javascript实现数据结构： 树和二叉树的应用--最优二叉树（赫夫曼树），回溯法与树的遍历--求集合幂集及八皇后问题

1 // 赫夫曼树和赫夫曼编码的存储结构
2 function HuffmanNode(weight, parent, leftChild, rightChild) {
3     this.weight = weight || 0;
4     this.parent = parent || 0;
5     this.leftChild = leftChild || 0;
6     this.rightChild = rightChild || 0;
7 }

 1 // 创建一棵叶子结点数为n的Huffman树
 2 function buildHuffmanTree(weights, n) {
 3     n = n || weights.length;
 4     var m = 2 * n - 1;
 5     var huffmanTree = [];
 6 
 7     // 初始化
 8     for (var i = 0; i < n; i++)
 9         huffmanTree[i] = new HuffmanNode(weights[i], 0, 0, 0);
10     for (; i < m; i++)
11         huffmanTree[i] = new HuffmanNode(0, 0, 0, 0);
12 
13     for (i = n; i < m; i++) {
14         // 在HT[1..i-1]选择parent为0且weight最小的两个结点，返回其序号为[s1, s2]
15         var ret = select(huffmanTree, i);
16         var s1 = ret[0];
17         var s2 = ret[1];
18         huffmanTree[s1].parent = i;
19         huffmanTree[s2].parent = i;
20         huffmanTree[i].leftChild = s1;
21         huffmanTree[i].rightChild = s2;
22         huffmanTree[i].weight = huffmanTree[s1].weight + huffmanTree[s2].weight;
23     }
24 
25     return huffmanTree;
26 }
27 
28 function select(huffmanTree, len) {
29     var ret = [];
30     for (var i = 0; i < len; i++) {
31         var node = huffmanTree[i];
32         if (node.parent !== 0) continue;
33 
34         if (ret.length < 2) {
35             ret.push(i);
36         } else {
37             var index = huffmanTree[ret[0]].weight > huffmanTree[ret[1]].weight
38                 ? 0 : 1;
39 
40             if (node.weight < huffmanTree[ret[index]].weight)
41                 ret[index] = i;
42         }
43     }
44 
45     if (ret[0] > ret[1]) {
46         var temp = ret[0];
47         ret[0] = ret[1];
48         ret[1] = temp;
49     }
50 
51     return ret;
52 }

 1 function huffManCoding(weights) {
 2     var n = weights.length;
 3     if (n < 1) return;
 4 
 5     var huffmanTree = buildHuffmanTree(weights, n);
 6 
 7     // 从叶子到根逆向求每个字符的赫夫曼编码
 8     var hc = calcHuffmanCode(huffmanTree, n);
 9 
10     return [huffmanTree, hc];
11 }
12 
13 function calcHuffmanCode(huffmanTree, n) {
14     // 从叶子到根逆向求每个字符的赫夫曼编码
15     var hc = [];
16     var cd = [];
17     for (var i = 0; i < n; i++) {
18         var start = n - 1;
19         for (var c = i, f = huffmanTree[i].parent; f != 0; c = f, f = huffmanTree[f].parent) {
20             if (huffmanTree[f].leftChild == c) cd[--start] = ‘0‘;
21             else cd[--start] = ‘1‘;
22         }
23 
24         hc[i] = strCopy(cd, start);
25     }
26 
27     return hc;
28 }
29 
30 function strCopy(str, start) {
31     var s = ‘‘;
32     for (; str[start]; start++) {
33         s += str[start];
34     }
35     return s;
36 }

 1 // 求含集合aList的幂集
 2 // 进入函数时已对A中前i-1个元素做了取舍处理
 3 function getPowerSet(i, aList) {
 4     var bList = [];
 5 
 6     void function recurse(i, aList) {
 7         if (i > aList.length - 1) console.log(‘set: ‘ + bList);
 8         else {
 9             var x = aList[i];
10             bList.push(x);
11             recurse(i + 1, aList);
12             bList.pop();
13             recurse(i + 1, aList);
14         }
15     }(i, aList);
16 
17     return bList;
18 }
19 
20 console.log(‘getPowerSet:‘);
21 var list = [1, 2, 3];
22 console.log(‘list: ‘ + getPowerSet(0, list));

  1 // 求n皇后问题的所有合法布局
  2 function Queen(n) {
  3     var board = [];
  4     var count = 0;
  5 
  6     this.init = function(){
  7         for(var i = 0; i < n; i++){
  8             board[i] = [];
  9             for(var j = 0; j < n; j++){
 10                 board[i][j] = 0;
 11             }
 12         }
 13     };
 14 
 15     this.init();
 16 
 17     this.getSolutionsCount = function(){
 18         return count;
 19     };
 20 
 21     this.printCurrentLayout = function () {
 22         ++count;
 23         console.log(board);
 24     };
 25 
 26     this.addPoint = function (i, j) {
 27         if(board[i][j] === 0){
 28             board[i][j] = 1;
 29             return true;
 30         } else {
 31             console.log(‘already occupated!‘);
 32             return false;
 33         }
 34     };
 35 
 36     this.isCurrentLayoutLegal = function (i, j) {
 37         return checkHorizontal(i, j) && checkVertical(i, j) && checkLeftTop2RightBottom(i, j) && checkRightTop2LeftBottom(i, j);
 38     };
 39 
 40     function checkHorizontal(x, y){
 41         for(var i = 0; i < y; i++){
 42             if(board[x][i] === 1) return false;
 43         }
 44         for(i = y + 1; i < n; i++){
 45             if(board[x][i] === 1) return false;
 46         }
 47         return true;
 48     }
 49 
 50     function checkVertical(x, y){
 51         for(var i = 0; i < x; i++){
 52             if(board[i][y] === 1) return false;
 53         }
 54         for(i = x + 1; i < n; i++){
 55             if(board[i][y] === 1) return false;
 56         }
 57         return true;
 58     }
 59 
 60     function checkLeftTop2RightBottom(x, y){
 61         for(var i = 1; x - i >= 0 && y - i >= 0; i++){
 62             if(board[x - i][y - i] === 1) return false;
 63         }
 64         for(i = 1; x + i < n && y + i < n; i++){
 65             if(board[x + i][y + i] === 1) return false;
 66         }
 67         return true;
 68     }
 69 
 70     function checkRightTop2LeftBottom(x, y){
 71         for(var i = 1; x - i >= 0 && y + i < n; i++){
 72             if(board[x - i][y + i] === 1) return false;
 73         }
 74         for(i = 1; x + i < n && y - i >= 0; i++){
 75             if(board[x + i][y - i] === 1) return false;
 76         }
 77         return true;
 78     }
 79 
 80     this.removePoint = function (i, j) {
 81         if(board[i][j] === 1){
 82             board[i][j] = 0;
 83         }
 84     };
 85 
 86     var me = this;
 87     this.trial = function trial(i) {
 88         i = i || 0;
 89         if (i > n - 1) {
 90             me.printCurrentLayout();
 91         } else {
 92             for (var j = 0; j < n; j++) {
 93                 if(me.addPoint(i, j)){
 94                     if (me.isCurrentLayoutLegal(i, j)) trial(i + 1);
 95                     me.removePoint(i, j);
 96                 }
 97             }
 98         }
 99     };
100 }
101 
102 var test = new Queen(8);
103 test.trial();
104 console.log(‘getSolutionsCount: ‘ + test.getSolutionsCount());