Add solution to LC Problem 795

dsa-solutions/lc-solutions/0700-0799/795 - Number of Subarrays with Bounded Maximum.md

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+---
+id: number-of-subarrays-with-bounded-maximum
+title: Number of Subarrays with Bounded Maximum
+sidebar_label: Number of Subarrays with Bounded Maximum
+tags: [Array, Sliding Window, C++, Python, Java]
+description: Solve the problem of finding the number of contiguous non-empty subarrays where the maximum element is within a given range.
+---
+
+## Problem Statement
+
+### Problem Description
+
+Given an integer array `nums` and two integers `left` and `right`, return the number of contiguous non-empty subarrays such that the value of the maximum array element in that subarray is in the range `[left, right]`.
+
+The test cases are generated so that the answer will fit in a 32-bit integer.
+
+### Example
+
+**Example 1:**
+```
+Input: nums = [2,1,4,3], left = 2, right = 3
+Output: 3
+```
+**Explanation:** There are three subarrays that meet the requirements: [2], [2, 1], [3].
+
+
+**Example 2:**
+```
+Input: nums = [2,9,2,5,6], left = 2, right = 8
+Output: 7
+```
+
+### Constraints
+
+- $1 \leq nums.length \leq 10^5$
+- $0 \leq nums[i] \leq 10^9$
+- $0 \leq left \leq right \leq 10^9$
+
+## Solution
+
+### Intuition
+
+To solve this problem, we can use a sliding window approach. The idea is to maintain a window of subarrays whose maximum elements are within the given range `[left, right]`. We can keep track of the start and end of this window and count the number of valid subarrays.
+
+### Time Complexity and Space Complexity Analysis
+
+- **Time Complexity**: The solution involves a single pass through the array, making the time complexity $O(n)$.
+- **Space Complexity**: The space complexity is $O(1)$ since we are using a constant amount of extra space.
+
+### Code
+
+#### C++
+
+```cpp
+class Solution {
+public:
+    int numSubarrayBoundedMax(vector<int>& nums, int left, int right) {
+        int count = 0, start = -1, last = -1;
+        for (int i = 0; i < nums.size(); i++) {
+            if (nums[i] > right) {
+                start = i;
+            }
+            if (nums[i] >= left) {
+                last = i;
+            }
+            count += last - start;
+        }
+        return count;
+    }
+};
+```
+
+#### Java
+```java
+class Solution {
+    public int numSubarrayBoundedMax(int[] nums, int left, int right) {
+        int count = 0, start = -1, last = -1;
+        for (int i = 0; i < nums.length; i++) {
+            if (nums[i] > right) {
+                start = i;
+            }
+            if (nums[i] >= left) {
+                last = i;
+            }
+            count += last - start;
+        }
+        return count;
+    }
+}
+```
+#### Python
+```python
+class Solution:
+    def numSubarrayBoundedMax(self, nums: List[int], left: int, right: int) -> int:
+        count = 0
+        start = -1
+        last = -1
+        for i in range(len(nums)):
+            if nums[i] > right:
+                start = i
+            if nums[i] >= left:
+                last = i
+            count += last - start
+        return count
+```