Leetcode #1856: Maximum Subarray Min-Product
In this guide, we solve Leetcode #1856 Maximum Subarray Min-Product in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
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.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Stack, Array, Prefix Sum, Monotonic Stack
Intuition
We need the next greater or smaller element efficiently, which is exactly what a monotonic stack offers.
Each element is pushed and popped at most once, yielding a linear-time scan.
Approach
Maintain a stack that is either increasing or decreasing, depending on the query.
When the invariant is broken, pop and resolve answers for those indices.
Steps:
- Scan elements once.
- Pop while the monotonic condition is violated.
- Use stack indices to update answers.
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).
2 * (2+3+2) = 2 * 7 = 14.
Python Solution
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
The time complexity is , and the space complexity is . The space complexity is .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.