Infix expressions evaluated in DSA?

Question

How can we evaluate infix expressions in Data Structures and Algorithms (DSA)?

Jayraj Chhaya · Answer

To evaluate infix expressions, we generally follow a two-step process: conversion to postfix notation (also known as Reverse Polish Notation) and then evaluation of the postfix expression. Conversion to Postfix : This can be achieved using the Shunting Yard algorithm developed by Edsger Dijkstra. The algorithm utilizes a stack to hold operators and ensures that the output maintains the correct order of operations (precedence and associativity). def infix_to_postfix(expression): precedence = {'+': 1, '-': 1, '*': 2, '/': 2, '^': 3} output = [] stack = [] for char in expression: if char.isalnum(): # If the character is an operand output.append(char) elif char in precedence: # If the character is an operator while (stack and stack[-1] != '(' and precedence[char] Evaluation of Postfix : Once we have the postfix expression, we can evaluate it using another stack. Each operand is pushed onto the stack, and when an operator is encountered, the required number of operands is popped from the stack, the operation is performed, and the result is pushed back onto the stack. def evaluate_postfix(expression): stack = [] for char in expression: if char.isdigit(): # If the character is an operand stack.append(int(char)) else: # The character is an operator b = stack.pop() a = stack.pop() if char == '+': stack.append(a + b) elif char == '-': stack.append(a - b) elif char == '*': stack.append(a * b) elif char == '/': stack.append(a / b) return stack[0]

Infix expressions evaluated in DSA?

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