查找节点树的最大路径总和

Question

我正试图编写一个程序，可以从一个文件构建节点树，然后找到它的最大路径总和。通过路径总和，我指的是沿给定的顶部到底部遍历的节点的值的总和。

我有一个工作程序，但速度不够快，因为我应该能够在10秒内解决深度为100的树。

我希望有人可以给我如何优化运行时间的指针，因为它开始约20

注意的树深度后能得到很慢：我没有处理常规一棵二叉树，树的格式如下。

例如，给定树

 12 
    20 30 
    50 07 30 
20 60 15 42 

最大总和路径上的节点将是12 20 50 60，具有横动路径：LLR，并且总和将等于142。

我目前的程序：

#include <iostream> 
    #include <stdio.h> 
    #include <math.h> 
    #include <string.h> 
    #include <fstream> 
    #include <sstream> 
    #include <vector> 
    using namespace std; 

    struct node 
    { 
     int value; 
     int depth; 
     int index; 
     struct node *left; 
     struct node *right; 
    }; 


    node * newNode(int value, int depth, int index) 
    { 
     node *temp = new node; 
     temp->value = value; 
     temp->depth = depth; 
     temp->index = index; 
     temp->left = temp->right = NULL; 
     return (temp); 
    } 



    struct node * vec_to_tree(vector<int> arr) 
    { 
     node *newNode1; 
     node *root; 
     vector<node*> node_list; 
     int i=0; 
     int depth=1; 

     root = newNode(arr[0],depth,i);; 
     int size = arr.size(); 

     //how to save current index? i I guess. 
     root = newNode(arr[0],depth,i); 
     node_list.push_back(root); 

     while(!node_list.empty()) 
     { 


      newNode1 = node_list.front(); 
      node_list.erase(node_list.begin()); 

      //do i need to keep track of the index? 
      //i = newNode->index; 
      depth = newNode1->depth; 

      //may need to double check on this one lol 
      if(depth + i + 1 >= size) 
       break; 

      newNode1->left = newNode(arr[depth+i],depth+1,depth+i); 
      node_list.push_back(newNode1->left); 


      if(depth+i+2 >= size) 
       break; 

      newNode1->right = newNode(arr[depth+i+1],depth+1,depth+i+1); 
      node_list.push_back(newNode1->right); 

      i++; 
      //we have 
      for(int j=0;j<depth-1;j++) 
      { 
       node *newNode2 = node_list.front(); 
       node_list.erase(node_list.begin()); 

       //assign newNode2's left child to newNode's right child 
       //this means we don't want to push it back onto the node_list 
       newNode2->left= newNode1->right; 

       newNode2->right = newNode(arr[depth+i+1],depth+1,depth+i+1); 
       node_list.push_back(newNode2->right); 

       newNode1=newNode2; 
       i++; 
      } 

     } 
     return root; 
    } 


    vector<int> readFileIntoVector(string fileName) 
    { 
     vector<int> data; 

     // Replace 'Plop' with your file name. 
     ifstream file(fileName); 

     std::string line; 
     // Read one line at a time into the variable line: 
     while(getline(file, line)) 
     { 
      //do we really need this? 
      //vector<int> lineData; 

      stringstream lineStream(line); 

      int value; 
      // Read an integer at a time from the line 
      while(lineStream >> value) 
      { 
       // Add the integers from a line to a 1D array (vector) 
       data.push_back(value); 
      } 
     } 
     file.close(); 

     return data; 
    } 


    // A utility function that prints all nodes 
    // on the path from root to target_leaf 
    void printPath (struct node *root, string path) 
    { 
     struct node * pNode = root; 
     // base case 
     if (root == NULL) 
     { 
      cout << "tree empty" << endl; 
      return ; 
     } 
     if (path.empty()) 
     { 
      cout << "string empty" << endl; 
      return ; 
     } 

     cout << pNode->value << " "; 

     for(int i =0; i<path.size();i++) 
     { 
      if(path[i] == 'L') 
      { 
       cout << pNode->left->value << " "; 
       pNode= pNode->left; 
      } 
      else if(path[i] == 'R') 
      { 
       cout << pNode->right->value << " "; 
       pNode= pNode->right; 
      } 
     } 

     return ; 
    } 

    // This function sets the target_leaf_ref to refer the leaf node of the maximum path sum. Also, returns the max_sum using max_sum_ref 
    int getTargetLeaf (struct node *node, int *max_sum_ref, int curr_sum, string *path_ref, string curr_path, struct node **target_leaf_ref) 
    { 

     if (node == NULL) 
     { 
      curr_path.pop_back(); 
      return 1; 
     } 

     // Update current sum to hold sum of nodes on pathfrom root to this node 
     curr_sum = curr_sum + node->value; 

     // If this is a leaf node and path to this node has maximum sum so far, then make this node target_leaf 
     if (node->left == NULL && node->right == NULL) 
     { 
      if (curr_sum > *max_sum_ref) 
      { 
       *max_sum_ref = curr_sum; 
       *path_ref= curr_path; 
       *target_leaf_ref = node; 
      } 
     } 

