遍历算法(1)

遍历算法主要用在在处理迷宫问题，图，最短路径，以及枚举所有可能等问题上。下面我们通过一个简单的例子，来入门深度优先和广度优先算法：

  1 package com.rampage.algorithm.base;
  2
  3 import java.util.ArrayList;
  4 import java.util.LinkedHashSet;
  5 import java.util.List;
  6 import java.util.Set;
  7
  8 /**
  9  * 相关的搜索算法实例 假设有1-9，9个数字，现在任意取三个，要求得到一共能得到多少个不同值的数字。如果可能的化输出所有可能的值。
 10  *
 11  * @author zyq
 12  *
 13  */
 14 public class SearchAlgorithm {
 15     private static int totalCount = 0; // 存储总计数
 16     private static Set<String> results = new LinkedHashSet<String>(); // 存储所有的结果
 17
 18     public static void main(String[] args) {
 19         deepFirstSearch();
 20         breadthFirstSearch();
 21     }
 22
 23     /**
 24      * 广度优先搜索：广度优先搜索算法的核心是列表。首先就得到第一步可以放的所有数，然后依次将其放入列表。接下来逐个处理列表中的每个数，给出接下来可能出现的第二个数，
 25      * 处理完列表中的一个数就将该数从列表中移除。依次类推，直到待处理的列表中的元素为空。
 26      */
 27     private static void breadthFirstSearch() {
 28         totalCount = 0;
 29         results.clear();
 30         List<String> possibleList = new ArrayList<String>();
 31
 32         // 初始化列表，开始时第一号盒子可以放入1-9
 33         for (int i = 1; i < 10; i++) {
 34             possibleList.add(i + "");
 35         }
 36
 37         // 列表不为空的时候循环处理，因为又要增加又要删除，此时逆序遍历(此时即使用iterator，但是iterator没法删除元素，所以仍然会报错。)
 38         while (!possibleList.isEmpty()) {
 39             for (int i=possibleList.size() - 1; i>=0; i--) {
 40                 String element = possibleList.get(i);
 41                 // 长度为3说明3个数都放过了
 42                 if (element.length() == 3) {
 43                     totalCount++;
 44                     results.add(element);
 45                     possibleList.remove(i);
 46                     continue;
 47                 }
 48
 49                 for (int j = 1; j < 10; j++) {
 50                     // 如果已经包含，则该数字不能再使用
 51                     if (element.contains(j + "")) {
 52                         continue;
 53                     } else {
 54                         // 如果没有包含对应的数字，则此时将数字加到元素后面，作为新的可能结果列表放入列表中
 55                         possibleList.add(element + j);
 56                     }
 57                 }
 58
 59                 // 移除已经处理过的元素
 60                 possibleList.remove(i);
 61             }
 62
 63         }
 64
 65         System.out.println("Total count:" + totalCount);
 66         System.out.println(results);
 67     }
 68
 69     /**
 70      * 采用深度优先算法实现：深度优先算法的核心思想是迭代。既然要迭代就应该先抽象出每一步需要重复处理的数据。 可以这样思考深度优先算法：
 71      * 假设有三个盒子，先往1号盒子放入1, 然后往2号盒子放入2,最后往3号盒子放入3.这样其实就组成了一个组合：123
 72      * 要想得到其他的组合，则必须先收回3号盒子中的3,然后放入剩下的任意一个。依次类推，当3号盒子可能的情况都放完了之后，就需要同时取回3号和2号盒子中的东西，
 73      * 然后在开始试。依次类推：
 74      *
 75      */
 76     private static void deepFirstSearch() {
 77         totalCount = 0;
 78         results.clear();
 79         int[] book = new int[10]; // 定义已经使用过的数字，如果使用过某数字i，那么book[i] = 1
 80         int[] result = new int[3]; // 存储当前的三个数字组成的数组
 81         go(book, result, 0);
 82         System.out.println("Total count:" + totalCount);
 83         System.out.println(results);
 84     }
 85
 86     /**
 87      * @param book
 88      *            存储已经放过的数字
 89      * @param step
 90      *            第几步，就相当于前面所说的放第几个盒子（第一个盒子对应第0步）
 91      */
 92     private static void go(int[] book, int[] result, int step) {
 93         if (step == 3) {
 94             totalCount++;
 95             results.add(new String(result[0] + "" + result[1] + "" + result[2]));
 96             return;
 97         }
 98         for (int i = 1; i < 10; i++) {
 99             if (book[i] == 1) {
100                 continue;
101             }
102             book[i] = 1; // 标记i已经被使用
103             result[step] = i;
104             // 因为是深度优先，所以需要继续往更深处遍历
105             go(book, result, step + 1);
106
107             // 因为还要尝试其他组合所以这里沿路返回
108             book[i] = 0;
109             result[step] = 0;
110         }
111     }
112 }

