LeetCode 102. Binary Tree Level Order Traversal

本文介绍了一种使用广度优先搜索(BFS)算法来实现二叉树层级遍历的方法。该方法通过队列和计数数组实现了按层打印节点,并详细解释了算法的工作原理。此外,还提到了稍作修改即可解决其他相关问题。

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这里写图片描述
题目大意是把一颗树的所有节点记录下来,但是要求要以行为单位按根到叶子的顺序记录,而每一行又是从左到右记录。

先贴代码再解释:

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
public:
    vector<vector<int> > levelOrder(TreeNode* root) {
        vector<vector<int> > level;
        if(root == NULL)
            return level;
        int temp[10000],num[10000];
        memset(num,0,sizeof(num));
        num[0] = 1;
        int sum = 1;
        int i = 1;
        int count = 0;
        queue<TreeNode*> bfs;
        bfs.push(root);
        while(!bfs.empty()){
            TreeNode* node = bfs.front();
            bfs.pop();
            temp[count] = node->val;
            count++;
            if(node->left!=NULL){
                bfs.push(node->left);
                num[i]++;
                sum++;
            }
            if(node->right!=NULL){
                bfs.push(node->right);
                num[i]++;
                sum++;
            }

            if(count>=sum-num[i]){
                i++;
            }
        }
        int push_num = 0;
        for(int j = 0;j < i-1;j++){
            vector<int> sub_level;
            for(int p = 0;p<num[j];p++){
                sub_level.push_back(temp[push_num]);
                push_num++;
            }
            level.push_back(sub_level);
        }

        return level;
    }
};

我的方法是用广搜去遍历整棵树,在遍历的过程中用num数组去记录每一行有几个节点,比如说num[0] = 1。因为如果根节点不为空那么树的第一行只有一个节点——根节点。用temp数组去记录每一个节点的数值。在这个广搜中,只有当某个节点被pop()出去了,我才会把他记在temp数组里。那么这个算法的关键点就在于num数组要如何得到了。
我这里的思路是每当队列中新push进来一个元素那么就有num[i]++,而每当temp里面的节点数量(count)大于num数组除去最后一个元素后所有元素之和时,i++。下面我来做一下解释。
广搜算法中在对第i层节点做遍历的时候,会把第i层节点的所有子节点push进队列之中。所以我们就应该利用这个时候去得到第i+1层到底有几个节点,这也就是为什么我在每当队列中新push进来一个元素那么就有num[i]++。而当第i层的节点的所有子节点都被push进来之后,我们就会开始遍历第i+1层的节点,这个时候就应该去记录第i+2层有多少节点。我们要清楚count是已经遍历了的节点的个数。而num[i]是始终快count一步的,也就是我们在遍历第i层的时候,num已经在记录i+1层的数量了。所以当我们遍历完第i层,count应该等于num数组求和但要除去最后一个元素,而当count大于num数组求和但要除去最后一个元素时,说明我们开始遍历i+1层了,这个时候num数组也应该结束当前元素的记录,而开始计算下一个元素的数值了。

同时这道题目只需要删改一下就可以完成:
104.Maximum Depth of Binary Tree (找到一颗树的深度)
107.Binary Tree Level Order Traversal II (和这道题类似只是输出顺序是从叶子的那一行到根的那一行,每一行还是从左到右)

1. Two Sum 2. Add Two Numbers 3. Longest Substring Without Repeating Characters 4. Median of Two Sorted Arrays 5. Longest Palindromic Substring 6. ZigZag Conversion 7. Reverse Integer 8. String to Integer (atoi) 9. Palindrome Number 10. Regular Expression Matching 11. Container With Most Water 12. Integer to Roman 13. Roman to Integer 14. Longest Common Prefix 15. 3Sum 16. 3Sum Closest 17. Letter Combinations of a Phone Number 18. 4Sum 19. Remove Nth Node From End of List 20. Valid Parentheses 21. Merge Two Sorted Lists 22. Generate Parentheses 23. Swap Nodes in Pairs 24. Reverse Nodes in k-Group 25. Remove Duplicates from Sorted Array 26. Remove Element 27. Implement strStr() 28. Divide Two Integers 29. Substring with Concatenation of All Words 30. Next Permutation 31. Longest Valid Parentheses 32. Search in Rotated Sorted Array 33. Search for a Range 34. Find First and Last Position of Element in Sorted Array 35. Valid Sudoku 36. Sudoku Solver 37. Count and Say 38. Combination Sum 39. Combination Sum II 40. First Missing Positive 41. Trapping Rain Water 42. Jump Game 43. Merge Intervals 44. Insert Interval 45. Unique Paths 46. Minimum Path Sum 47. Climbing Stairs 48. Permutations 49. Permutations II 50. Rotate Image 51. Group Anagrams 52. Pow(x, n) 53. Maximum Subarray 54. Spiral Matrix 55. Jump Game II 56. Merge k Sorted Lists 57. Insertion Sort List 58. Sort List 59. Largest Rectangle in Histogram 60. Valid Number 61. Word Search 62. Minimum Window Substring 63. Unique Binary Search Trees 64. Unique Binary Search Trees II 65. Interleaving String 66. Maximum Product Subarray 67. Binary Tree Inorder Traversal 68. Binary Tree Preorder Traversal 69. Binary Tree Postorder Traversal 70. Flatten Binary Tree to Linked List 71. Construct Binary Tree from Preorder and Inorder Traversal 72. Construct Binary Tree from Inorder and Postorder Traversal 73. Binary Tree Level Order Traversal 74. Binary Tree Zigzag Level Order Traversal 75. Convert Sorted Array to Binary Search Tree 76. Convert Sorted List to Binary Search Tree 77. Recover Binary Search Tree 78. Sum Root to Leaf Numbers 79. Path Sum 80. Path Sum II 81. Binary Tree Maximum Path Sum 82. Populating Next Right Pointers in Each Node 83. Populating Next Right Pointers in Each Node II 84. Reverse Linked List 85. Reverse Linked List II 86. Partition List 87. Rotate List 88. Remove Duplicates from Sorted List 89. Remove Duplicates from Sorted List II 90. Intersection of Two Linked Lists 91. Linked List Cycle 92. Linked List Cycle II 93. Reorder List 94. Binary Tree Upside Down 95. Binary Tree Right Side View 96. Palindrome Linked List 97. Convert Binary Search Tree to Sorted Doubly Linked List 98. Lowest Common Ancestor of a Binary Tree 99. Lowest Common Ancestor of a Binary Search Tree 100. Binary Tree Level Order Traversal II
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