The 'seen' set pattern

The seen pattern keeps a set (or map) of values encountered so far as you make a single pass, so you can detect duplicates or find complements in O(1). It converts many nested-loop searches into one linear scan.

Example: two-sum on an unsorted array

Unlike the sorted two-pointer version, an unsorted two-sum uses a map from value to index. For each number, check whether its complement (target - num) is already in the map; if so you are done in one pass.

def two_sum(nums, target):
    seen = {}                       # value -> index
    for i, num in enumerate(nums):
        need = target - num
        if need in seen:
            return [seen[need], i]  # found the complement
        seen[num] = i
    return []

• Contains duplicate: add each element to a set; if it is already there, you found a repeat.
• First unique / first repeat: one pass to count, a second pass to find the target.
• Cycle / revisit detection: track visited nodes or states in a set.