Basic Calculator Ii

To solve this coding challenge, let's break down the problem and understand the requirements and constraints. We need to evaluate a given mathematical expression represented by a string. The expression consists of non-negative integers and the operators '+', '-', '*', '/'. The order of operations should adhere to standard mathematical rules: multiplication and division should be performed before addition and subtraction. Additionally, we should handle spaces in the string and ensure that integer division truncates towards zero.

Explanation

This problem can be solved through an algorithm that parses the expression character by character and evaluates it using a stack-based approach. The stack will help manage the order of operations due to its Last-In-First-Out (LIFO) nature. We will use the following steps:
  1. Initialize a stack to keep track of numbers and intermediate results.
  2. Iterate through each character in the string while keeping track of the current number being processed and the last seen operator.
  3. Process the characters :
    • If the character is a digit, we update the current number.
    • If the character is an operator or the end of the string is reached, perform the operation indicated by the last seen operator on the current number and update the stack accordingly.
    • After processing the operator, reset the current number and update the last seen operator.
  4. Sum the stack at the end to obtain the final result.

Detailed Steps in Pseudocode

Step 1: Initialize Variables
  • stack
    to store intermediate results.
  • current_number
    to build multi-digit numbers.
  • last_operator
    initially set to '+' since the first number is either positive or added.
Step 2: Iterate Through Characters in String
  • For each character
    char
    in the string
    expression
    :
    • If
      char
      is a digit, update
      current_number
      by appending the digit.
    • If
      char
      is an operator or the end of the string:
      • Apply
        last_operator
        on
        current_number
        :
        • If
          last_operator
          is '+', push
          current_number
          onto
          stack
          .
        • If
          last_operator
          is '-', push
          -current_number
          onto
          stack
          .
        • If
          last_operator
          is '*', multiply the top of the stack with
          current_number
          and push the result back.
        • If
          last_operator
          is '/', perform integer division of the top of the stack by
          current_number
          (handle truncation toward zero).
      • Reset
        current_number
        and update
        last_operator
        to
        char
        .
Step 3: Sum the Stack
  • Sum all values in the stack to obtain the final result.

Pseudocode

                                            
# Initialize stack to store intermediate results
stack = []

# Initialize current_number to build multi-digit numbers
current_number = 0

# Initialize last_operator to '+'
last_operator = '+'

# Iterate over each character in the string 'expression'
for each char in expression:
    # If char is a digit, build the current number
    if char is digit:
        current_number = current_number * 10 + integer_value_of(char)

    # If char is an operator or end of string is reached
    if char is operator or end of string:
        # Process based on the last seen operator
        if last_operator is '+':
            push current_number onto stack
        if last_operator is '-':
            push -current_number onto stack
        if last_operator is '*':
            top_number = pop from stack
            push (top_number * current_number) onto stack
        if last_operator is '/':
            top_number = pop from stack
            push (integer_divide top_number by current_number with truncation) onto stack
        
        # Reset current_number
        current_number = 0

        # Update last_operator
        last_operator = char

# Sum all values in the stack to get the final result
result = sum all values in stack

                                        
This thorough explanation and the pseudocode provided should assist in tackling the given coding challenge efficiently. The key is maintaining the stack for intermediate results and managing the precedence of operations correctly.