c++ - 查找节点树的最大路径总和

Question

我正在尝试编写一个程序，它可以从一个文件构建一个节点树，然后找到它的最大路径和。通过路径总和，我的意思是沿着给定的自上而下遍历的节点值的总和。

我有一个工作程序，但它的速度还不够快，因为我应该能够在 10 秒内解决一棵深度为 100 的树。

我希望有人能给我一些关于如何优化运行时间的指示，因为在大约 20 的树深度后它开始变得非常慢。

注意:我不是在处理常规的二叉树，树的格式如下。

例如，给定一棵树

      12 
    20  30
  50  07  30
20  60  15  42

最大总和路径上的节点为 12 20 50 60，遍历路径为:LLR，总和为 142。

我目前的计划:

    #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

您的算法是自上而下的:它从根开始。如果从树叶开始，您的效率会更高。

您可以将叶子存储在 vector 中的 pair<int, path_to_the_max> .

然后对于由 i 索引的每一对叶子和 i+1 ，您选择最大值并将其父级添加到 int 中部分;不要忘记在 path_to_the_max 中插入这个选择部分。结果可以存储在索引 i 处的同一 vector 中.

然后你继续使用新的 vector 。您现在处于叶的父级别。

您可以重复此过程，直到您的 vector 只包含一个元素。 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 一起使用比较。

更新

以下是自下而上算法在您的示例中的工作方式 - 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

这里是对你的代码的一些修改 - 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;
}

请注意，您的树存在内存泄漏，因为单元格的左节点与其兄弟的右节点共享。对于给定级别的四肢，情况并非如此。由于您没有垃圾收集器，在 C++ 中，您应该知道您是否拥有子结构的所有权。