SearchAlgorithm

输出结果为：

1 Total count:504
2 [123, 124, 125, 126, 127, 128, 129, 132, 134, 135, 136, 137, 138, 139, 142, 143, 145, 146, 147, 148, 149, 152, 153, 154, 156, 157, 158, 159, 162, 163, 164, 165, 167, 168, 169, 172, 173, 174, 175, 176, 178, 179, 182, 183, 184, 185, 186, 187, 189, 192, 193, 194, 195, 196, 197, 198, 213, 214, 215, 216, 217, 218, 219, 231, 234, 235, 236, 237, 238, 239, 241, 243, 245, 246, 247, 248, 249, 251, 253, 254, 256, 257, 258, 259, 261, 263, 264, 265, 267, 268, 269, 271, 273, 274, 275, 276, 278, 279, 281, 283, 284, 285, 286, 287, 289, 291, 293, 294, 295, 296, 297, 298, 312, 314, 315, 316, 317, 318, 319, 321, 324, 325, 326, 327, 328, 329, 341, 342, 345, 346, 347, 348, 349, 351, 352, 354, 356, 357, 358, 359, 361, 362, 364, 365, 367, 368, 369, 371, 372, 374, 375, 376, 378, 379, 381, 382, 384, 385, 386, 387, 389, 391, 392, 394, 395, 396, 397, 398, 412, 413, 415, 416, 417, 418, 419, 421, 423, 425, 426, 427, 428, 429, 431, 432, 435, 436, 437, 438, 439, 451, 452, 453, 456, 457, 458, 459, 461, 462, 463, 465, 467, 468, 469, 471, 472, 473, 475, 476, 478, 479, 481, 482, 483, 485, 486, 487, 489, 491, 492, 493, 495, 496, 497, 498, 512, 513, 514, 516, 517, 518, 519, 521, 523, 524, 526, 527, 528, 529, 531, 532, 534, 536, 537, 538, 539, 541, 542, 543, 546, 547, 548, 549, 561, 562, 563, 564, 567, 568, 569, 571, 572, 573, 574, 576, 578, 579, 581, 582, 583, 584, 586, 587, 589, 591, 592, 593, 594, 596, 597, 598, 612, 613, 614, 615, 617, 618, 619, 621, 623, 624, 625, 627, 628, 629, 631, 632, 634, 635, 637, 638, 639, 641, 642, 643, 645, 647, 648, 649, 651, 652, 653, 654, 657, 658, 659, 671, 672, 673, 674, 675, 678, 679, 681, 682, 683, 684, 685, 687, 689, 691, 692, 693, 694, 695, 697, 698, 712, 713, 714, 715, 716, 718, 719, 721, 723, 724, 725, 726, 728, 729, 731, 732, 734, 735, 736, 738, 739, 741, 742, 743, 745, 746, 748, 749, 751, 752, 753, 754, 756, 758, 759, 761, 762, 763, 764, 765, 768, 769, 781, 782, 783, 784, 785, 786, 789, 791, 792, 793, 794, 795, 796, 798, 812, 813, 814, 815, 816, 817, 819, 821, 823, 824, 825, 826, 827, 829, 831, 832, 834, 835, 836, 837, 839, 841, 842, 843, 845, 846, 847, 849, 851, 852, 853, 854, 856, 857, 859, 861, 862, 863, 864, 865, 867, 869, 871, 872, 873, 874, 875, 876, 879, 891, 892, 893, 894, 895, 896, 897, 912, 913, 914, 915, 916, 917, 918, 921, 923, 924, 925, 926, 927, 928, 931, 932, 934, 935, 936, 937, 938, 941, 942, 943, 945, 946, 947, 948, 951, 952, 953, 954, 956, 957, 958, 961, 962, 963, 964, 965, 967, 968, 971, 972, 973, 974, 975, 976, 978, 981, 982, 983, 984, 985, 986, 987]
