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What is a monotonic stack and when do you use it?

Q: What is a monotonic stack and when do you use it?

**Intuition.** A **monotonic stack** keeps its elements sorted (increasing or decreasing) by **popping** any element that would break the order before pushing the new one. That popping moment is exactly when you've found a "next greater/smaller element," which is why it solves those problems in a single O(n) pass. daily temperatures: pop colder days when a warmer one arrives 75 <rect x="100"

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Explain monotonic stacks.

stackmonotonic

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Daily temperatures (next greater)

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def daily_temperatures(temps):
    n = len(temps)
    answer = [0] * n
    stack = []                          # indices, temperatures decreasing
    for i, t in enumerate(temps):
        while stack and temps[stack[-1]] < t:
            j = stack.pop()
            answer[j] = i - j           # days until a warmer temperature
        stack.append(i)
    return answer


# --- demo ---
print(daily_temperatures([73, 74, 75, 71, 69, 72, 76, 73]))
# [1, 1, 4, 2, 1, 1, 0, 0]

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