Program to evaluate one mathematical expression without built-in functions in python

Sometimes we need to evaluate mathematical expressions without using Python's built-in eval() function. This requires parsing the expression manually while respecting operator precedence rules.

So, if the input is like s = "2+3*5/7", then the output will be 4, as 2 + ((3 * 5) / 7) = 4.

Algorithm Overview

To solve this, we follow these steps ?

• Reverse the input string to process from right to left
• Create a get_value() function to parse numbers and handle signs
• Create a get_term() function to handle multiplication and division (higher precedence)
• In the main function, handle addition and subtraction (lower precedence)

Implementation

Let us see the following implementation to get better understanding ?

from math import floor

class Solution:
    def solve(self, s):
        s = list(s[::-1])

        def get_value():
            sign = 1
            if s and s[-1] == "-":
                s.pop()
                sign = -1
            value = 0
            while s and s[-1].isdigit():
                value *= 10
                value += int(s.pop())
            return sign * value

        def get_term():
            term = get_value()
            while s and s[-1] in "*/":
                op = s.pop()
                value = get_value()
                if op == "*":
                    term *= value
                else:
                    term = floor(1.0 * term / value)
            return term

        ans = get_term()
        while s:
            op, term = s.pop(), get_term()
            if op == "+":
                ans += term
            else:
                ans -= term
        return ans

# Test the solution
ob = Solution()
s = "2+3*5/7"
print(f"Expression: {s}")
print(f"Result: {ob.solve(s)}")

The output of the above code is ?

Expression: 2+3*5/7
Result: 4

How It Works

The algorithm works by processing the expression in reverse order:

• get_value(): Extracts numbers and handles negative signs
• get_term(): Processes multiplication and division operations first (higher precedence)
• Main loop: Handles addition and subtraction operations last (lower precedence)

Step-by-Step Execution

For the expression "2+3*5/7":

1. Reverse string: "7/5*3+2"
2. First term: 2
3. Operator: +
4. Second term: 3*5/7 = 15/7 = 2 (integer division)
5. Final result: 2 + 2 = 4

Conclusion

This approach correctly evaluates mathematical expressions by respecting operator precedence without using built-in functions. The key insight is processing the expression in reverse order and handling multiplication/division before addition/subtraction.