     // If this is not a leaf node, then recur down to find the 
     int result = getTargetLeaf (node->left, max_sum_ref, curr_sum, path_ref, curr_path.insert(curr_path.size(),"L"), target_leaf_ref); 
     if(result == 0)//result 0 is if its a leaf node 
     { 
      //the path keeps getting messed up. 
      curr_path.pop_back(); 
     }; 
     result = getTargetLeaf (node->right, max_sum_ref, curr_sum, path_ref,curr_path.insert(curr_path.size(),"R"), target_leaf_ref); 

     return 0; 
    } 



    // Returns the maximum sum and prints the nodes on max sum path 
    int maxSumPath (struct node *node) 
    { 
     // base case 
     if (node == NULL) 
      return 0; 

     struct node *target_leaf; 


     int max_sum = INT_MIN; 
     string path = ""; 

     // find the target leaf and maximum sum 
     getTargetLeaf (node, &max_sum, 0, &path,"", &target_leaf); 

     // print the path from root to the target leaf 
     printPath (node,path); 

     cout << endl << "traverse path : " << path << endl; 
     return max_sum; // return maximum sum 
    } 

    int main() 
    { 
     struct node *treeRoot; 
     int arr[] = { 2, 3, 4, 6,9,1 }; 
     vector<int> vec (arr, arr + sizeof(arr)/sizeof(arr[0])); 

     cout << "printing test vector" <<endl; 
     for (std::vector<int>::const_iterator i = vec.begin(); i != vec.end(); ++i) 
     std::cout << *i << ' '; 

     cout << endl; 
     //{2,3,4,6,9,1}; 

     treeRoot = vec_to_tree(vec); 

     cout << "Following are the nodes on the maximum sum path" << endl; 
     int sum = maxSumPath(treeRoot); 
     cout << "Sum of the nodes is " << sum << endl; 


     cout << "Now lets try to get the largest path sum from the tree in the small file" << endl; 
     vector<int> fileData2 = readFileIntoVector("GG-test-tree2.txt"); 

     cout << "printing vector" <<endl; 
     for (vector<int>::const_iterator i = fileData2.begin(); i != fileData2.end(); ++i) 
     cout << *i << ' '; 

     treeRoot = vec_to_tree(fileData2); 

     cout << endl << "Following are the nodes on the maximum sum path" << endl; 

     sum = maxSumPath(treeRoot); 

     cout << "Sum of the nodes is " << sum << endl; 

     cout << endl << endl <<endl; 

     cout << "Now to get the largest path sum from the tree in file" << endl; 
     vector<int> fileData = readFileIntoVector("GG-test-tree.txt"); 

     cout << "printing vector" <<endl; 
     for (vector<int>::const_iterator i = fileData.begin(); i != fileData.end(); ++i) 
     cout << *i << ' '; 

     treeRoot = vec_to_tree(fileData); 

     cout << endl << "Following are the nodes on the maximum sum path" << endl; 

     sum = maxSumPath(treeRoot); 

     cout << "Sum of the nodes is" << sum << endl; 

