寻找树中和为定值的所有路径

2016.8.18改

You are given a binary tree in which each node contains a value. Design an algorithm to print all paths which sum up to that value. Note that it can be any path in the tree-it does not have to start at the root.

思路：
一层一层的遍历，保存当前节点到根节点的完整路径，然后从当前节点向上扫描，如果找到了当前节点到某个节点的和等于给定值，则输出之。程序对每个节点都需要遍历一遍，还要扫描当前节点到根节点的路径，且需要保存每个节点到根节点的路径，所以时间复杂度为O（nlgn)，空间复杂度为O(nlgn)。

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#include<iostream>

#include<assert.h>

#include<vector>

#include<malloc.h>

using namespace std;

struct treeNode

{

    struct treeNode *pLeft,*pRight;    

    int p_val;

};

struct treeNode *createShortestTree(int *a,int lo,int hi)//构建高度最小的树  二分查找的方法

{

    if (lo > hi)//注意着里没有等号,这里不能省略，否则段错误

        return NULL;

    else

    {

        int mid = (lo+hi)/2;

        int key = a[mid];

        struct treeNode *pRoot = NULL;

        pRoot = (struct treeNode *)malloc(sizeof(struct treeNode));

        pRoot->p_val = key;

        pRoot->pLeft = createShortestTree(a,lo,mid-1);

        pRoot->pRight = createShortestTree(a,mid+1,hi);

        return pRoot;

    }

}

void insetLastLeft(struct treeNode *&pRoot,struct treeNode *pNew)

{

        assert(pRoot != NULL && pNew != NULL);

        struct treeNode *root = pRoot;

        while (root->pLeft)

        {

            root = root->pLeft;

        }

        root->pLeft = pNew;

}

void insertLastRight(struct treeNode *&pRoot,struct treeNode *pNew)

{

    assert(pRoot != NULL && pNew != NULL);//这里别忘了判断pNew

    struct treeNode *root = pRoot;

    while (root->pRight)

    {

        root = root->pRight;

    }

    root->pRight = pNew;

}

void print(vector<int> buffer,int first,int last)//顺序打印

{

    for (int i = first;i <= last;i++)

    {

        cout << buffer[i]<< "\t";

    }

    cout << "\n";

}

void findsum(struct treeNode *pRoot,int sum,vector<int> &buffer,int level)

{

    if (pRoot == NULL) return ;//这个终止条件别忘写了

    int tmp = sum;

    int i = 0;

    buffer.push_back(pRoot->p_val);

    for (i = level;i >= 0;i--)

    {

        tmp -= buffer[i];

        if (tmp == 0) print(buffer,i,level);

    }

    vector<int> bufferl(buffer);//buffer1[0] = buffer[0],bufferl[1] = 新加入的节点的值....

    vector<int> bufferr(buffer);

    findsum(pRoot->pLeft,sum,bufferl,level+1);

    findsum(pRoot->pRight,sum,bufferr,level+1);

}

int main()

{

    int i = 0;

    int a[10];

    vector<int> vec;

    for (i = 0;i < 10;i++)

    {

        a[i] = i+1;

    }

    struct treeNode *pRoot = NULL;

    pRoot = createShortestTree(a,0,9);

    if (pRoot == NULL)

    {

        cout << "pRoot is null" << endl;

    }

    struct treeNode *new1 = (struct treeNode *)malloc(sizeof(struct treeNode));

    new1->p_val = 11;

    new1->pLeft = NULL;

    new1->pRight = NULL;

    struct treeNode *new2 = (struct treeNode *)malloc(sizeof(struct treeNode));

    new2->p_val = 4;

    new2->pLeft = NULL;

    new2->pRight = NULL;

    insetLastLeft(pRoot,new1);

    insertLastRight(pRoot,new2);

    findsum(pRoot,14,vec,0);

    return 0;

}

运行结果:

[root@localhost c++]# ./a.out

2       1       11

5       2       3       4

8       6

10      4


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