Massive Algorithms: Lintcode - Expression Tree Build

Lintcode - Expression Tree Build

[Lintcode] Expression Tree Build - F_G - 博客园

The structure of Expression Tree is a binary tree to evaluate certain expressions.
All leaves of the Expression Tree have an number string value. All non-leaves of the Expression Tree have an operator string value.

Now, given an expression array, build the expression tree of this expression, return the root of this expression tree.

Example

For the expression (2*6-(23+7)/(1+2)) (which can be represented by ["2" "*" "6" "-" "(" "23" "+" "7" ")" "/" "(" "1" "+" "2" ")"]).
The expression tree will be like

                 [ - ]
             /          \
        [ * ]              [ / ]
      /     \           /         \
    [ 2 ]  [ 6 ]      [ + ]        [ + ]
                     /    \       /      \
                   [ 23 ][ 7 ] [ 1 ]   [ 2 ] .

After building the tree, you just need to return root node [-].

https://wxx5433.gitbooks.io/interview-preparation/content/part_ii_leetcode_lintcode/stack/expression_tree_build.html

  public ExpressionTreeNode build(String[] expression) {
    if (expression == null || expression.length == 0) {
      return null;
    }
    Stack<ExpressionTreeNode> numStack = new Stack<>();
    Stack<String> opStack = new Stack<>();
    for (String token : expression) {
      if (isNumber(token)) {
        numStack.push(new ExpressionTreeNode(token));
      } else if (token.equals("(")) {
        opStack.push(token);
      } else if (token.equals(")")) {
        while (!opStack.peek().equals("(")) {
          numStack.push(buildNode(numStack.pop(), numStack.pop(), opStack.pop()));
        }
        opStack.pop();
      } else {
        while (!opStack.isEmpty() && getPriority(opStack.peek()) >= getPriority(token)) {
          numStack.push(buildNode(numStack.pop(), numStack.pop(), opStack.pop()));
        }
        opStack.push(token);
      }
    }
    while (!opStack.isEmpty()) {
      numStack.push(buildNode(numStack.pop(), numStack.pop(), opStack.pop()));
    }
    return numStack.isEmpty() ? null : numStack.pop();
  }

  private boolean isNumber(String token) {
    return Character.isDigit(token.charAt(0));
  }

  private int getPriority(String op) {
    if (op.equals("(")) {
      return 0;
    } else if (op.equals("+") || op.equals("-")) {
      return 1;
    } else {
      return 2;
    }
  }

  private ExpressionTreeNode buildNode(ExpressionTreeNode node2, ExpressionTreeNode node1, String op) {
    ExpressionTreeNode root = new ExpressionTreeNode(op);
    root.left = node1;
    root.right = node2;
    return root;
  }

https://xmruibi.gitbooks.io/interview-preparation-notes/content/Algorithm/Expression/ExpressionTreeBuild.html

Two stacks, one is only for operator, another is for build the result tree.
The idea is similar with RPN.
One pass the expression array, when it get a operand, insert as new treenode in result tree, when it get a operator, insert as new treenode in operator tree and compare the priority, if the current is less than stack top element, build a new node with operator in stack top and two node from result tree as its right and left child, then insert back to result tree with this new node.

    public ExpressionTreeNode build(String[] expression) {
        Stack<ExpressionTreeNode> ops = new Stack<>();
        Stack<ExpressionTreeNode> data = new Stack<>();
        for( int i = 0; i < expression.length; i++) {
            String str = expression[i];
            if(str.equals("+") || str.equals("-") ||str.equals("*") ||str.equals("/")) {
                while(!ops.isEmpty() && operatorLevel(ops.peek().symbol) >= operatorLevel(str)) {
                    newNodeGtr(ops, data);
                }
                ops.push(new ExpressionTreeNode(str));
            }else if(str.equals("(")){
                ops.push(new ExpressionTreeNode(str));
            }else if(str.equals(")")) {
                while(!ops.isEmpty() && !ops.peek().symbol.equals("("))
                    newNodeGtr(ops, data);
                if(!ops.isEmpty()) 
                    ops.pop(); // pop the "("
            }else
                data.push(new ExpressionTreeNode(str));
        }

