Maximum Subarray Min-Product — LeetCode 1856 Python Solution

MediumStackArrayPrefix SumMonotonic Stack
Problem
#1856
Pattern
Prefix Sum
Reading time
4 min

The problem

The min-product of an array is equal to the minimum value in the array multiplied by the array's sum. For example, the array [3,2,5] (minimum value is 2) has a min-product of 2 * (3+2+5) = 2 * 10 = 20.

Example

Input
nums = [1,2,3,2]
Output
14
Explanation
The maximum min-product is achieved with the subarray [2,3,2] (minimum value is 2).

Python solution

Python
class Solution:
    def maxSumMinProduct(self, nums: List[int]) -> int:
        n = len(nums)
        left = [-1] * n
        right = [n] * n
        stk = []
        for i, x in enumerate(nums):
            while stk and nums[stk[-1]] >= x:
                stk.pop()
            if stk:
                left[i] = stk[-1]
            stk.append(i)
        stk = []
        for i in range(n - 1, -1, -1):
            while stk and nums[stk[-1]] > nums[i]:
                stk.pop()
            if stk:
                right[i] = stk[-1]
            stk.append(i)
        s = list(accumulate(nums, initial=0))
        mod = 10**9 + 7
        return max((s[right[i]] - s[left[i] + 1]) * x for i, x in enumerate(nums)) % mod

Complexity

MeasureComplexity
TimeO(n)
SpaceO(n) auxiliary

Pattern: Prefix Sum

Precompute running totals once so any range query becomes a single subtraction. LeetCode 1856. Maximum Subarray Min-Product is filed here because LeetCode tags it Prefix Sum, which is the vocabulary this hub collects.

The prefix sum guide has the Python template for the pattern and the 157 LeetCode problems that use it.

Related problems

Frequently asked questions

How hard is LeetCode 1856. Maximum Subarray Min-Product?
LeetCode 1856. Maximum Subarray Min-Product is rated Medium on LeetCode.
What is the time complexity of LeetCode 1856. Maximum Subarray Min-Product?
The Python solution on this page runs in O(n).
What is the space complexity of LeetCode 1856. Maximum Subarray Min-Product?
The Python solution on this page uses O(n) auxiliary space.
What topics does LeetCode 1856. Maximum Subarray Min-Product cover?
LeetCode 1856. Maximum Subarray Min-Product is tagged Stack, Array, Prefix Sum and Monotonic Stack on LeetCode.

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