Two Pointer Fundamentals

Two Pointer Fundamentals — Tech Epitome

The core argument

Two pointers is fast because each iteration discards a candidate forever. If you cannot say which candidate a step eliminates and why it can never be part of the answer, the technique does not apply — it will just be a loop that happens to have two indices.

Concept

The question to answer before you write the loop

Given what I just observed, which side can I rule out entirely? For a sorted pair sum that is: the sum is too small, so the smallest value — already paired with the largest available partner — can never reach the target. It is eliminated.

Two shapes

Shape	Start	Typical use
Opposite direction	Both ends, closing in	Pair sums, symmetry, container problems
Same direction	Both at the front, different speeds	Filtering, compacting, windows

The two arrangements and what they are for.

python

1def opposite_ends(nums, target):2    left, right = 0, len(nums) - 13    while left < right:4        total = nums[left] + nums[right]5        if total == target:6            return [left, right]7        if total < target:8            left += 1     # nums[left] can never work: eliminated9        else:10            right -= 111    return []

Opposite direction

Step through both pointers

When it does not apply

The condition is not monotonic — if moving a pointer can help or hurt unpredictably, you cannot decide which to move.
Original indices are needed but sorting destroyed them.
Every pair must be reported, which is inherently quadratic.

Can you recognise the pattern?

A sorted array, and a question about a pair or a span that satisfies a numeric condition.

Practise

Quick quiz

Two pointers

1In a sorted array you look for a pair summing to a target. The two ends sum to less than the target. Which element is now provably useless?

The larger one, at the right pointer

The smaller one, at the left pointer

The middle element

None — you must check both

2What bug does this loop condition introduce?

left, right = 0, len(nums) - 1
while left <= right:
    ...

It skips the last element

It allows an element to pair with itself

It never terminates

No bug

3Two pointers can be applied to any array, sorted or not, as long as you use two indices.

True

False