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2444. Count Subarrays With Fixed Bounds

Description

You are given an integer array nums and two integers minK and maxK.

A fixed-bound subarray of nums is a subarray that satisfies the following conditions:

  • The minimum value in the subarray is equal to minK.
  • The maximum value in the subarray is equal to maxK.

Return the number of fixed-bound subarrays.

A subarray is a contiguous part of an array.

 

Example 1:

Input: nums = [1,3,5,2,7,5], minK = 1, maxK = 5
Output: 2
Explanation: The fixed-bound subarrays are [1,3,5] and [1,3,5,2].

Example 2:

Input: nums = [1,1,1,1], minK = 1, maxK = 1
Output: 10
Explanation: Every subarray of nums is a fixed-bound subarray. There are 10 possible subarrays.

 

Constraints:

  • 2 <= nums.length <= 105
  • 1 <= nums[i], minK, maxK <= 106

Solutions

Solution 1: Enumeration of Right Endpoint

From the problem description, we know that all elements of the bounded subarray are in the interval [minK, maxK], and the minimum value must be minK, and the maximum value must be maxK.

We traverse the array $nums$, count the number of bounded subarrays with nums[i] as the right endpoint, and then add all the counts.

The specific implementation logic is as follows:

  1. Maintain the index $k$ of the most recent element not in the interval [minK, maxK], initially set to $-1$. Therefore, the left endpoint of the current element nums[i] must be greater than $k$.
  2. Maintain the index $j_1$ of the most recent element with a value of minK, and the index $j_2$ of the most recent element with a value of maxK, both initially set to $-1$. Therefore, the left endpoint of the current element nums[i] must be less than or equal to $\min(j_1, j_2)$.
  3. In summary, the number of bounded subarrays with the current element as the right endpoint is $\max(0, \min(j_1, j_2) - k)$. Add up all the counts to get the result.

The time complexity is $O(n)$, and the space complexity is $O(1)$. Here, $n$ is the length of the array $nums$.

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class Solution:
    def countSubarrays(self, nums: List[int], minK: int, maxK: int) -> int:
        j1 = j2 = k = -1
        ans = 0
        for i, v in enumerate(nums):
            if v < minK or v > maxK:
                k = i
            if v == minK:
                j1 = i
            if v == maxK:
                j2 = i
            ans += max(0, min(j1, j2) - k)
        return ans

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class Solution {
    public long countSubarrays(int[] nums, int minK, int maxK) {
        long ans = 0;
        int j1 = -1, j2 = -1, k = -1;
        for (int i = 0; i < nums.length; ++i) {
            if (nums[i] < minK || nums[i] > maxK) {
                k = i;
            }
            if (nums[i] == minK) {
                j1 = i;
            }
            if (nums[i] == maxK) {
                j2 = i;
            }
            ans += Math.max(0, Math.min(j1, j2) - k);
        }
        return ans;
    }
}

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class Solution {
public:
    long long countSubarrays(vector<int>& nums, int minK, int maxK) {
        long long ans = 0;
        int j1 = -1, j2 = -1, k = -1;
        for (int i = 0; i < nums.size(); ++i) {
            if (nums[i] < minK || nums[i] > maxK) k = i;
            if (nums[i] == minK) j1 = i;
            if (nums[i] == maxK) j2 = i;
            ans += max(0, min(j1, j2) - k);
        }
        return ans;
    }
};

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func countSubarrays(nums []int, minK int, maxK int) int64 {
    ans := 0
    j1, j2, k := -1, -1, -1
    for i, v := range nums {
        if v < minK || v > maxK {
            k = i
        }
        if v == minK {
            j1 = i
        }
        if v == maxK {
            j2 = i
        }
        ans += max(0, min(j1, j2)-k)
    }
    return int64(ans)
}

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function countSubarrays(nums: number[], minK: number, maxK: number): number {
    let res = 0;
    let minIndex = -1;
    let maxIndex = -1;