Problem statement
Evaluate the value of an arithmetic expression in Reverse Polish Notation.
Valid operators are +, -, , and */. Each operand may be an integer or another expression.
Note that division between two integers should truncate toward zero.
It is guaranteed that the given RPN expression is always valid. That means the expression would always evaluate to a result, and there will not be any division by zero operation.
Problem statement taken from: https://leetcode.com/problems/evaluate-reverse-polish-notation
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 <= 10^4
- tokens[i] is either an operator: "+", "-", "*", or "/", or an integer in the range [-200, 200]
Explanation
Reverse Polish Notation is a mathematical notation in which operators follow their operands.
The basic approach is using the stack. Let's check the algorithm directly:
- create stack st
initialize int op1, op2
- loop for i = 0; i < tokens.size; i++
- if tokens[i] != "+" && tokens[i] != "-" && tokens[i] != "*" && tokens[i] != "/"
- push to stack st.push(tokens[i])
- else
- set op2 = st.pop()
set op1 = st.pop()
- if tokens[i] == "+"
- st.push(op1 + op2)
- else if tokens[i] == "-"
- st.push(op1 - op2)
- else if tokens[i] == "*"
- st.push(op1 * op2)
- else
- st.push(op1 / op2)
- for end
- return st.top()
This function's time complexity is O(N), and the space complexity is O(N).
Let's check our solutions in C++, Golang, and Javascript.
C++ solution
typedef long long ll;
class Solution {
public:
int evalRPN(vector<string>& tokens) {
stack<ll> st;
ll op1, op2;
for(int i = 0; i < tokens.size(); i++) {
if(tokens[i] != "+" && tokens[i] != "-" && tokens[i] != "*" && tokens[i] != "/") {
st.push(stol(tokens[i]));
} else {
op2 = st.top();
st.pop();
op1 = st.top();
st.pop();
if(tokens[i] == "+")
st.push(op1 + op2);
else if(tokens[i] == "-")
st.push(op1 - op2);
else if(tokens[i] == "*")
st.push(op1 * op2);
else
st.push(op1 / op2);
}
}
return (int) st.top();
}
};
Golang solution
func evalRPN(tokens []string) int {
st := []int{}
for _, token := range tokens {
if token == "+" {
st[len(st) - 2] += st[len(st) - 1]
st = st[:len(st) - 1]
} else if token == "-" {
st[len(st) - 2] -= st[len(st) - 1]
st = st[:len(st) - 1]
} else if token == "*" {
st[len(st) - 2] *= st[len(st) - 1]
st = st[:len(st) - 1]
} else if token == "/" {
st[len(st) - 2] /= st[len(st) - 1]
st = st[:len(st) - 1]
} else {
num, _ := strconv.Atoi(token)
st = append(st, num)
}
}
return st[0]
}
Javascript solution
var evalRPN = function(tokens) {
let st = [];
let op1, op2;
for(let i = 0; i < tokens.length; i++) {
if(tokens[i] != "+" && tokens[i] != "-" && tokens[i] != "*" && tokens[i] != "/") {
st.push(parseInt(tokens[i]));
} else {
op2 = st.pop();
op1 = st.pop();
if(tokens[i] === "+")
st.push(op1 + op2);
else if(tokens[i] === "-")
st.push(op1 - op2);
else if(tokens[i] === "*")
st.push(op1 * op2);
else
st.push(op1 / op2 | 0);
}
}
return st[0];
};
Let's dry-run our algorithm to see how the solution works.
Input: tokens = ["2", "1", "+", "3", "*"]
Step 1: stack<ll> st
int op1, op2
Step 2: loop for int i = 0; i < tokens.size()
i < tokens.size()
0 < 5
true
if tokens[i] != "+" && tokens[i] != "-" && tokens[i] != "*" && tokens[i] != "/"
tokens[0] is "2"
true
st.push(stoi(tokens[i]))
st.push(stoi(tokens[0]))
st.push(2)
st = [2]
i++
i = 1
Step 3: loop for i < tokens.size()
1 < 5
true
if tokens[i] != "+" && tokens[i] != "-" && tokens[i] != "*" && tokens[i] != "/"
tokens[1] is "1"
true
st.push(stoi(tokens[i]))
st.push(stoi(tokens[1]))
st.push(1)
st = [2, 1]
i++
i = 2
Step 4: loop for i < tokens.size()
2 < 5
true
if tokens[i] != "+" && tokens[i] != "-" && tokens[i] != "*" && tokens[i] != "/"
tokens[1] is "+"
false
else
op2 = st.top()
= 1
st.pop()
st = [2]
op1 = st.top()
= 2
st.pop()
st = []
if tokens[i] == "+"
true
st.push(op1 + op2)
st.push(2 + 1)
st.push(3)
st = [3]
i++
i = 3
Step 5: loop for i < tokens.size()
3 < 5
true
if tokens[i] != "+" && tokens[i] != "-" && tokens[i] != "*" && tokens[i] != "/"
tokens[3] is "3"
true
st.push(stoi(tokens[i]))
st.push(stoi(tokens[3]))
st.push(3)
st = [3, 3]
i++
i = 4
Step 6: loop for i < tokens.size()
4 < 5
true
if tokens[i] != "+" && tokens[i] != "-" && tokens[i] != "*" && tokens[i] != "/"
tokens[4] is "*"
false
else
op2 = st.top()
= 3
st.pop()
st = [3]
op1 = st.top()
= 3
st.pop()
st = []
if tokens[i] == "+"
false
else if tokens[i] == "-"
false
else if tokens[i] == "*"
st.push(op1 * op2)
st.push(3 * 3)
st.push(9)
st = [9]
i++
i = 5
Step 7: loop for i < tokens.size()
5 < 5
false
Step 8: return st[0]
We return the answer as 9.
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