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How do you find the maximum product subarray?

Q: How do you find the maximum product subarray?

**Intuition.** Unlike a max *sum*, products flip sign: a large **negative** can become the maximum the instant it's multiplied by another negative. So at each index track **both** the max and the min product ending there. When the current number is negative, the roles swap before you extend. track max AND min; a negative makes the min become the max -2 <rect x="134" y="50" width="44" height=

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Explain max product subarray.

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Track running max and min

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def max_product(nums):
    best = cur_max = cur_min = nums[0]
    for x in nums[1:]:
        if x < 0:
            cur_max, cur_min = cur_min, cur_max     # negative swaps roles
        cur_max = max(x, cur_max * x)
        cur_min = min(x, cur_min * x)
        best = max(best, cur_max)
    return best


# --- demo ---
print(max_product([2, 3, -2, 4]))   # 6   ([2,3])
print(max_product([-2, 0, -1]))     # 0
print(max_product([-2, 3, -4]))     # 24  (all three)

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