     return 0; 
    } 


    //sample tree 
    /* 
    59 
    73 41 
    51 40 08 
    26 53 06 34 
    10 51 87 86 81 
    61 95 66 57 25 68 
    91 81 80 38 92 67 73 
    30 28 51 76 81 18 75 44 
    84 14 95 87 62 81 17 78 58 
    21 46 71 58 02 79 62 39 31 09 
    56 34 35 53 78 31 81 18 90 93 15 
    78 53 04 21 84 93 32 13 97 11 37 51 
    45 03 81 79 05 18 78 86 13 30 63 99 95 
    39 87 96 28 03 38 42 17 82 87 58 07 22 57 
    06 17 51 17 07 93 09 07 75 97 95 78 87 08 53 
    67 66 59 60 88 99 94 65 55 77 55 34 27 53 78 28 
    76 40 41 04 87 16 09 42 75 69 23 97 30 60 10 79 87 
    12 10 44 26 21 36 32 84 98 60 13 12 36 16 63 31 91 35 
    70 39 06 05 55 27 38 48 28 22 34 35 62 62 15 14 94 89 86 
    66 56 68 84 96 21 34 34 34 81 62 40 65 54 62 05 98 03 02 60 
    38 89 46 37 99 54 34 53 36 14 70 26 02 90 45 13 31 61 83 73 47 
    36 10 63 96 60 49 41 05 37 42 14 58 84 93 96 17 09 43 05 43 06 59 
    66 57 87 57 61 28 37 51 84 73 79 15 39 95 88 87 43 39 11 86 77 74 18 
    54 42 05 79 30 49 99 73 46 37 50 02 45 09 54 52 27 95 27 65 19 45 26 45 
    71 39 17 78 76 29 52 90 18 99 78 19 35 62 71 19 23 65 93 85 49 33 75 09 02 
    33 24 47 61 60 55 32 88 57 55 91 54 46 57 07 77 98 52 80 99 24 25 46 78 79 05 
    92 09 13 55 10 67 26 78 76 82 63 49 51 31 24 68 05 57 07 54 69 21 67 43 17 63 12 
    24 59 06 08 98 74 66 26 61 60 13 03 09 09 24 30 71 08 88 70 72 70 29 90 11 82 41 34 
    66 82 67 04 36 60 92 77 91 85 62 49 59 61 30 90 29 94 26 41 89 04 53 22 83 41 09 74 90 
    48 28 26 37 28 52 77 26 51 32 18 98 79 36 62 13 17 08 19 54 89 29 73 68 42 14 08 16 70 37 
    37 60 69 70 72 71 09 59 13 60 38 13 57 36 09 30 43 89 30 39 15 02 44 73 05 73 26 63 56 86 12 
    55 55 85 50 62 99 84 77 28 85 03 21 27 22 19 26 82 69 54 04 13 07 85 14 01 15 70 59 89 95 10 19 
    04 09 31 92 91 38 92 86 98 75 21 05 64 42 62 84 36 20 73 42 21 23 22 51 51 79 25 45 85 53 03 43 22 
    75 63 02 49 14 12 89 14 60 78 92 16 44 82 38 30 72 11 46 52 90 27 08 65 78 03 85 41 57 79 39 52 33 48 
    78 27 56 56 39 13 19 43 86 72 58 95 39 07 04 34 21 98 39 15 39 84 89 69 84 46 37 57 59 35 59 50 26 15 93 
    42 89 36 27 78 91 24 11 17 41 05 94 07 69 51 96 03 96 47 90 90 45 91 20 50 56 10 32 36 49 04 53 85 92 25 65 
    52 09 61 30 61 97 66 21 96 92 98 90 06 34 96 60 32 69 68 33 75 84 18 31 71 50 84 63 03 03 19 11 28 42 75 45 45 
    61 31 61 68 96 34 49 39 05 71 76 59 62 67 06 47 96 99 34 21 32 47 52 07 71 60 42 72 94 56 82 83 84 40 94 87 82 46 
    01 20 60 14 17 38 26 78 66 81 45 95 18 51 98 81 48 16 53 88 37 52 69 95 72 93 22 34 98 20 54 27 73 61 56 63 60 34 63 
    93 42 94 83 47 61 27 51 79 79 45 01 44 73 31 70 83 42 88 25 53 51 30 15 65 94 80 44 61 84 12 77 02 62 02 65 94 42 14 94 
    32 73 09 67 68 29 74 98 10 19 85 48 38 31 85 67 53 93 93 77 47 67 39 72 94 53 18 43 77 40 78 32 29 59 24 06 02 83 50 60 66 
    32 01 44 30 16 51 15 81 98 15 10 62 86 79 50 62 45 60 70 38 31 85 65 61 64 06 69 84 14 22 56 43 09 48 66 69 83 91 60 40 36 61 
    92 48 22 99 15 95 64 43 01 16 94 02 99 19 17 69 11 58 97 56 89 31 77 45 67 96 12 73 08 20 36 47 81 44 50 64 68 85 40 81 85 52 09 
    91 35 92 45 32 84 62 15 19 64 21 66 06 01 52 80 62 59 12 25 88 28 91 50 40 16 22 99 92 79 87 51 21 77 74 77 07 42 38 42 74 83 02 05 
    46 19 77 66 24 18 05 32 02 84 31 99 92 58 96 72 91 36 62 99 55 29 53 42 12 37 26 58 89 50 66 19 82 75 12 48 24 87 91 85 02 07 03 76 86 
    99 98 84 93 07 17 33 61 92 20 66 60 24 66 40 30 67 05 37 29 24 96 03 27 70 62 13 04 45 47 59 88 43 20 66 15 46 92 30 04 71 66 78 70 53 99 
    67 60 38 06 88 04 17 72 10 99 71 07 42 25 54 05 26 64 91 50 45 71 06 30 67 48 69 82 08 56 80 67 18 46 66 63 01 20 08 80 47 07 91 16 03 79 87 
    18 54 78 49 80 48 77 40 68 23 60 88 58 80 33 57 11 69 55 53 64 02 94 49 60 92 16 35 81 21 82 96 25 24 96 18 02 05 49 03 50 77 06 32 84 27 18 38 
    68 01 50 04 03 21 42 94 53 24 89 05 92 26 52 36 68 11 85 01 04 42 02 45 15 06 50 04 53 73 25 74 81 88 98 21 67 84 79 97 99 20 95 04 40 46 02 58 87 
