLinkNode bucketHeadPointer = circleUnion[counter];
                        while (bucketHeadPointer != null) {
                            System.out.print(bucketHeadPointer.getVertexId() + " ");
                            bucketHeadPointer = bucketHeadPointer.prePointer;
                        }
                        System.out.println();
                    }
                    System.out.println("集合歸并結(jié)束");
                    break;
                }
                currentPointer = currentPointer.nextPointer;
            } else {
                System.out.println("舍去");
                currentPointer.nextPointer = currentPointer.nextPointer.nextPointer;
            }
            System.out.println("打印調(diào)整后的各結(jié)點(diǎn)的集合歸屬狀態(tài)");
            for (int counter = 0;counter < arrayLength;counter++) {
                System.out.println(counter + "-->" + vertexMarkArray[counter]);
            }
            System.out.println("打印調(diào)整后各集合桶的狀態(tài)變化");
            for (int counter = 0;counter < arrayLength;counter++) {
                System.out.print("桶" + counter + ":");
                DoubleLinkNode bucketHeadPointer = circleUnion[counter];
                while (bucketHeadPointer != null) {
                    System.out.print(bucketHeadPointer.getVertexId() + " ");
                    bucketHeadPointer = bucketHeadPointer.prePointer;
                }
                System.out.println();
            }
            System.out.println();
        }
        System.out.println("\n結(jié)果集為:");
        while (headPointer.nextPointer != null) {
            System.out.println("(" + headPointer.nextPointer.getSourceNode() + "," + headPointer.nextPointer.getTargetNode() + ")-->" + headPointer.nextPointer.getWeight());
            headPointer = headPointer.nextPointer;
        }
    }
}

package com.company;

public class SingleLinkNode {
    private int sourceNode;
    private int targetNode;
    private int weight;
    public SingleLinkNode nextPointer = null;

    public SingleLinkNode(int sourceNode, int targetNode, int weight) {
        this.sourceNode = sourceNode;
        this.targetNode = targetNode;
        this.weight = weight;
    }

    public int getWeight() {
        return weight;
    }

    public int getSourceNode() {
        return sourceNode;
    }

    public int getTargetNode() {
        return targetNode;
    }
}

package com.company;

public class DoubleLinkNode {
    private int counter;
    private int vertexId;
    public DoubleLinkNode prePointer = null;
    public DoubleLinkNode nextPointer = null;

    public DoubleLinkNode(int counter, int vertexId) {
        this.counter = counter;
        this.vertexId = vertexId;
    }

    public int getCounter() {
        return counter;
    }

    public void setCounter(int counter) {
        this.counter = counter;
    }

    public int getVertexId() {
        return vertexId;
    }
}

輸出如下

打印調(diào)整前的各結(jié)點(diǎn)的集合歸屬狀態(tài)
0-->0
1-->1
2-->2
3-->3
4-->4
5-->5
6-->6
打印調(diào)整前各集合桶的狀態(tài)變化
桶0:0 
桶1:1 
桶2:2 
桶3:3 
桶4:4 
桶5:5 
桶6:6 
新頂點(diǎn)對:(2,4)
對應(yīng)的桶編號為:(2,4)
打印調(diào)整后的各結(jié)點(diǎn)的集合歸屬狀態(tài)
0-->0
1-->1
2-->2
3-->3
4-->2
5-->5
6-->6
打印調(diào)整后各集合桶的狀態(tài)變化
桶0:0 
桶1:1 
桶2:2 4 
桶3:3 
桶4:
桶5:5 
桶6:6 

打印調(diào)整前的各結(jié)點(diǎn)的集合歸屬狀態(tài)
0-->0
1-->1
2-->2
3-->3
4-->2
5-->5
6-->6
打印調(diào)整前各集合桶的狀態(tài)變化
桶0:0 
桶1:1 
桶2:2 4 
桶3:3 
桶4:
桶5:5 
桶6:6 
新頂點(diǎn)對:(0,3)
對應(yīng)的桶編號為:(0,3)
打印調(diào)整后的各結(jié)點(diǎn)的集合歸屬狀態(tài)
0-->0
1-->1
2-->2
3-->0
4-->2
5-->5
6-->6
打印調(diào)整后各集合桶的狀態(tài)變化
桶0:0 3 
桶1:1 
桶2:2 4 
桶3:
桶4:
桶5:5 
桶6:6 

