Two Sum

Check every pair of numbers. For each i, loop j from i+1 to the end and test whether nums[i] + nums[j] equals target.

for i in 0 .. len(nums) - 1:
    for j in i + 1 .. len(nums) - 1:    # ← the nested loop is the trap
        if nums[i] + nums[j] == target:
            return [i, j]

Before any code, every problem starts with a question. For the Hash Map pattern, that question is:

“How can I solve this in one pass by remembering numbers I’ve already seen?”

Whenever the problem asks 'How do I know I've seen the thing I need?' — that's the hash map pattern. Here, for each number we're asking: 'have I already seen its complement (target − current)?'

Five rungs. Click for the next one only when you genuinely need it — each rung is a stronger nudge than the one before.

Walk through the array once. At each number, ask: 'is its complement already in my hash map?' If yes, return the two indexes. If not, add this number to the map and continue.

seen = empty map  # value -> index

for i, n in enumerate(nums):
    complement = target - n
    if complement in seen:
        return [seen[complement], i]
    seen[n] = i

Trace it with the first example — nums = [2, 7, 11, 15], target = 9.

You've seen the pseudocode and the dry run — try writing the solution yourself in the editor on the right. Run your tests there first. The reveal stays here when you're ready to check.