Sunday, May 15, 2016

Tree S Expression


https://github.com/xieqilu/Qilu-leetcode/blob/master/B219.GetSExpressionBT.cs
You are given a binary tree as a sequence of parent-child pairs.
For example, the tree represented by the node pairs below:
(A,B) (A,C) (B,G) (C,H) (E,F) (B,D) (C,E)
may be illustrated in many ways, with two possible representations below:
     A   /  \  B    C / \  / \G  D  E   H       \            F      
     A   /  \  B    C / \  / \D  G H   E        /       F
Below is the recursive definition for the S-expression of a tree:
S-exp(node) = ( node->val
(S-exp(node->first_child))(S-exp(node->second_child))), if node != NULL
                         = "", node == NULL
   where, first_child->val < second_child->val (lexicographically smaller)
This tree can be represented in a S-expression in multiple ways.
The lexicographically smallest way of expressing this is as follows:
(A(B(D)(G))(C(E(F))(H)))
We need to translate the node-pair representation into an S-expression
(lexicographically smallest one), and report any errors that do not conform to the definition of a binary tree.
The list of errors with their codes is as follows:
Error Code          Type of error
E1                 More than 2 children
E2                 Duplicate Edges
E3                 Cycle present
E4                 Multiple roots
E5                 Any other error
Input Format:
Input must be read from standard input.
Input will consist of on line of parent-child pairs. Each pair consists of two node names separated by a single comma and enclosed in parentheses. A single space separates the pairs.
Output:
The function must write to standard output.
Output the given tree in the S-expression representation described above.
There should be no spaces in the output.
Constraints:
There is no specific sequence in which the input (parent,child) pairs are represented.
The name space is composed of upper case single letter (A-Z) so the maximum size is 26 nodes.
Error cases are to be tagged in the order they appear on the list. For example,
if one input pair raises both error cases 1 and 2, the output must be E1.
Sample Input #00
(B,D) (D,E) (A,B) (C,F) (E,G) (A,C)
Sample Output #00
(A(B(D(E(G))))(C(F)))
Sample Input #01
(A,B) (A,C) (B,D) (D,C)
Sample Output #01
E3
Explanation
Node D is both a child of B and a parent of C, but C and B are both child nodes of A.
Since D tries to attach itself as parent to a node already above it in the tree, this forms a cycle.
Idea:
Use a 26*26 graph to represent the input tree. Then check for each error in the order, finally use
a recursive DFS to form the tree and the output SExpression.
E1: More than 2 children. Check if graph[i][j], j from 0 to 25 has more than two cell that is true.
E2: Duplicate Edge. Check when constructing the graph, if graph[x][y] is already true, E2=true.
E3: Cycle Present: Check when looking for the root, starting from each root, use recursive DFS to check if there is
a cycle in the graph.
E4: Multiple roots: traverse all nodes in the HashSet, if no edge connected TO this node, then it must be a root.
即这个顶点没有入度,没有其他的点指向这个点,那么这个点必然是root. If number of roots > 1, return "E4".
Note: if number of roots == 0, then there must also be a cycle, return "E3".
public static string GetSExpression(string s){
bool[,] graph = new bool [26,26];
HashSet<char> nodes = new HashSet<char>();
//construct graph and check error E2: duplicate edges
bool E2 = false;
for(int i=1;i<s.Length;i+=6){
int x = s[i]-'A', y = s[i+2]-'A';
if(graph[x,y]) //duplicate edge
E2 = true;
graph[x,y] = true;
nodes.Add(s[i]);
nodes.Add(s[i+2]);
}
//check error E1: more than 2 children
bool E1 = false;
for(int i=0;i<26;i++){
int count = 0; //number of child
for(int j=0;j<26;j++){
if(graph[i,j])
count++;
}
if(count>2)
return "E1";
}
if(E2) return "E2"; //return E2 after checking E1

//check E3: cycle present and E4: multiple roots
int numOfRoots = 0;
char root =' ';
foreach(char node in nodes){ //only check char that in the tree
for(int i=0;i<26;i++){
if(graph[i,node-'A'])
break;
if(i==25){
numOfRoots++;
root = node;
bool[] visited = new bool[26];
if(IsCycle(node, graph, visited))
return "E3";
}
}
}
if(numOfRoots==0) return "E3"; //if no root, must be a cycle
if(numOfRoots>1) return "E4"; //if more than one roots
if(root==' ') return "E5"; //if no edge in input string, invalid input error
return GetExpressionHelper(root, graph);

}

//true means there is a cycle, false means no cycle
private static bool IsCycle(char node, bool[,] graph, bool[] visited){
if(visited[node-'A']) //node has already been visited, must has a cycle
return true;
visited[node-'A'] = true;
for(int i=0;i<26;i++){
if(graph[node-'A',i]){
if(IsCycle((char)(i+'A'), graph, visited))
return true;
}
}
return false;
}

//Recursive DFS to get the expression/construct the tree
private static string GetExpressionHelper(char root, bool[,] graph){
string left = "", right = ""; //if no children, left and right should be empty
for(int i=0;i<26;i++){
if(graph[root-'A',i]){
left = GetExpressionHelper((char)(i+'A'), graph);
for(int j=i+1;j<26;j++){
if(graph[root-'A',j]){
right = GetExpressionHelper((char)(j+'A') ,graph);
break;
}
}
break;
}
}
return "("+root+left+right+")";
}
http://likemyblogger.blogspot.com/2016/02/mj-53-tree-s-expression.html
https://en.wikipedia.org/wiki/S-expression

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