    94 10 02 78 88 52 21 03 88 60 06 53 49 71 20 91 12 65 07 49 21 22 11 41 58 99 36 16 09 48 17 24 52 36 23 15 72 16 84 56 02 99 43 76 81 71 29 39 49 17 
    64 39 59 84 86 16 17 66 03 09 43 06 64 18 63 29 68 06 23 07 87 14 26 35 17 12 98 41 53 64 78 18 98 27 28 84 80 67 75 62 10 11 76 90 54 10 05 54 41 39 66 
    43 83 18 37 32 31 52 29 95 47 08 76 35 11 04 53 35 43 31 12 52 57 12 36 20 39 40 55 78 44 07 31 38 26 08 15 56 88 86 01 52 62 10 24 32 05 60 65 53 28 57 99 
    03 50 03 52 07 73 49 92 66 80 01 46 08 67 25 36 73 93 07 42 25 53 13 96 76 83 87 90 54 89 78 22 78 91 73 51 69 09 79 94 83 53 09 40 69 62 10 79 49 47 03 81 30 
    71 54 73 33 51 76 59 54 79 37 56 45 84 17 62 21 98 69 41 95 65 24 39 37 62 03 24 48 54 64 46 82 71 78 33 67 09 16 96 68 52 74 79 68 32 21 13 78 96 60 09 69 20 36 
    73 26 21 44 46 38 17 83 65 98 07 23 52 46 61 97 33 13 60 31 70 15 36 77 31 58 56 93 75 68 21 36 69 53 90 75 25 82 39 50 65 94 29 30 11 33 11 13 96 02 56 47 07 49 02 
    76 46 73 30 10 20 60 70 14 56 34 26 37 39 48 24 55 76 84 91 39 86 95 61 50 14 53 93 64 67 37 31 10 84 42 70 48 20 10 72 60 61 84 79 69 65 99 73 89 25 85 48 92 56 97 16 
    03 14 80 27 22 30 44 27 67 75 79 32 51 54 81 29 65 14 19 04 13 82 04 91 43 40 12 52 29 99 07 76 60 25 01 07 61 71 37 92 40 47 99 66 57 01 43 44 22 40 53 53 09 69 26 81 07 
    49 80 56 90 93 87 47 13 75 28 87 23 72 79 32 18 27 20 28 10 37 59 21 18 70 04 79 96 03 31 45 71 81 06 14 18 17 05 31 50 92 79 23 47 09 39 47 91 43 54 69 47 42 95 62 46 32 85 
    37 18 62 85 87 28 64 05 77 51 47 26 30 65 05 70 65 75 59 80 42 52 25 20 44 10 92 17 71 95 52 14 77 13 24 55 11 65 26 91 01 30 63 15 49 48 41 17 67 47 03 68 20 90 98 32 04 40 68 
    90 51 58 60 06 55 23 68 05 19 76 94 82 36 96 43 38 90 87 28 33 83 05 17 70 83 96 93 06 04 78 47 80 06 23 84 75 23 87 72 99 14 50 98 92 38 90 64 61 58 76 94 36 66 87 80 51 35 61 38 
    57 95 64 06 53 36 82 51 40 33 47 14 07 98 78 65 39 58 53 06 50 53 04 69 40 68 36 69 75 78 75 60 03 32 39 24 74 47 26 90 13 40 44 71 90 76 51 24 36 50 25 45 70 80 61 80 61 43 90 64 11 
    18 29 86 56 68 42 79 10 42 44 30 12 96 18 23 18 52 59 02 99 67 46 60 86 43 38 55 17 44 93 42 21 55 14 47 34 55 16 49 24 23 29 96 51 55 10 46 53 27 92 27 46 63 57 30 65 43 27 21 20 24 83 
    81 72 93 19 69 52 48 01 13 83 92 69 20 48 69 59 20 62 05 42 28 89 90 99 32 72 84 17 08 87 36 03 60 31 36 36 81 26 97 36 48 54 56 56 27 16 91 08 23 11 87 99 33 47 02 14 44 73 70 99 43 35 33 
    90 56 61 86 56 12 70 59 63 32 01 15 81 47 71 76 95 32 65 80 54 70 34 51 40 45 33 04 64 55 78 68 88 47 31 47 68 87 03 84 23 44 89 72 35 08 31 76 63 26 90 85 96 67 65 91 19 14 17 86 04 71 32 95 
    37 13 04 22 64 37 37 28 56 62 86 33 07 37 10 44 52 82 52 06 19 52 57 75 90 26 91 24 06 21 14 67 76 30 46 14 35 89 89 41 03 64 56 97 87 63 22 34 03 79 17 45 11 53 25 56 96 61 23 18 63 31 37 37 47 
    77 23 26 70 72 76 77 04 28 64 71 69 14 85 96 54 95 48 06 62 99 83 86 77 97 75 71 66 30 19 57 90 33 01 60 61 14 12 90 99 32 77 56 41 18 14 87 49 10 14 90 64 18 50 21 74 14 16 88 05 45 73 82 47 74 44 
    22 97 41 13 34 31 54 61 56 94 03 24 59 27 98 77 04 09 37 40 12 26 87 09 71 70 07 18 64 57 80 21 12 71 83 94 60 39 73 79 73 19 97 32 64 29 41 07 48 84 85 67 12 74 95 20 24 52 41 67 56 61 29 93 35 72 69 
    72 23 63 66 01 11 07 30 52 56 95 16 65 26 83 90 50 74 60 18 16 48 43 77 37 11 99 98 30 94 91 26 62 73 45 12 87 73 47 27 01 88 66 99 21 41 95 80 02 53 23 32 61 48 32 43 43 83 14 66 95 91 19 81 80 67 25 88 
    08 62 32 18 92 14 83 71 37 96 11 83 39 99 05 16 23 27 10 67 02 25 44 11 55 31 46 64 41 56 44 74 26 81 51 31 45 85 87 09 81 95 22 28 76 69 46 48 64 87 67 76 27 89 31 11 74 16 62 03 60 94 42 47 09 34 94 93 72 
    56 18 90 18 42 17 42 32 14 86 06 53 33 95 99 35 29 15 44 20 49 59 25 54 34 59 84 21 23 54 35 90 78 16 93 13 37 88 54 19 86 67 68 55 66 84 65 42 98 37 87 56 33 28 58 38 28 38 66 27 52 21 81 15 08 22 97 32 85 27 
