Leetcode #907: Sum of Subarray Minimums
In this guide, we solve Leetcode #907 Sum of Subarray Minimums 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
Given an array of integers arr, find the sum of min(b), where b ranges over every (contiguous) subarray of arr. Since the answer may be large, return the answer modulo 109 + 7.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Stack, Array, Dynamic Programming, Monotonic Stack
Intuition
The problem breaks into overlapping subproblems, so caching results prevents exponential repetition.
A carefully chosen DP state captures exactly what we need to build the final answer.
Approach
Define the DP state and recurrence, then compute states in the correct order.
Optionally compress space once the recurrence is clear.
Steps:
- Choose a DP state definition.
- Write the recurrence and base cases.
- Compute states in the correct order.
Example
Input: arr = [3,1,2,4]
Output: 17
Explanation:
Subarrays are [3], [1], [2], [4], [3,1], [1,2], [2,4], [3,1,2], [1,2,4], [3,1,2,4].
Minimums are 3, 1, 2, 4, 1, 1, 2, 1, 1, 1.
Sum is 17.
Python Solution
class Solution:
def sumSubarrayMins(self, arr: List[int]) -> int:
n = len(arr)
left = [-1] * n
right = [n] * n
stk = []
for i, v in enumerate(arr):
while stk and arr[stk[-1]] >= v:
stk.pop()
if stk:
left[i] = stk[-1]
stk.append(i)
stk = []
for i in range(n - 1, -1, -1):
while stk and arr[stk[-1]] > arr[i]:
stk.pop()
if stk:
right[i] = stk[-1]
stk.append(i)
mod = 10**9 + 7
return sum((i - left[i]) * (right[i] - i) * v for i, v in enumerate(arr)) % mod
Complexity
The time complexity is , and the space complexity is , where is the length of the array . The space complexity is , where is the length of the array .
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.