907.Sum of Subarray Minimums

tags: Medium,Array,DP,Stack

907. Sum of Subarray Minimums

題目描述

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

${10}^9+7$ .

範例

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.

Input: arr = [11,81,94,43,3]
Output: 444

Constraints:

• 1 <= arr.length <=
  $3\ast {10}^4$
• 1 <= arr[i] <=
  $3\ast {10}^4$

解答

Python

class Solution:
    def sumSubarrayMins(self, arr: List[int]) -> int:
        arr = [0] + arr
        stack = [0]
        dp = [0] * len(arr)

        for i, n in enumerate(arr):
            while arr[stack[-1]] > n:
                stack.pop()
            j = stack[-1]
            dp[i] = dp[j] + (i-j) * n
            stack.append(i)
        
        return sum(dp) % 1000000007

Yen-Chi ChenFri, Nov 25, 2022 10:40 PM

class Solution:
    def sumSubarrayMins(self, arr: List[int]) -> int:
        res = 0
        stack = []
        arr = [0] + arr + [0]

        for idx, num in enumerate(arr):
            while stack and arr[stack[-1]] > num:
                cur = stack.pop()
                res += arr[cur] * (idx-cur) * (cur-stack[-1])
            stack.append(idx)
        
        return res% (10**9+7)

DanSat, Jan 20, 2024 08:03 PM

C++

class Solution {
public:
    int sumSubarrayMins(vector<int>& arr) {
        stack<int> s;
        vector<int> dp(arr.size());
        for (int i = 0; i < arr.size(); i++) {
            int n = arr[i];
            while(!s.empty() && arr[s.top()] >= n) {
                s.pop();
            }
            if (s.empty()) {
                dp[i] = (i + 1) * n;
            } else {
                int j = s.top();
                dp[i] = dp[j] + (i - j) * n;
            }
            s.push(i);
        }
        int result = 0;
        for (auto t : dp) {
            result = (result + t) % 1000000007;
        }
        return result;
    }
};

Time:

$O(n)$
Extra Space:

$O(n)$

Yen-Chi ChenFri, Nov 25, 2022 10:40 PM

Reference

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