    91 53 40 28 13 34 91 25 01 63 50 37 22 49 71 58 32 28 30 18 68 94 23 83 63 62 94 76 80 41 90 22 82 52 29 12 18 56 10 08 35 14 37 57 23 65 67 40 72 39 93 39 70 89 40 34 07 46 94 22 20 05 53 64 56 30 05 56 61 88 27 
    23 95 11 12 37 69 68 24 66 10 87 70 43 50 75 07 62 41 83 58 95 93 89 79 45 39 02 22 05 22 95 43 62 11 68 29 17 40 26 44 25 71 87 16 70 85 19 25 59 94 90 41 41 80 61 70 55 60 84 33 95 76 42 63 15 09 03 40 38 12 03 32 
    09 84 56 80 61 55 85 97 16 94 82 94 98 57 84 30 84 48 93 90 71 05 95 90 73 17 30 98 40 64 65 89 07 79 09 19 56 36 42 30 23 69 73 72 07 05 27 61 24 31 43 48 71 84 21 28 26 65 65 59 65 74 77 20 10 81 61 84 95 08 52 23 70 
    49 81 28 09 98 51 67 64 35 51 59 36 92 82 77 65 80 24 72 53 22 07 27 10 21 28 30 22 48 82 80 48 56 20 14 43 18 25 50 95 90 31 77 08 09 48 44 80 90 22 93 45 82 17 13 96 25 26 08 73 34 99 06 49 24 06 83 51 40 14 15 10 25 01 
    54 25 10 81 30 64 24 74 75 80 36 75 82 60 22 69 72 91 45 67 03 62 79 54 89 74 44 83 64 96 66 73 44 30 74 50 37 05 09 97 70 01 60 46 37 91 39 75 75 18 58 52 72 78 51 81 86 52 08 97 01 46 43 66 98 62 81 18 70 93 73 08 32 46 34 
    96 80 82 07 59 71 92 53 19 20 88 66 03 26 26 10 24 27 50 82 94 73 63 08 51 33 22 45 19 13 58 33 90 15 22 50 36 13 55 06 35 47 82 52 33 61 36 27 28 46 98 14 73 20 73 32 16 26 80 53 47 66 76 38 94 45 02 01 22 52 47 96 64 58 52 39 
    88 46 23 39 74 63 81 64 20 90 33 33 76 55 58 26 10 46 42 26 74 74 12 83 32 43 09 02 73 55 86 54 85 34 28 23 29 79 91 62 47 41 82 87 99 22 48 90 20 05 96 75 95 04 43 28 81 39 81 01 28 42 78 25 39 77 90 57 58 98 17 36 73 22 63 74 51 
    29 39 74 94 95 78 64 24 38 86 63 87 93 06 70 92 22 16 80 64 29 52 20 27 23 50 14 13 87 15 72 96 81 22 08 49 72 30 70 24 79 31 16 64 59 21 89 34 96 91 48 76 43 53 88 01 57 80 23 81 90 79 58 01 80 87 17 99 86 90 72 63 32 69 14 28 88 69 
    37 17 71 95 56 93 71 35 43 45 04 98 92 94 84 96 11 30 31 27 31 60 92 03 48 05 98 91 86 94 35 90 90 08 48 19 33 28 68 37 59 26 65 96 50 68 22 07 09 49 34 31 77 49 43 06 75 17 81 87 61 79 52 26 27 72 29 50 07 98 86 01 17 10 46 64 24 18 56 
    51 30 25 94 88 85 79 91 40 33 63 84 49 67 98 92 15 26 75 19 82 05 18 78 65 93 61 48 91 43 59 41 70 51 22 15 92 81 67 91 46 98 11 11 65 31 66 10 98 65 83 21 05 56 05 98 73 67 46 74 69 34 08 30 05 52 07 98 32 95 30 94 65 50 24 63 28 81 99 57 
    19 23 61 36 09 89 71 98 65 17 30 29 89 26 79 74 94 11 44 48 97 54 81 55 39 66 69 45 28 47 13 86 15 76 74 70 84 32 36 33 79 20 78 14 41 47 89 28 81 05 99 66 81 86 38 26 06 25 13 60 54 55 23 53 27 05 89 25 23 11 13 54 59 54 56 34 16 24 53 44 06 
    13 40 57 72 21 15 60 08 04 19 11 98 34 45 09 97 86 71 03 15 56 19 15 44 97 31 90 04 87 87 76 08 12 30 24 62 84 28 12 85 82 53 99 52 13 94 06 65 97 86 09 50 94 68 69 74 30 67 87 94 63 07 78 27 80 36 69 41 06 92 32 78 37 82 30 05 18 87 99 72 19 99 
    44 20 55 77 69 91 27 31 28 81 80 27 02 07 97 23 95 98 12 25 75 29 47 71 07 47 78 39 41 59 27 76 13 15 66 61 68 35 69 86 16 53 67 63 99 85 41 56 08 28 33 40 94 76 90 85 31 70 24 65 84 65 99 82 19 25 54 37 21 46 33 02 52 99 51 33 26 04 87 02 08 18 96 
    54 42 61 45 91 06 64 79 80 82 32 16 83 63 42 49 19 78 65 97 40 42 14 61 49 34 04 18 25 98 59 30 82 72 26 88 54 36 21 75 03 88 99 53 46 51 55 78 22 94 34 40 68 87 84 25 30 76 25 08 92 84 42 61 40 38 09 99 40 23 29 39 46 55 10 90 35 84 56 70 63 23 91 39 
    52 92 03 71 89 07 09 37 68 66 58 20 44 92 51 56 13 71 79 99 26 37 02 06 16 67 36 52 58 16 79 73 56 60 59 27 44 77 94 82 20 50 98 33 09 87 94 37 40 83 64 83 58 85 17 76 53 02 83 52 22 27 39 20 48 92 45 21 09 42 24 23 12 37 52 28 50 78 79 20 86 62 73 20 59 
    54 96 80 15 91 90 99 70 10 09 58 90 93 50 81 99 54 38 36 10 30 11 35 84 16 45 82 18 11 97 36 43 96 79 97 65 40 48 23 19 17 31 64 52 65 65 37 32 65 76 99 79 34 65 79 27 55 33 03 01 33 27 61 28 66 08 04 70 49 46 48 83 01 45 19 96 13 81 14 21 31 79 93 85 50 05 
