README_EN.md

907. Sum of Subarray Minimums

中文文档

Description

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.

 

Example 1:

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.

Example 2:

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

 

Constraints:

• 1 <= arr.length <= 3 * 104
• 1 <= arr[i] <= 3 * 104

Solutions

Python3

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

Java

class Solution {
    public int sumSubarrayMins(int[] arr) {
        int n = arr.length;
        int[] left = new int[n];
        int[] right = new int[n];
        Arrays.fill(left, -1);
        Arrays.fill(right, n);
        Deque<Integer> stk = new ArrayDeque<>();
        for (int i = 0; i < n; ++i) {
            while (!stk.isEmpty() && arr[stk.peek()] >= arr[i]) {
                stk.pop();
            }
            if (!stk.isEmpty()) {
                left[i] = stk.peek();
            }
            stk.push(i);
        }
        stk.clear();
        for (int i = n - 1; i >= 0; --i) {
            while (!stk.isEmpty() && arr[stk.peek()] > arr[i]) {
                stk.pop();
            }
            if (!stk.isEmpty()) {
                right[i] = stk.peek();
            }
            stk.push(i);
        }
        int mod = (int) 1e9 + 7;
        long ans = 0;
        for (int i = 0; i < n; ++i) {
            ans += (long) (i - left[i]) * (right[i] - i) % mod * arr[i] % mod;
            ans %= mod;
        }
        return (int) ans;
    }
}

C++

using ll = long long;
const int mod = 1e9 + 7;

class Solution {
public:
    int sumSubarrayMins(vector<int>& arr) {
        int n = arr.size();
        vector<int> left(n, -1);
        vector<int> right(n, n);
        stack<int> stk;
        for (int i = 0; i < n; ++i) {
            while (!stk.empty() && arr[stk.top()] >= arr[i]) stk.pop();
            if (!stk.empty()) left[i] = stk.top();
            stk.push(i);
        }
        stk = stack<int>();
        for (int i = n - 1; i >= 0; --i) {
            while (!stk.empty() && arr[stk.top()] > arr[i]) stk.pop();
            if (!stk.empty()) right[i] = stk.top();
            stk.push(i);
        }
        ll ans = 0;
        for (int i = 0; i < n; ++i) {
            ans += (ll)(i - left[i]) * (right[i] - i) * arr[i] % mod;
            ans %= mod;
        }
        return ans;
    }
};

Go

func sumSubarrayMins(arr []int) int {
	mod := int(1e9) + 7
	n := len(arr)
	left := make([]int, n)
	right := make([]int, n)
	for i := range left {
		left[i] = -1
		right[i] = n
	}
	stk := []int{}
	for i, v := range arr {
		for len(stk) > 0 && arr[stk[len(stk)-1]] >= v {
			stk = stk[:len(stk)-1]
		}
		if len(stk) > 0 {
			left[i] = stk[len(stk)-1]
		}
		stk = append(stk, i)
	}
	stk = []int{}
	for i := n - 1; i >= 0; i-- {
		for len(stk) > 0 && arr[stk[len(stk)-1]] > arr[i] {
			stk = stk[:len(stk)-1]
		}
		if len(stk) > 0 {
			right[i] = stk[len(stk)-1]
		}
		stk = append(stk, i)
	}
	ans := 0
	for i, v := range arr {
		ans += (i - left[i]) * (right[i] - i) * v % mod
		ans %= mod
	}
	return ans
}

TypeScript

function sumSubarrayMins(arr: number[]): number {
    const n = arr.length;
    function getEle(i: number): number {
        if (i == -1 || i == n) return Number.MIN_SAFE_INTEGER;
        return arr[i];
    }
    let ans = 0;
    const mod = 10 ** 9 + 7;
    let stack = [];
    for (let i = -1; i <= n; i++) {
        while (stack.length && getEle(stack[0]) > getEle(i)) {
            const idx = stack.shift();
            ans = (ans + arr[idx] * (idx - stack[0]) * (i - idx)) % mod;
        }
        stack.unshift(i);
    }
    return ans;
}

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