Prompt

You are given an array of strings tokens that represents an arithmetic expression in a Reverse Polish Notation.

Evaluate the expression. Return an integer that represents the value of the expression.

Note that:

  • The valid operators are '+', '-', '*', and '/'.
  • Each operand may be an integer or another expression.
  • The division between two integers always truncates toward zero.
  • There will not be any division by zero.
  • The input represents a valid arithmetic expression in a reverse polish notation.
  • The answer and all the intermediate calculations can be represented in a 32-bit integer.

Examples

  • Example 1:
    • Input: tokens = [“2”,“1”,”+”,“3”,”*”]
    • Output: 9
    • Explanation: ((2 + 1) * 3) = 9
  • Example 2:
    • Input: tokens = [“4”,“13”,“5”,”/”,”+”]\
    • Output: 6
    • Explanation: (4 + (13 / 5)) = 6
  • Example 3:
    • Input: tokens = [“10”,“6”,“9”,“3”,”+”,“-11”,”*”,”/”,”*”,“17”,”+”,“5”,”+”]
    • Output: 22
    • Explanation:
      • ((10 * (6 / ((9 + 3) * -11))) + 17) + 5
      • = ((10 * (6 / (12 * -11))) + 17) + 5
      • = ((10 * (6 / -132)) + 17) + 5
      • = ((10 * 0) + 17) + 5
      • = (0 + 17) + 5
      • = 17 + 5
      • = 22

Solution

In C++

bool is_op(string str) {
	return 
		str == "+" ||
		str == "-" ||
		str == "*" ||
		str == "/";
}
 
int apply_op(int a, int b, char op) {
	switch (op) {
		case '+': return a + b;
		case '*': return a * b;
		case '/': return a / b;
		case '-': return a - b;
	}
	return 0;
}
 
int evalRPN(vector<string>& tokens) {
	stack<int> stack;
	for (const string& str : tokens) {
		if (is_op(str)) {
			int b = stack.top(); stack.pop();
			int a = stack.top(); stack.pop();
			char op = str[0];
			int answer = apply_op(a, b, op);
			stack.push(answer);
		} else {
			stack.push(stoi(str));
		}
	}
	return stack.top();
}

Explanation

Use a stack. Store the answer on the stack as well. Once the entire expression is evaluated, the final remaining element of the stack will be the final answer.

Big O Analysis

Time Complexity

Auxiliary Space Complexity