【面试题025】二叉树中和为某一值的路径
只有前序遍历，首先访问根结点。
前序遍历访问到某个结点，把该结点添加到路径上，并累加该结点的值，
递归函数推出前，要在路径上删除当前结点，并且减去当前结点的值，
递归返回的条件是到了叶子结点。
保存路径的数据结构实际上就是一个栈。
PathInTree.cpp:
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#include <iostream>
#include <cstdio> #include <vector> #include "BinaryTree.h" using namespace std; void FindPath(BinaryTreeNode *pRoot, int expectedSum, vector<int> &path, int ¤tSum); void FindPath(BinaryTreeNode *pRoot, int expectedSum) { if(pRoot == NULL) return; vector<int> path; int currentSum = 0; FindPath(pRoot, expectedSum, path, currentSum); } void FindPath ( BinaryTreeNode *pRoot, int expectedSum, vector<int> &path, int ¤tSum ) { currentSum += pRoot->m_nValue; path.push_back(pRoot->m_nValue); // 如果是叶结点，并且路径上结点的和等于输入的值 // 打印出这条路径 bool isLeaf = pRoot->m_pLeft == NULL && pRoot->m_pRight == NULL; if(currentSum == expectedSum && isLeaf) { printf("A path is found: "); vector<int>::iterator iter = path.begin(); for(; iter != path.end(); ++ iter) printf("%d ", *iter); printf(" "); } // 如果不是叶结点，则遍历它的子结点 if(pRoot->m_pLeft != NULL) FindPath(pRoot->m_pLeft, expectedSum, path, currentSum); if(pRoot->m_pRight != NULL) FindPath(pRoot->m_pRight, expectedSum, path, currentSum); // 在返回到父结点之前，在路径上删除当前结点， // 并在currentSum中减去当前结点的值 currentSum -= pRoot->m_nValue; path.pop_back(); } // 10 // / // 5 12 // / // 4 7 // 有两条路径上的结点和为22 int main() { BinaryTreeNode *pNode10 = CreateBinaryTreeNode(10); BinaryTreeNode *pNode5 = CreateBinaryTreeNode(5); BinaryTreeNode *pNode12 = CreateBinaryTreeNode(12); BinaryTreeNode *pNode4 = CreateBinaryTreeNode(4); BinaryTreeNode *pNode7 = CreateBinaryTreeNode(7); ConnectTreeNodes(pNode10, pNode5, pNode12); ConnectTreeNodes(pNode5, pNode4, pNode7); BinaryTreeNode *pRoot = pNode10; int expectedSum = 22; FindPath(pRoot, expectedSum); printf(" "); DestroyTree(pNode10); return 0; } |
BinaryTree.h:
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#ifndef _BINARY_TREE_H_
#define _BINARY_TREE_H_ struct BinaryTreeNode { int m_nValue; BinaryTreeNode *m_pLeft; BinaryTreeNode *m_pRight; }; BinaryTreeNode *CreateBinaryTreeNode(int value); void ConnectTreeNodes( BinaryTreeNode *pParent, BinaryTreeNode *pLeft, BinaryTreeNode *pRight); void PrintTreeNode(BinaryTreeNode *pNode); void PrintTree(BinaryTreeNode *pRoot); void DestroyTree(BinaryTreeNode *pRoot); #endif /*_BINARY_TREE_H_*/ |
BinaryTree.cpp:
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#include <iostream>
#include <cstdio> #include "BinaryTree.h" using namespace std; BinaryTreeNode *CreateBinaryTreeNode(int value) { BinaryTreeNode *pNode = new BinaryTreeNode(); pNode->m_nValue = value; pNode->m_pLeft = NULL; pNode->m_pRight = NULL; return pNode; } void ConnectTreeNodes( BinaryTreeNode *pParent, BinaryTreeNode *pLeft, BinaryTreeNode *pRight) { if(pParent != NULL) { pParent->m_pLeft = pLeft; pParent->m_pRight = pRight; } } void PrintTreeNode(BinaryTreeNode *pNode) { if(pNode != NULL) { printf("value of this node is: %d ", pNode->m_nValue); if(pNode->m_pLeft != NULL) printf("value of its left child is: %d. ", pNode->m_pLeft->m_nValue); else printf("left child is null. "); if(pNode->m_pRight != NULL) printf("value of its right child is: %d. ", pNode->m_pRight->m_nValue); else printf("right child is null. "); } else { printf("this node is null. "); } printf(" "); } void PrintTree(BinaryTreeNode *pRoot) { PrintTreeNode(pRoot); if(pRoot != NULL) { if(pRoot->m_pLeft != NULL) PrintTree(pRoot->m_pLeft); if(pRoot->m_pRight != NULL) PrintTree(pRoot->m_pRight); } } void DestroyTree(BinaryTreeNode *pRoot) { if(pRoot != NULL) { BinaryTreeNode *pLeft = pRoot->m_pLeft; BinaryTreeNode *pRight = pRoot->m_pRight; delete pRoot; pRoot = NULL; DestroyTree(pLeft); DestroyTree(pRight); } } |
Makefile:
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.PHONY:clean
CPP=g++ CFLAGS=-Wall -g BIN=test OBJS=PathInTree.o BinaryTree.o LIBS= $(BIN):$(OBJS) $(CPP) $(CFLAGS) $^ -o $@ $(LIBS) %.o:%.cpp $(CPP) $(CFLAGS) -c $< -o $@ clean: rm -f *.o $(BIN) |
运行结果：
A path is found: 10 5 7
A path is found: 10 12