Merge pull request #1785 from Aditi22Bansal/main

Solving issue #1782 -  solution to 3171. Find Subarray With Bitwise OR Closest to K

Author: ajay-dhangar

dsa-solutions/lc-solutions/3100-3199/3171. Find Subarray With Bitwise OR Closest to K.md

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+---
+id: Find-Subarray-With-Bitwise-OR-Closest-to-K
+title: Find Subarray With Bitwise OR Closest to K (LeetCode)
+level: hard
+sidebar_label: 3171-Find Subarray With Bitwise OR Closest to K
+tags:
+  - Dynamic Programming
+  - Bit Manipulation
+  - Sliding Window
+  - Hash Set
+description: This description is for the solution of Find Subarray With Bitwise OR Closest to K
+sidebar_position: 3171
+---
+
+## Problem statement:
+
+Given an array of integers `arr` and an integer `k`, return the maximum possible bitwise OR of a subarray of `arr` that is closest to `k`.
+
+The bitwise OR of an array of numbers is defined as `a1 | a2 | ... | an`, where `|` denotes the bitwise OR operator.
+
+**Example 1:**
+
+Input: arr = [5,6,7,8,9], k = 10
+Output: 10
+
+Explanation: The subarray [6,7] has bitwise OR = 6 | 7 = 7, which is closest to 10.
+
+**Example 2:**
+
+Input: arr = [1,2,4,8,16], k = 32
+Output: 31
+
+Explanation: The subarray [1,2,4,8,16] has bitwise OR = 1 | 2 | 4 | 8 | 16 = 31, which is closest to 32.
+
+**Constraints:**
+
+- `1 <= arr.length <= 10^5`
+- `1 <= arr[i], k <= 10^9`
+
+## Solutions:
+
+### Approach 1: Sliding Window with Bitmasking
+
+```python
+class Solution:
+    def closestToTarget(self, arr: List[int], k: int) -> int:
+        ans = float('inf')
+        current = set()
+        
+        for num in arr:
+            current = {num & val for val in current} | {num}
+            for val in current:
+                ans = min(ans, abs(val - k))
+        
+        return ans
+```
+
+### Approach 2: Efficient Bitmasking with Set Operations
+
+```python
+class Solution:
+    def closestToTarget(self, arr: List[int], k: int) -> int:
+        ans = float('inf')
+        current = set()
+        next_set = set()
+        
+        for num in arr:
+            next_set = {num & val for val in current} | {num}
+            for val in next_set:
+                ans = min(ans, abs(val - k))
+            current = next_set
+        
+        return ans
+```
+
+### Approach 3: Optimized Sliding Window with Prefix Bitmasking
+
+```python
+class Solution:
+    def closestToTarget(self, arr: List[int], k: int) -> int:
+        ans = float('inf')
+        current = set()
+        
+        for num in arr:
+            new_current = {num}
+            for val in current:
+                new_current.add(val | num)
+            current = new_current
+            for val in current:
+                ans = min(ans, abs(val - k))
+        
+        return ans
+```
+## Complexity Analysis:
+
+### Approach 1: Sliding Window with Bitmasking
+
+- **Time Complexity:** $O(n⋅log(max_element))$
+  - Where \( n \) is the number of elements in the array `arr`, and `max_element` is the maximum element in `arr`.
+  - The logarithmic factor comes from the bitwise operations and set operations involved.
+
+- **Space Complexity:** $O(log(max_element))$
+  - Space used by the set `current` to store intermediate bitwise OR values.
+
+### Approach 2: Efficient Bitmasking with Set Operations
+
+- **Time Complexity:** $O(n⋅log(max_element))$
+  - Same as Approach 1, due to similar operations on sets.
+
+- **Space Complexity:** $O(log(max_element))$
+  - Similar to Approach 1, space used by the sets `current` and `next_set`.
+
+### Approach 3: Optimized Sliding Window with Prefix Bitmasking
+
+- **Time Complexity:** $O(n⋅log(max_element))$
+  - Same as Approach 1 and 2, as it involves bitwise OR operations and set updates.
+
+- **Space Complexity:** $O(log(max_element))$
+  - Space used by the set `current` to store intermediate bitwise OR values.
+
+Here, `max_element` refers to the maximum element present in the array `arr`, which affects the logarithmic factor in the time and space complexities due to bitwise operations and set operations involved in each approach.