        while(!ops.isEmpty())
            newNodeGtr(ops, data);

        return data.isEmpty()? null : data.pop();
    }

    private void newNodeGtr(Stack<ExpressionTreeNode> ops, Stack<ExpressionTreeNode> data) {
        if(ops.isEmpty())
            return;
        ExpressionTreeNode node = ops.pop();
        node.right = data.isEmpty() ? null : data.pop();
        node.left = data.isEmpty() ? null : data.pop();
        data.push(node);
    }

    private int operatorLevel(String op) {
        if(op.equals("+") || op.equals("-")) 
            return 1;
        else if(op.equals("*") ||op.equals("/"))
            return 2;
        else
            return 0;
    }

原先计算的结果是当做一个数字push到数据栈当中的，现在变成了节点。而且这里的特点是，根部没有计算问题，只需要在优先级的基础上构建表达式树

3  * public class ExpressionTreeNode {
 4  *     public String symbol;
 5  *     public ExpressionTreeNode left, right;
 6  *     public ExpressionTreeNode(String symbol) {
 7  *         this.symbol = symbol;
 8  *         this.left = this.right = null;
 9  *     }
10  * }
19     public ExpressionTreeNode build(String[] expression) {
20         // write your code here
21         Stack<ExpressionTreeNode> op   = new Stack<ExpressionTreeNode>();
22         Stack<ExpressionTreeNode> data = new Stack<ExpressionTreeNode>();
23         for(int i=0;i<expression.length;i++){
24             String tmp = expression[i];
25             char firstc = tmp.charAt(0);
26             if(!(firstc<='9'&&firstc>='0')){
27                 //System.out.println("get op "+ tmp);
28                 switch(firstc){
29                     case '(':
30                         ExpressionTreeNode node = new ExpressionTreeNode(tmp);
31                         op.push(node);
32                         break;
33                     case '+':
34                     case '-':
35                         while(!op.isEmpty()&&op.peek().symbol.charAt(0)!='('){
36                             ExpressionTreeNode opnode = op.pop();
37                             ExpressionTreeNode data1 = data.pop();
38                             ExpressionTreeNode data2 = data.pop();
39                             opnode.left = data2;
40                             opnode.right = data1;
41                             data.push(opnode);
42                         }
43                         ExpressionTreeNode node2 = new ExpressionTreeNode(tmp);
44                         op.push(node2);
45                         break;
46                     case '*':
47                     case '/':
48                         while(!op.isEmpty()&&(op.peek().symbol.charAt(0)=='*'||op.peek().symbol.charAt(0)=='/')){
49                             ExpressionTreeNode opnode = op.pop();
50                             ExpressionTreeNode data1 = data.pop();
51                             ExpressionTreeNode data2 = data.pop();
52                             opnode.left = data2;
53                             opnode.right = data1;
54                             data.push(opnode);
55                         }
56                         ExpressionTreeNode node3 = new ExpressionTreeNode(tmp);
57                         op.push(node3);
58                         break;
59                     case ')':
60                         while(op.peek().symbol.charAt(0)!='('){
61                             ExpressionTreeNode opnode = op.pop();
62                             ExpressionTreeNode data1 = data.pop();
63                             ExpressionTreeNode data2 = data.pop();
64                             opnode.left = data2;
65                             opnode.right = data1;
66                             data.push(opnode);
67                         }
68                         op.pop();
69                 }
70             }else{
71                 //System.out.println("add data "+tmp);
72                 ExpressionTreeNode data1 = new ExpressionTreeNode(tmp);
73                 data.push(data1);
74             }
75         }
76         while(!op.isEmpty()){
77             ExpressionTreeNode opnode = op.pop();
78             ExpressionTreeNode data1 = data.pop();
79             ExpressionTreeNode data2 = data.pop();
80             opnode.left = data2;
81             opnode.right = data1;
82             data.push(opnode);
83         }
84         if(data.isEmpty()) return null;
85         return data.pop();
86     }

