Stack applications (expression evaluation, backtracking) in Data Structures Theory - Time & Space Complexity

Time Complexity: Stack applications (expression evaluation, backtracking)

O(n)

Understanding Time Complexity

Stacks help solve problems like checking expressions or exploring choices step-by-step.

We want to know how the time needed grows as the input or problem size grows.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

function evaluateExpression(expr) {
  let stack = [];
  for (let char of expr) {
    if (isOperand(char)) {
      stack.push(char);
    } else if (isOperator(char)) {
      let b = stack.pop();
      let a = stack.pop();
      let result = applyOperator(a, b, char);
      stack.push(result);
    }
  }
  return stack.pop();
}
    

This code evaluates a simple expression using a stack by processing each character once.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Looping through each character of the expression once.
• How many times: Exactly once per character, so as many times as the expression length.

How Execution Grows With Input

As the expression gets longer, the number of steps grows directly with its length.

Input Size (n)	Approx. Operations
10	About 10 steps
100	About 100 steps
1000	About 1000 steps

Pattern observation: Doubling the input roughly doubles the work needed.

Final Time Complexity

Time Complexity: O(n)

This means the time to evaluate grows in a straight line with the size of the expression.

Common Mistake

[X] Wrong: "Because there are nested operations, the time must be quadratic or worse."

[OK] Correct: Each character is processed once; the stack operations are quick and do not multiply the work.

Interview Connect

Understanding how stacks handle tasks like expression evaluation or backtracking shows you can manage step-by-step problem solving efficiently.

Self-Check

"What if the expression included nested parentheses requiring recursive evaluation? How would the time complexity change?"