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:- Initialize a stack to keep track of numbers and intermediate results.
- Iterate through each character in the string while keeping track of the current number being processed and the last seen operator.
- 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.
- Sum the stack at the end to obtain the final result.
Detailed Steps in Pseudocode
Step 1: Initialize Variables
-
stack
-
current_number
-
last_operator
Step 2: Iterate Through Characters in String
-
For each character
char
expression
-
If
char
current_number
-
If
char
-
Apply
last_operator
current_number
-
If
last_operator
current_number
stack
-
If
last_operator
-current_number
stack
-
If
last_operator
current_number
-
If
last_operator
current_number
-
Reset
current_number
last_operator
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.