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题目大意:输入一颗无根树的括号序列,求这棵树的普吕弗序列。
分析思路:
1)普吕弗序列,可以参考维基百科,其做法是找出树中编号最小的叶子节点,并将此叶子节点及边删除,并输出其邻接的节点标号;
2)递归地构造树,可以使用list<int> 数组来表示一个“邻接表”,以存储构造的树;
3)使用优先队列来进行删除,奈何priority_queue没有迭代器访问,只能用堆排序,取最值;
代码:
#include<iostream> #include<vector> #include<map> #include<queue> #include<string> #include<algorithm> #include<fstream> #include<list> using namespace std; struct nodeAndDegree { int degree; //度 int nodeNumber; //结点编号 bool operator < (const nodeAndDegree& n1)const { return degree == n1.degree ? (nodeNumber > n1.nodeNumber) : (degree > n1.degree); } }; const int MAX_LEN = 55; list<int> vGraph[MAX_LEN]; vector<int> v; int rootNumber = 0; void dfs(int start, int end, int parent, string str) { if (start == end) //只有单个点 { return; } //放入邻接矩阵 int currentNode = 0; for (int i = start + 1; i <= end - 1; i++) { if (str[i] == ‘ ‘ || str[i] == ‘\0‘ || str[i] == ‘(‘) { break; } currentNode = currentNode * 10 + (int)(str[i] - 48); } //放入邻接矩阵 vGraph[parent].push_back(currentNode); vGraph[currentNode].push_back(parent); v.push_back(currentNode); int mark = 0; int tmpStart = -1; for (int i = start + 1; i <= end - 1; i++) { if (str[i] == ‘(‘) { mark++; if (tmpStart == -1) tmpStart = i; continue; } if (str[i] == ‘)‘) { mark--; if (mark == 0) { dfs(tmpStart, i, currentNode, str); tmpStart = -1; } } } } void print_prufer_sequnce() { //首先修改根节点对应的长度 int tmp = vGraph[0].front(); vGraph[tmp].remove(0); vector<nodeAndDegree> listNodeDegree; for (int i = 0; i < v.size(); i++) { nodeAndDegree *nd = new nodeAndDegree(); nd->nodeNumber = v[i]; nd->degree = vGraph[v[i]].size(); listNodeDegree.push_back(*nd); } int n = v.size() - 1; int index = 0; while (index < n) { make_heap(listNodeDegree.begin(), listNodeDegree.end()); int number = listNodeDegree[0].nodeNumber; //当前结点 int front = vGraph[number].front(); cout << front ; if (index != n - 1) { cout << " "; } vGraph[front].remove(number); vGraph[number].remove(front); for (int j = 1; j < listNodeDegree.size(); j++) { if (listNodeDegree[j].nodeNumber == front) { listNodeDegree[j].degree--; break; } } listNodeDegree.erase(listNodeDegree.begin()); index++; } } int main() { string s; //fstream cin("1097.txt"); while (getline(cin, s)) { for (int i = 0; i < MAX_LEN; i++) { vGraph[i].clear(); } v.clear(); dfs(0, s.size() - 1, 0, s); print_prufer_sequnce(); cout << endl; } return 0; }
以纪念我那逝去的耗费精力的兴奋的AC。
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原文地址:http://www.cnblogs.com/pengzhen/p/4375827.html