对于给定的二叉树,为其返回以下值。
对于每个级别,如果此级别有叶子,则计算所有叶子的总和。否则忽略它。
计算所有总和的乘法并返回。
Root of following tree 3 / \ 8 6 \ 10
输出结果
80
第一层没有叶子。第二层有一个叶子8,第三层也有一个叶子10。所以结果是8 * 10 = 80
Root of following tree 3 / \ 8 6 / \ \ 9 7 10 / \ / \ 2 12 5 11
输出结果
270
前两个级别没有叶子。第三级具有单叶9。最后一级具有四叶2、12、5和11。因此结果为9 *(2 + 12 + 5 + 11)= 270
关于一个简单的解决方案,我们从上到下递归计算所有级别的叶子和。之后,将具有叶子的水平的总和相乘。在这里,该解决方案的时间复杂度将为O(n ^ 2)。
再次,关于有效解决方案,我们实现了基于队列的级别顺序遍历。在这里,遍历时我们会分别处理所有不同的级别,对于每个已处理的级别,请验证其是否具有叶子。在这种情况下,如果已经计算出叶节点的总和。最后,归还所有金额。
/* Iterative C++ program to find sum of data of all leaves of a binary tree on same level and then multiply sums obtained of all levels. */ #include <bits/stdc++.h> using namespace std; // Shows a Binary Tree Node struct Node1 { int data1; struct Node1 *left1, *right1; }; // Shows helper function to check if a Node is leaf of tree bool isLeaf(Node1* root1){ return (!root1->left1 && !root1->right1); } /* Compute sum of all leaf Nodes at each level and returns multiplication of sums */ int sumAndMultiplyLevelData(Node1* root1){ // Here tree is empty if (!root1) return 0; int mul1 = 1; /* Used To store result */ // Build an empty queue for level order tarversal queue<Node1*> q1; // Used to Enqueue Root and initialize height q1.push(root1); // Perform level order traversal of tree while (1) { // NodeCount1 (queue size) indicates number of Nodes // at current lelvel. int NodeCount1 = q1.size(); // Now if there are no Nodes at current level, we are done if (NodeCount1 == 0) break; // Used to initialize leaf sum for current level int levelSum1 = 0; // Shows a boolean variable to indicate if found a leaf // Node at current level or not bool leafFound1 = false; // Used to Dequeue all Nodes of current level and Enqueue all // Nodes of next level while (NodeCount1 > 0) { // Process next Node of current level Node1* Node1 = q1.front(); /* Now if Node is a leaf, update sum at the level */ if (isLeaf(Node1)) { leafFound1 = true; levelSum1 += Node1->data1; } q1.pop(); // Add children of Node if (Node1->left1 != NULL) q1.push(Node1->left1); if (Node1->right1 != NULL) q1.push(Node1->right1); NodeCount1--; } // Now if we found at least one leaf, we multiply // result with level sum. if (leafFound1) mul1 *= levelSum1; } return mul1; // Here, return result } //Shows utility function to create a new tree Node Node1* newNode(int data1){ Node1* temp1 = new Node1; temp1->data1 = data1; temp1->left1 = temp1->right1 = NULL; return temp1; } // Driver program to test above functions int main(){ Node1* root1 = newNode(3); root1->left1 = newNode(8); root1->right1 = newNode(6); root1->left1->right1 = newNode(7); root1->left1->left1 = newNode(9); root1->left1->right1->left1 = newNode(2); root1->left1->right1->right1 = newNode(12); root1->right1->right1 = newNode(10); root1->right1->right1->left1 = newNode(5); root1->right1->right1->right1 = newNode(11); cout << "Final product value = " << sumAndMultiplyLevelData(root1) <<endl; return 0; }
输出结果
Final product value = 270