    92 92 48 84 59 98 31 53 23 27 15 22 79 95 24 76 05 79 16 93 97 89 38 89 42 83 02 88 94 95 82 21 01 97 48 39 31 78 09 65 50 56 97 61 01 07 65 27 21 23 14 15 80 97 44 78 49 35 33 45 81 74 34 05 31 57 09 38 94 07 69 54 69 32 65 68 46 68 78 90 24 28 49 51 45 86 35 
    41 63 89 76 87 31 86 09 46 14 87 82 22 29 47 16 13 10 70 72 82 95 48 64 58 43 13 75 42 69 21 12 67 13 64 85 58 23 98 09 37 76 05 22 31 12 66 50 29 99 86 72 45 25 10 28 19 06 90 43 29 31 67 79 46 25 74 14 97 35 76 37 65 46 23 82 06 22 30 76 93 66 94 17 96 13 20 72 
    63 40 78 08 52 09 90 41 70 28 36 14 46 44 85 96 24 52 58 15 87 37 05 98 99 39 13 61 76 38 44 99 83 74 90 22 53 80 56 98 30 51 63 39 44 30 91 91 04 22 27 73 17 35 53 18 35 45 54 56 27 78 48 13 69 36 44 38 71 25 30 56 15 22 73 43 32 69 59 25 93 83 45 11 34 94 44 39 92 
    12 36 56 88 13 96 16 12 55 54 11 47 19 78 17 17 68 81 77 51 42 55 99 85 66 27 81 79 93 42 65 61 69 74 14 01 18 56 12 01 58 37 91 22 42 66 83 25 19 04 96 41 25 45 18 69 96 88 36 93 10 12 98 32 44 83 83 04 72 91 04 27 73 07 34 37 71 60 59 31 01 54 54 44 96 93 83 36 04 45 
    30 18 22 20 42 96 65 79 17 41 55 69 94 81 29 80 91 31 85 25 47 26 43 49 02 99 34 67 99 76 16 14 15 93 08 32 99 44 61 77 67 50 43 55 87 55 53 72 17 46 62 25 50 99 73 05 93 48 17 31 70 80 59 09 44 59 45 13 74 66 58 94 87 73 16 14 85 38 74 99 64 23 79 28 71 42 20 37 82 31 23 
    51 96 39 65 46 71 56 13 29 68 53 86 45 33 51 49 12 91 21 21 76 85 02 17 98 15 46 12 60 21 88 30 92 83 44 59 42 50 27 88 46 86 94 73 45 54 23 24 14 10 94 21 20 34 23 51 04 83 99 75 90 63 60 16 22 33 83 70 11 32 10 50 29 30 83 46 11 05 31 17 86 42 49 01 44 63 28 60 07 78 95 40 
    44 61 89 59 04 49 51 27 69 71 46 76 44 04 09 34 56 39 15 06 94 91 75 90 65 27 56 23 74 06 23 33 36 69 14 39 05 34 35 57 33 22 76 46 56 10 61 65 98 09 16 69 04 62 65 18 99 76 49 18 72 66 73 83 82 40 76 31 89 91 27 88 17 35 41 35 32 51 32 67 52 68 74 85 80 57 07 11 62 66 47 22 67 
    65 37 19 97 26 17 16 24 24 17 50 37 64 82 24 36 32 11 68 34 69 31 32 89 79 93 96 68 49 90 14 23 04 04 67 99 81 74 70 74 36 92 68 09 64 39 88 35 54 89 96 58 66 27 88 97 32 14 06 35 78 20 71 06 85 66 57 02 58 91 72 05 29 56 73 48 86 52 09 93 22 57 79 42 12 01 31 68 17 59 63 76 07 77 
    73 81 14 13 17 20 11 09 01 83 08 85 91 70 84 63 62 77 37 07 47 01 59 95 39 69 39 21 99 09 87 02 97 16 92 36 74 71 90 66 33 73 73 75 52 91 11 12 26 53 05 26 26 48 61 50 90 65 01 87 42 47 74 35 22 73 24 26 56 70 52 05 48 41 31 18 83 27 21 39 80 85 26 08 44 02 71 07 63 22 05 52 19 08 20 
    17 25 21 11 72 93 33 49 64 23 53 82 03 13 91 65 85 02 40 05 42 31 77 42 05 36 06 54 04 58 07 76 87 83 25 57 66 12 74 33 85 37 74 32 20 69 03 97 91 68 82 44 19 14 89 28 85 85 80 53 34 87 58 98 88 78 48 65 98 40 11 57 10 67 70 81 60 79 74 72 97 59 79 47 30 20 54 80 89 91 14 05 33 36 79 39 
    60 85 59 39 60 07 57 76 77 92 06 35 15 72 23 41 45 52 95 18 64 79 86 53 56 31 69 11 91 31 84 50 44 82 22 81 41 40 30 42 30 91 48 94 74 76 64 58 74 25 96 57 14 19 03 99 28 83 15 75 99 01 89 85 79 50 03 95 32 67 44 08 07 41 62 64 29 20 14 76 26 55 48 71 69 66 19 72 44 25 14 01 48 74 12 98 07 
    64 66 84 24 18 16 27 48 20 14 47 69 30 86 48 40 23 16 61 21 51 50 26 47 35 33 91 28 76 64 43 68 04 79 51 08 19 60 52 95 06 68 46 86 35 97 27 58 04 65 30 58 99 12 12 75 91 39 50 31 42 64 70 04 46 07 98 73 98 93 37 89 77 91 64 71 64 65 66 21 78 62 81 74 42 20 83 70 73 95 78 45 92 27 34 53 71 15 
    30 11 85 31 34 71 13 48 05 14 44 03 19 67 23 73 19 57 06 90 94 72 57 69 81 62 59 68 88 57 55 69 49 13 07 87 97 80 89 05 71 05 05 26 38 40 16 62 45 99 18 38 98 24 21 26 62 74 69 04 85 57 77 35 58 67 91 79 79 57 86 28 66 34 72 51 76 78 36 95 63 90 08 78 47 63 45 31 22 70 52 48 79 94 15 77 61 67 68 
    23 33 44 81 80 92 93 75 94 88 23 61 39 76 22 03 28 94 32 06 49 65 41 34 18 23 08 47 62 60 03 63 33 13 80 52 31 54 73 43 70 26 16 69 57 87 83 31 03 93 70 81 47 95 77 44 29 68 39 51 56 59 63 07 25 70 07 77 43 53 64 03 94 42 95 39 18 01 66 21 16 97 20 50 90 16 70 10 95 69 29 06 25 61 41 26 15 59 63 35 
    */ 