3 Total count:504
4 [918, 917, 916, 915, 914, 913, 912, 928, 927, 926, 925, 924, 923, 921, 938, 937, 936, 935, 934, 932, 931, 948, 947, 946, 945, 943, 942, 941, 958, 957, 956, 954, 953, 952, 951, 968, 967, 965, 964, 963, 962, 961, 978, 976, 975, 974, 973, 972, 971, 987, 986, 985, 984, 983, 982, 981, 819, 817, 816, 815, 814, 813, 812, 829, 827, 826, 825, 824, 823, 821, 839, 837, 836, 835, 834, 832, 831, 849, 847, 846, 845, 843, 842, 841, 859, 857, 856, 854, 853, 852, 851, 869, 867, 865, 864, 863, 862, 861, 879, 876, 875, 874, 873, 872, 871, 897, 896, 895, 894, 893, 892, 891, 719, 718, 716, 715, 714, 713, 712, 729, 728, 726, 725, 724, 723, 721, 739, 738, 736, 735, 734, 732, 731, 749, 748, 746, 745, 743, 742, 741, 759, 758, 756, 754, 753, 752, 751, 769, 768, 765, 764, 763, 762, 761, 789, 786, 785, 784, 783, 782, 781, 798, 796, 795, 794, 793, 792, 791, 619, 618, 617, 615, 614, 613, 612, 629, 628, 627, 625, 624, 623, 621, 639, 638, 637, 635, 634, 632, 631, 649, 648, 647, 645, 643, 642, 641, 659, 658, 657, 654, 653, 652, 651, 679, 678, 675, 674, 673, 672, 671, 689, 687, 685, 684, 683, 682, 681, 698, 697, 695, 694, 693, 692, 691, 519, 518, 517, 516, 514, 513, 512, 529, 528, 527, 526, 524, 523, 521, 539, 538, 537, 536, 534, 532, 531, 549, 548, 547, 546, 543, 542, 541, 569, 568, 567, 564, 563, 562, 561, 579, 578, 576, 574, 573, 572, 571, 589, 587, 586, 584, 583, 582, 581, 598, 597, 596, 594, 593, 592, 591, 419, 418, 417, 416, 415, 413, 412, 429, 428, 427, 426, 425, 423, 421, 439, 438, 437, 436, 435, 432, 431, 459, 458, 457, 456, 453, 452, 451, 469, 468, 467, 465, 463, 462, 461, 479, 478, 476, 475, 473, 472, 471, 489, 487, 486, 485, 483, 482, 481, 498, 497, 496, 495, 493, 492, 491, 319, 318, 317, 316, 315, 314, 312, 329, 328, 327, 326, 325, 324, 321, 349, 348, 347, 346, 345, 342, 341, 359, 358, 357, 356, 354, 352, 351, 369, 368, 367, 365, 364, 362, 361, 379, 378, 376, 375, 374, 372, 371, 389, 387, 386, 385, 384, 382, 381, 398, 397, 396, 395, 394, 392, 391, 219, 218, 217, 216, 215, 214, 213, 239, 238, 237, 236, 235, 234, 231, 249, 248, 247, 246, 245, 243, 241, 259, 258, 257, 256, 254, 253, 251, 269, 268, 267, 265, 264, 263, 261, 279, 278, 276, 275, 274, 273, 271, 289, 287, 286, 285, 284, 283, 281, 298, 297, 296, 295, 294, 293, 291, 129, 128, 127, 126, 125, 124, 123, 139, 138, 137, 136, 135, 134, 132, 149, 148, 147, 146, 145, 143, 142, 159, 158, 157, 156, 154, 153, 152, 169, 168, 167, 165, 164, 163, 162, 179, 178, 176, 175, 174, 173, 172, 189, 187, 186, 185, 184, 183, 182, 198, 197, 196, 195, 194, 193, 192]

Result