🧠 How to Think Like a Problem Solver – A Practical, Step‑by‑Step System

20 February 2021 - 5 mins read time
Tags: Software Development Programming ProblemSolver LastMinutePrep

Discover how to think like a programmer beyond just writing code.

This post breaks down a practical, repeatable framework to approach problems step‑by‑step — from understanding and restating the question, to spotting constraints, sketching brute‑force ideas, optimizing with patterns and data structures, and analyzing complexity. Learn to see coding challenges not as isolated puzzles, but as opportunities to build deep, transferable problem‑solving skills that make you a better developer, interviewer, and architect.

Instead of jumping straight to code, build a thinking system that helps you approach any coding interview or real‑life problem: ✅ Calmly, ✅ Structurally, ✅ Confidently.

This is the same process senior engineers and strong interviewers actually look for.

✏ The Big Picture: The Thinking Ladder

🧰 Why this system works

• Shows you think before you type.
• Prevents classic mistake: solving wrong question.
• Makes it repeatable: after 10–20 problems, it feels automatic.

✅ Let’s see it in action with a real example

(practical, not just theory)

🧩 Problem statement (variant of Two Sum):

“Given an array nums and integer k, return all unique pairs of numbers whose sum == k.”

🧠 1️⃣ Restate (in your own words)

“So: I have an unsorted list of integers, can be negative, can have duplicates. Need to return all unique pairs [num1, num2] whose sum is exactly k. No indices, just numbers. [2,3] and [3,2] count as the same pair.”

✅ Why restate?

• Confirms understanding before writing code.
• Avoids “solved wrong problem” trap.
• Aligns you with the interviewer.

🔍 2️⃣ Notice constraints

Start simple → refine later:

• n can be large → O(n²) may be too slow.
• Array unsorted.
• Numbers can be negative.
• May have duplicates.
• Output must have unique pairs → [2,3] and [3,2] collapse.

⚡ Tip: don’t freeze trying to list every edge case at once. Start with core, then expand.

🧩 3️⃣ Brute force idea

“For each number, check every other number → nested loop. If sum == k, store the pair.”

• Time: O(n²)
• Space: depends (need to store unique pairs).

⚡ 4️⃣ Better idea (HashSet + pattern)

“Instead of nested loop, scan array once. For each number num, compute complement k - num. If complement already seen → found a pair.”

• Store pair as sorted [min, max] → ensures uniqueness.
• Use a Set to store these pairs.

✏ Ruby code:

require 'set'

def all_unique_pairs(nums, k)
  seen = Set.new
  result = Set.new

  nums.each do |num|
    complement = k - num
    if seen.include?(complement)
      pair = [num, complement].sort
      result << pair
    end
    seen << num
  end

  result.to_a
end

nums = [1, 2, 3, 2, 4, 3, 5]
k = 5
puts all_unique_pairs(nums, k).inspect

⏱ 5️⃣ Complexity analysis

Much better than brute force O(n²).

🔄 6️⃣ Variants & “what if” questions

📌 Why each step matters

🧠 7️⃣ The real superpower:

After 10–20 problems:

• You don’t “memorize solutions.”
• You build a mental template:

“Restate → Constraints → Brute → Optimal → Complexity → Variants”

It becomes automatic, and makes even new unseen problems less scary.

✅ 💡 Final takeaways:

• Think → code → explain → analyze.
• Restate first → solves 90% of confusion.
• Start simple brute → then optimize.
• Variants show depth.