打印調(diào)整前的各結(jié)點(diǎn)的集合歸屬狀態(tài)
0-->0
1-->1
2-->2
3-->0
4-->2
5-->5
6-->6
打印調(diào)整前各集合桶的狀態(tài)變化
桶0:0 3 
桶1:1 
桶2:2 4 
桶3:
桶4:
桶5:5 
桶6:6 
新頂點(diǎn)對:(3,5)
對應(yīng)的桶編號為:(0,5)
打印調(diào)整后的各結(jié)點(diǎn)的集合歸屬狀態(tài)
0-->0
1-->1
2-->2
3-->0
4-->2
5-->0
6-->6
打印調(diào)整后各集合桶的狀態(tài)變化
桶0:0 3 5 
桶1:1 
桶2:2 4 
桶3:
桶4:
桶5:
桶6:6 

打印調(diào)整前的各結(jié)點(diǎn)的集合歸屬狀態(tài)
0-->0
1-->1
2-->2
3-->0
4-->2
5-->0
6-->6
打印調(diào)整前各集合桶的狀態(tài)變化
桶0:0 3 5 
桶1:1 
桶2:2 4 
桶3:
桶4:
桶5:
桶6:6 
新頂點(diǎn)對:(1,4)
對應(yīng)的桶編號為:(1,2)
打印調(diào)整后的各結(jié)點(diǎn)的集合歸屬狀態(tài)
0-->0
1-->2
2-->2
3-->0
4-->2
5-->0
6-->6
打印調(diào)整后各集合桶的狀態(tài)變化
桶0:0 3 5 
桶1:
桶2:2 4 1 
桶3:
桶4:
桶5:
桶6:6 

打印調(diào)整前的各結(jié)點(diǎn)的集合歸屬狀態(tài)
0-->0
1-->2
2-->2
3-->0
4-->2
5-->0
6-->6
打印調(diào)整前各集合桶的狀態(tài)變化
桶0:0 3 5 
桶1:
桶2:2 4 1 
桶3:
桶4:
桶5:
桶6:6 
新頂點(diǎn)對:(0,1)
對應(yīng)的桶編號為:(0,2)
打印調(diào)整后的各結(jié)點(diǎn)的集合歸屬狀態(tài)
0-->0
1-->0
2-->0
3-->0
4-->0
5-->0
6-->6
打印調(diào)整后各集合桶的狀態(tài)變化
桶0:0 3 5 1 4 2 
桶1:
桶2:
桶3:
桶4:
桶5:
桶6:6 

打印調(diào)整前的各結(jié)點(diǎn)的集合歸屬狀態(tài)
0-->0
1-->0
2-->0
3-->0
4-->0
5-->0
6-->6
打印調(diào)整前各集合桶的狀態(tài)變化
桶0:0 3 5 1 4 2 
桶1:
桶2:
桶3:
桶4:
桶5:
桶6:6 
新頂點(diǎn)對:(4,5)
舍去
打印調(diào)整后的各結(jié)點(diǎn)的集合歸屬狀態(tài)
0-->0
1-->0
2-->0
3-->0
4-->0
5-->0
6-->6
打印調(diào)整后各集合桶的狀態(tài)變化
桶0:0 3 5 1 4 2 
桶1:
桶2:
桶3:
桶4:
桶5:
桶6:6 

打印調(diào)整前的各結(jié)點(diǎn)的集合歸屬狀態(tài)
0-->0
1-->0
2-->0
3-->0
4-->0
5-->0
6-->6
打印調(diào)整前各集合桶的狀態(tài)變化
桶0:0 3 5 1 4 2 
桶1:
桶2:
桶3:
桶4:
桶5:
桶6:6 
新頂點(diǎn)對:(1,2)
舍去
打印調(diào)整后的各結(jié)點(diǎn)的集合歸屬狀態(tài)
0-->0
1-->0
2-->0
3-->0
4-->0
5-->0
6-->6
打印調(diào)整后各集合桶的狀態(tài)變化
桶0:0 3 5 1 4 2 
桶1:
桶2:
桶3:
桶4:
桶5:
桶6:6 

打印調(diào)整前的各結(jié)點(diǎn)的集合歸屬狀態(tài)
0-->0
1-->0
2-->0
3-->0
4-->0
5-->0
6-->6
打印調(diào)整前各集合桶的狀態(tài)變化
桶0:0 3 5 1 4 2 
桶1:
桶2:
桶3:
桶4:
桶5:
桶6:6 
新頂點(diǎn)對:(4,6)
對應(yīng)的桶編號為:(0,6)
打印調(diào)整后各集合桶的狀態(tài)變化
桶0:0 3 5 1 4 2 6 
桶1:
桶2:
桶3:
桶4:
桶5:
桶6:
集合歸并結(jié)束

結(jié)果集為:
(2,4)-->5
(0,3)-->5
(3,5)-->6
(1,4)-->7
(0,1)-->7
(4,6)-->9

最后編輯于：2018.02.22 08:58:38

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