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150. Evaluate Reverse Polish Notation

Description

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.

 

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

 

Constraints:

  • 1 <= tokens.length <= 104
  • tokens[i] is either an operator: "+", "-", "*", or "/", or an integer in the range [-200, 200].

Solutions

Solution 1

Thinking

Reverse Polish notation puts the operator after its operands, so evaluation order is already fixed and we need no parentheses or precedence. \(n\le 10^4\). Push numbers; on an operator pop two values, compute, and push back. The stack holds pending intermediates; one value remains.

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import operator


class Solution:
    def evalRPN(self, tokens: List[str]) -> int:
        opt = {
            "+": operator.add,
            "-": operator.sub,
            "*": operator.mul,
            "/": operator.truediv,
        }
        s = []
        for token in tokens:
            if token in opt:
                s.append(int(opt[token](s.pop(-2), s.pop(-1))))
            else:
                s.append(int(token))
        return s[0]

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class Solution {
    public int evalRPN(String[] tokens) {
        Deque<Integer> stk = new ArrayDeque<>();
        for (String t : tokens) {
            if (t.length() > 1 || Character.isDigit(t.charAt(0))) {
                stk.push(Integer.parseInt(t));
            } else {
                int y = stk.pop();
                int x = stk.pop();
                switch (t) {
                case "+":
                    stk.push(x + y);
                    break;
                case "-":
                    stk.push(x - y);
                    break;
                case "*":
                    stk.push(x * y);
                    break;
                default:
                    stk.push(x / y);
                    break;
                }
            }
        }
        return stk.pop();
    }
}

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class Solution {
public:
    int evalRPN(vector<string>& tokens) {
        stack<int> stk;
        for (auto& t : tokens) {
            if (t.size() > 1 || isdigit(t[0])) {
                stk.push(stoi(t));
            } else {
                int y = stk.top();
                stk.pop();
                int x = stk.top();
                stk.pop();
                if (t[0] == '+')
                    stk.push(x + y);
                else if (t[0] == '-')
                    stk.push(x - y);
                else if (t[0] == '*')
                    stk.push(x * y);
                else
                    stk.push(x / y);
            }
        }
        return stk.top();
    }
};

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func evalRPN(tokens []string) int {
    // https://github.com/emirpasic/gods#arraystack
    stk := arraystack.New()
    for _, token := range tokens {
        if len(token) > 1 || token[0] >= '0' && token[0] <= '9' {
            num, _ := strconv.Atoi(token)
            stk.Push(num)
        } else {
            y := popInt(stk)
            x := popInt(stk)
            switch token {
            case "+":
                stk.Push(x + y)
            case "-":
                stk.Push(x - y)
            case "*":
                stk.Push(x * y)
            default:
                stk.Push(x / y)
            }
        }
    }
    return popInt(stk)
}

func popInt(stack *arraystack.Stack) int {
    v, _ := stack.Pop()
    return v.(int)
}

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function evalRPN(tokens: string[]): number {
    const stack = [];
    for (const token of tokens) {
        if (/\d/.test(token)) {
            stack.push(Number(token));
        } else {
            const a = stack.pop();
            const b = stack.pop();
            switch (token) {
                case '+':
                    stack.push(b + a);
                    break;
                case '-':
                    stack.push(b - a);
                    break;
                case '*':
                    stack.push(b * a);
                    break;
                case '/':
                    stack.push(~~(b / a));
                    break;
            }
        }
    }
    return stack[0];
}

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impl Solution {
    pub fn eval_rpn(tokens: Vec<String>) -> i32 {
        let mut stack = vec![];
        for token in tokens {
            match token.parse() {
                Ok(num) => stack.push(num),
                Err(_) => {
                    let a = stack.pop().unwrap();
                    let b = stack.pop().unwrap();
                    stack.push(match token.as_str() {
                        "+" => b + a,
                        "-" => b - a,
                        "*" => b * a,
                        "/" => b / a,
                        _ => 0,
                    });
                }
            }
        }
        stack[0]
    }
}

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public class Solution {
    public int EvalRPN(string[] tokens) {
        var stack = new Stack<int>();
        foreach (var token in tokens) {
            switch (token) {
                case "+":
                    stack.Push(stack.Pop() + stack.Pop());
                    break;
                case "-":
                    stack.Push(-stack.Pop() + stack.Pop());
                    break;
                case "*":
                    stack.Push(stack.Pop() * stack.Pop());
                    break;
                case "/":
                    var right = stack.Pop();
                    stack.Push(stack.Pop() / right);
                    break;
                default:
                    stack.Push(int.Parse(token));
                    break;
            }
        }
        return stack.Pop();
    }
}

Solution 2

Thinking

Solution 1 maps operators to functions. This version mutates the stack top in place, branching on the four operators, and watches operand order and truncation toward zero. Same structure, no function table.

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class Solution:
    def evalRPN(self, tokens: List[str]) -> int:
        nums = []
        for t in tokens:
            if len(t) > 1 or t.isdigit():
                nums.append(int(t))
            else:
                if t == "+":
                    nums[-2] += nums[-1]
                elif t == "-":
                    nums[-2] -= nums[-1]
                elif t == "*":
                    nums[-2] *= nums[-1]
                else:
                    nums[-2] = int(nums[-2] / nums[-1])
                nums.pop()
        return nums[0]

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