X. https://github.com/nanwan03/lintcode/blob/master/Expression%20Tree%20Build.java
public ExpressionTreeNode build(String[] expression) {
if (expression == null || expression.length == 0) {
return null;
}
String ops = "()+-*/";
List<String> rpn = getRPN(expression, ops);
ExpressionTreeNode root = buildTree(rpn, ops);
return root;
}
private ExpressionTreeNode buildTree(List<String> rpn, String ops) {
Stack<ExpressionTreeNode> stack = new Stack<ExpressionTreeNode>();
for (String str : rpn) {
if (str.equals("+") || str.equals("-") || str.equals("*") || str.equals("/")) {
ExpressionTreeNode newNode = new ExpressionTreeNode(str);
ExpressionTreeNode right = stack.pop();
ExpressionTreeNode left = stack.pop();
newNode.left = left;
newNode.right = right;
stack.push(newNode);
} else {
stack.push(new ExpressionTreeNode(str));
}
}
return stack.isEmpty() ? null : stack.pop();
}
private List<String> getRPN(String[] expression, String ops) {
List<String> rpn = new ArrayList<String>();
Stack<String> stack = new Stack<String>();
for (String str : expression) {
if (str.equals("(") || str.equals(")") || str.equals("+") || str.equals("-") || str.equals("*") || str.equals("/")) {
if (stack.isEmpty()) {
stack.push(str);
} else if (str.equals("(")) {
stack.push(str);
} else if (str.equals(")")) {
while (!stack.isEmpty()) {
String op = stack.pop();
if (op.equals("(")) {
break;
}
rpn.add(op);
}
} else {
if (mycmp(stack.peek(), str) == 1) {
stack.push(str);
} else {
while (!stack.isEmpty() && mycmp(stack.peek(), str) == 0) {
rpn.add(stack.pop());
}
stack.push(str);
}
}
} else {
rpn.add(str);
}
}
while (!stack.isEmpty()) {
rpn.add(stack.pop());
}
return rpn;
}
private int mycmp(String a, String b) {
if(b.equals("(")) {
return 1;//左括号直接入栈
} else if((b.equals("*") || b.equals("/")) &&(a.equals("+") || a.equals("-") || a.equals("("))) {
return 1;//*、/优先级高于+、-、(，入栈
} else if((b.equals("+") || b.equals("-")) && (a.equals("("))) {
return 1;//+、-优先级高于(，入栈
} else {
return 0;
}
}

X. http://www.jiuzhang.com/solutions/expression-tree-build/

class TreeNode {
 public int val;
 public String s;
 public ExpressionTreeNode root; 

 public TreeNode(int val, String ss) {
  this.val = val;
  this.root = new ExpressionTreeNode(ss);
 }

}

public class Solution {

 int get(String a, Integer base) {
  if (a.equals("+") || a.equals("-"))
   return 1 + base;
  if (a.equals("*") || a.equals("/"))
   return 2 + base;

  return Integer.MAX_VALUE;
 }



 public ExpressionTreeNode build(String[] expression) {
  // write your code here
  Stack<TreeNode> stack = new Stack<TreeNode>();
  TreeNode root = null;
  int val = 0;
  Integer base = 0;
  for (int i = 0; i <= expression.length; i++) {
   if(i != expression.length)
   {
    
    if (expression[i].equals("(")) {
     base += 10;
     continue;
    }
    if (expression[i].equals(")")) {
     base -= 10;
     continue;
    }
    val = get(expression[i], base);

   }
   TreeNode right = i == expression.length ? new TreeNode(
     Integer.MIN_VALUE, "") : new TreeNode(val,
     expression[i]);
   while (!stack.isEmpty()) {
    if (right.val <= stack.peek().val) {
     TreeNode nodeNow = stack.pop();

     if (stack.isEmpty()) {
      right.root.left = nodeNow.root;

     } else {
      TreeNode left = stack.peek();
      if (left.val < right.val) {
       right.root.left = nodeNow.root;
      } else {
       left.root.right = nodeNow.root;
      }
     }
    } else {
     break;
    }
   }
   stack.push(right);
  }

 
  
  return stack.peek().root.left;
 }


};

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Lintcode - Expression Tree Build

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