Incremental Updates (Maintaining results as data changes)

Incremental maintenance updates aggregates as data streams in—running sum, frequency map adjustments, sliding window deltas—instead of recomputing from scratch each time.

Why this shows up in the real world

Stock tickers adjust moving averages per trade. IDE file watchers incrementally update symbol tables.

Core idea (explained for students)

On insert/delete, update O(1) or O(log n) structures: total += x, cnt[x]+=1, tree order-statistics. Pair with lazy propagation when range batch updates exist.

Try this in Python

class RunningAverage:
    def __init__(self) -> None:
        self.s = 0
        self.n = 0

    def add(self, x: float) -> None:
        self.s += x
        self.n += 1

    def mean(self) -> float:
        return self.s / self.n if self.n else 0.0


ra = RunningAverage()
ra.add(10)
ra.add(20)
print(ra.mean())

Common mistakes

• Forgetting to decrement counts when sliding window leaves an element—staleness bugs.
• Integer overflow in rolling sums—use wider types in other languages.

Key takeaways

• Keep symmetric add/remove helpers so updates stay consistent.
• Log rolling state snapshots in tests for tricky streams.