Answer 1

你的算法是自上而下的：它从根开始。如果你从树叶开始，你可能会更有效率。

您可以将叶子存储在pair<int, path_to_the_max>的vector中。

然后，对于由i和i+1索引的每对树叶，选择max并在int部分中添加它们的父亲;不要忘记在path_to_the_max部分推动这个选择。结果可以存储在索引号为i的同一个向量中。

然后，你去了新的载体。你现在处于树叶父母的层面。

您可以迭代此过程，直到您的向量仅包含一个元素。 max的连续选择是您的解决方案 - 它是元素对的第二个元素。

初始算法应该使用2 ** (depth-1)比较。 此算法应与(depth * (depth-1))/2比较。

UPDATE

这里是自下而上的算法如何工作在你的例子 - 请参见下面的代码。

  12 
     20 30 
    50 07 30 
    20 60 15 42 

current_nodes 20 60 15 42 
maxAtDepth  20,0 60,0 15,0 42,0 
       | /| /| /
next iterate m=60 m=60 m=42 
current_nodes 50  07 30 
maxAtDepth  110,1 67,0 72,1 
       | /| /
next iterate m=110 m=72 
current_nodes 20  30 
maxAtDepth  130,01 102,10 
       | /
next iterate m=130 
current_nodes 12 
maxAtDepth  142,001 

result = 142, path = 001 = left-left-right 

这里是你的代码进行一些修改 - 没有测试，也没有调试

struct node 
{ 
    int value; 
    ... 
    struct node *parent_left; // new 
    struct node *parent_right; // new 
}; 

