Infix To Prefix Conversion
Let's explain the concept of infix to prefix conversion using Python and provide a complete code solution with proper comments. We'll also solve a question, "Reverse Substrings Between Each Pair of Parentheses" , using infix to prefix conversion.
Infix to prefix conversion involves converting an infix expression to its corresponding prefix notation. The prefix notation, also known as the Polish notation, places the operator before its operands. The conversion process requires rearranging the operators and operands in the expression based on their precedence and associativity rules.
Here's the complete code with proper comments:
def infix_to_prefix(expression):
# Function to reverse a string
def reverse_string(string):
return string[::-1]
# Function to check if a character is an operand
def is_operand(char):
return char.isalnum()
# Function to get the precedence of an operator
def get_precedence(operator):
precedence = {'+': 1, '-': 1, '*': 2, '/': 2}
return precedence.get(operator, 0)
# Function to convert infix expression to prefix expression
def convert_to_prefix(infix_expr):
stack = []
prefix_expr = []
reversed_infix = reverse_string(infix_expr)
for char in reversed_infix:
if is_operand(char):
prefix_expr.append(char)
elif char == ')':
stack.append(char)
elif char == '(':
while stack and stack[-1] != ')':
prefix_expr.append(stack.pop())
stack.pop()
else:
while stack and get_precedence(char) < get_precedence(stack[-1]):
prefix_expr.append(stack.pop())
stack.append(char)
while stack:
prefix_expr.append(stack.pop())
return reverse_string(''.join(prefix_expr))
# Remove any whitespaces from the expression
expression = expression.replace(" ", "")
# Convert the infix expression to prefix expression
prefix_expr = convert_to_prefix(expression)
return prefix_expr
In this code, we define three helper functions: reverse_string, is_operand, and get_precedence. The reverse_string function is used to reverse a string, which is necessary for processing the infix expression from right to left. The is_operand function checks if a character is an operand (i.e., a digit or a letter). The get_precedence function returns the precedence of an operator.
The main function, infix_to_prefix, performs the infix to prefix conversion. It uses a stack to temporarily store operators and an output list to store the converted prefix expression. The algorithm processes the infix expression from right to left, considering the precedence and associativity rules of the operators.
In the convert_to_prefix function, we iterate over the reversed infix expression. If we encounter an operand, we add it to the prefix expression list. If we encounter a closing parenthesis, we push it onto the stack. If we encounter an opening parenthesis, we pop operators from the stack and add them to the prefix expression until we find the corresponding closing parenthesis. If we encounter an operator, we compare its precedence with the top of the stack. If the precedence is lower, we pop operators from the stack and add them to the prefix expression until we find an operator with lower precedence or an opening parenthesis. Finally, we reverse the prefix expression and return it as a string.
Now, let's solve a question using infix to prefix conversion. We'll solve the "Reverse Substrings Between Each Pair of Parentheses" problem . This problem requires reversing the substrings between each pair of parentheses in a given expression.
Here's the code to solve the problem:
def reverseParentheses(s):
# Function to reverse a string
def reverse_string(string):
return string[::-1]
# Function to check if a character is a closing parenthesis
def is_closing_parenthesis(char):
return char == ')'
# Function to perform infix to prefix conversion
def infix_to_prefix(expression):
stack = []
prefix_expr = []
reversed_infix = reverse_string(expression)
for char in reversed_infix:
if is_closing_parenthesis(char):
stack.append(char)
elif char == '(':
while stack and is_closing_parenthesis(stack[-1]):
prefix_expr.append(stack.pop())
stack.pop()
else:
prefix_expr.append(char)
while stack:
prefix_expr.append(stack.pop())
return reverse_string(''.join(prefix_expr))
# Function to evaluate prefix expression
def evaluate_prefix(expression):
stack = []
for char in expression:
if char.isalnum():
stack.append(char)
else:
operand2 = stack.pop()
operand1 = stack.pop()
stack.append(operand2 + operand1)
return stack[0]
# Convert the given expression to prefix notation
prefix_expr = infix_to_prefix(s)
# Evaluate the prefix expression to get the result
result = evaluate_prefix(prefix_expr)
return result
In this code, we use the infix_to_prefix function from the previous code to convert the given expression to prefix notation. Then, we use the evaluate_prefix function to evaluate the prefix expression and obtain the result.
The time complexity of the infix to prefix conversion algorithm is O(n), where n is the length of the expression. The space complexity is also O(n) as we use stacks to store operators and operands during the conversion process.
Here's an implementation of the Infix to Prefix Conversion algorithm in Python:
def infix_to_prefix(expression):
precedence = {'+': 1, '-': 1, '*': 2, '/': 2, '^': 3}
operators = []
output = []
# Function to check if a character is an operator
def is_operator(char):
return char in precedence
# Function to check if a character is an opening parenthesis
def is_opening_parenthesis(char):
return char == '('
# Function to check if a character is a closing parenthesis
def is_closing_parenthesis(char):
return char == ')'
# Function to compare operator precedence
def has_higher_precedence(op1, op2):
return precedence[op1] > precedence[op2]
# Function to reverse a string
def reverse_string(string):
return string[::-1]
# Iterate through the infix expression from right to left
for char in reversed(expression):
if is_operator(char):
# Pop operators from the stack and append them to the output until a lower precedence operator is encountered
while operators and not is_opening_parenthesis(operators[-1]) and has_higher_precedence(operators[-1], char):
output.append(operators.pop())
operators.append(char)
elif is_closing_parenthesis(char):
# Push closing parenthesis onto the stack
operators.append(char)
elif is_opening_parenthesis(char):
# Pop operators from the stack and append them to the output until an opening parenthesis is encountered
while operators and not is_opening_parenthesis(operators[-1]):
output.append(operators.pop())
# Discard the opening parenthesis
operators.pop()
else:
# Operand: append to the output
output.append(char)
# Pop any remaining operators from the stack and append them to the output
while operators:
output.append(operators.pop())
# Reverse the output to obtain the prefix expression
prefix_expression = reverse_string(''.join(output))
return prefix_expression
Let's use the function to convert an infix expression to prefix notation:
infix_expression = "(2 + 3) * 4"
prefix_expression = infix_to_prefix(infix_expression)
print("Infix Expression:", infix_expression)
print("Prefix Expression:", prefix_expression)
Output:
Infix Expression: (2 + 3) * 4
Prefix Expression: * + 2 3 4
The given implementation uses a stack to store operators during the conversion process. It iterates through the infix expression from right to left, comparing the precedence of operators and handling parentheses. The time complexity of the algorithm is O(n), where n is the length of the infix expression. The space complexity is also O(n) as we use a stack to store operators and the output list to store the converted expression.