struct node * vec_to_tree(vector<int> arr) 
{ ... 
     newNode1->left = newNode(arr[depth+i],depth+1,depth+i); 
     newNode1->left->parent_right = newNode1; // new 
    ... 
     newNode1->right = newNode(arr[depth+i+1],depth+1,depth+i+1); 
     newNode1->right->parent_left = newNode1; // new 
    ... 
      newNode2->left= newNode1->right; 
      newNode2->left->parent_right = newNode2; // new 
      newNode2->right = newNode(arr[depth+i+1],depth+1,depth+i+1); 
      newNode2->right->parent_left = newNode2; // new 
} 

class PathToMax { 
    public: 
    class BitAccess { 
    private: 
     unsigned* _cell; 
     int _index; 
    public: 
     BitAccess(unsigned* cell, int index) : _cell(cell), _index(index) {} 
     operator bool() const { return (*_cell >> _index) & 1U; } 
     BitAccess& operator=(bool val) 
     { *_cell &= ~(1U << _index); *_cell |= (val << _index); return *this; } 
    }; 

    private: 
    unsigned _path[10]; // depth <= 320 

    public: 
    PathToMax() { for (int i = 0; i<10; ++i) _path[i] =0; } 

    BitAccess operator[](int index) 
     { assert(index < (int) (10*sizeof(unsigned)*8)); 
     return BitAccess(&_path[index/(sizeof(unsigned)*8)], index % (sizeof(unsigned)*8)); 
     } 
}; 

int maxSumPath (struct node *node, int depth) 
{ 
    typedef vector<std::pair<int, PathToMax> > MaxAtDepth; 
    typedef vector<struct node*> NodesLevel; 

    // go to the leaves 
    NodesLevel current_nodes, next_nodes; 
    current_nodes.push_back(node); 
    for (int i = 0; i < depth; ++i) { 
     next_nodes.clear(); 
     for (struct node* node : current_nodes) 
     next_nodes.push_back(node->left); // test if NULL 
     next_nodes.push_back(current_nodes.back()->right); 
     current_nodes.swap(next_nodes); 
    }; 

    // build initial maxAtDepth 
    MaxAtDepth maxAtDepth; 
    for (struct node* node : current_nodes) 
     maxAtDepth.push_back(std::make_pair(node->value, PathToMax())); 

    // apply the algorithm 
    int inverse_depth = 0; 
    while (maxAtDepth.size() > 1) { 
     next_nodes.clear(); 
     MaxAtDepth upMaxAtDepth; 

     MaxAtDepth::const_iterator iter_max = maxAtDepth.begin(), 
           iter_max_next = maxAtDepth.begin() + 1, 
           iter_max_end = maxAtDepth.end(); 
     NodesLevel::const_iterator iter = current_nodes.begin(), 
           iter_next = current_nodes.begin() + 1, 
           iter_end = current_nodes.end(); 
     for (; iter_next != iter_end; ++iter, ++iter_next, ++iter_max, ++iter_max_next) { 
     assert((*iter)->parent_right == (*iter_next)->parent_left); 
     next_nodes.push_back((*iter)->parent_right); 
     assert(iter_max_next != iter_max_end); 
     if ((*iter)->value >= (*iter_next)->value) { 
      upMaxAtDepth.push_back(std::make_pair(
        (*iter)->parent_right->value + iter_max->first, 
        iter_max->second)); 
      upMaxAtDepth.back().second[inverse_depth] = false /* left path */; 
     } 
     else { 
      upMaxAtDepth.push_back(std::make_pair(
        (*iter_next)->parent_left->value + iter_max_next->first, 
        iter_max_next->second)); 
      upMaxAtDepth.back().second[inverse_depth] = true /* right path */; 
     } 
     }; 
     next_nodes.swap(current_nodes); 
     maxAtDepth.swap(upMaxAtDepth); 
     ++inverse_depth; 
    }; 

    return maxAtDepth[0].first; 
    // the path is in maxAtDepth[0].snd from index 0 to inverse_depth-1; 
} 

注意，由于小区的左节点共享其弟弟的右节点的树有内存泄漏。在特定水平的极端情况并非如此。由于您没有垃圾收集器，所以您应该知道您是否拥有子结构的所有权。

Answer 2

我不知道我理解得问题，但如果我是，我会在这里发布我的答案（请让我知道如果你的意思是在这个问题别的东西）：

你可以开始从根目录并在O(n)中执行递归方法，其中n是树上的节点数。

让我们将max_sum(node)定义为您可以通过深入（到底部）从当前节点获得的最大总和。现在，你的函数将被定义为（伪这里）：

max_sum(node) { 
    if (node.is_leaf()) { 
     return node.value; 
    } 
    left_sum = max_sum(node.left_child); 
    right_sum = max_sum(node.right_child); 
    return max(left_sum, right_sum) + node.value; 
} 

正如你所看到的，你可以为你的当前节点的总和台机器最多值是两个儿子的机器最多可以值（左，右）+您当前节点的值。这是有效的，因为你清楚地选择了你从两个儿子身上所能得到的最好结果。

希望它有帮助:)