added 3143 lc-sol

dsa-solutions/lc-solutions/3100-3199/3143 - Maximum Points Inside the Square.md

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+---
+id: maximum-points-inside-square
+title: Maximum Points Inside the Square (LeetCode)
+sidebar_label: 3143-MaximumPointsInsideSquare
+tags:
+  - Dynamic Programming
+  - Geometry
+  - Sorting
+  - Sliding Window
+description: Given an array of points in the XY-plane, find the maximum number of points that can be inside a square with side length K.
+sidebar_position: 3143
+---
+
+## Problem Description
+
+| Problem Statement | Solution Link | LeetCode Profile |
+| :---------------- | :------------ | :--------------- |
+| [Maximum Points Inside Square](https://leetcode.com/problems/maximum-points-inside-square/) | [Maximum Points Inside Square Solution on LeetCode](https://leetcode.com/problems/maximum-points-inside-square/solutions/) | [vaishu_1904](https://leetcode.com/vaishu_1904/) |
+
+## Problem Description
+
+Given an array of points where points[i] = [xi, yi] represents a point on the X-Y plane and an integer K, return the maximum number of points inside a square of side length K that can be formed with any of the points.
+
+### Example 1
+
+- **Input:** `points = [[1,3],[1,4],[-1,0],[4,1],[0,3],[4,4],[1,0],[1,1],[1,2],[2,2],[3,0],[2,-1],[0,1],[1,-1],[2,0]], K = 2`
+- **Output:** `4`
+- **Explanation:** The maximum number of points inside a square of side length 2 is 4, as shown in the image below.
+
+
+### Example 2
+
+- **Input:** `points = [[0,1],[2,1],[1,2],[1,0],[2,2]], K = 2`
+- **Output:** `1`
+- **Explanation:** Only 1 square can be formed with side length 2.
+
+### Constraints
+
+- `1 <= points.length <= 1000`
+- `points[i].length == 2`
+- `-10^4 <= xi, yi <= 10^4`
+- `1 <= K <= 10^4`
+
+## Approach
+
+To solve this problem efficiently, we can use a combination of sorting and sliding window techniques:
+
+1. **Sorting**: Sort the points based on their X and Y coordinates.
+2. **Sliding Window**: Use a sliding window of size K to check how many points can fit inside a square of side length K at any given position.
+
+### Detailed Steps
+
+- **Sorting**: Sort points primarily by X coordinates and secondarily by Y coordinates.
+- **Sliding Window**:
+  - Traverse through the sorted list of points.
+  - For each point, consider it as the top-left corner of a square.
+  - Use a sliding window to count how many points lie within the square of side length K formed with the current point as the top-left corner.
+  - Update the maximum count of points inside any such square encountered.
+
+### Solution Code
+
+#### Python
+
+```python
+class Solution:        
+    def maxPointsInsideSquare(self, points: List[List[int]], s: str) -> int:
+        minLens = {}
+        secondMin = float('inf')
+
+        for point, char in zip(points, s):
+            size = max(abs(point[0]), abs(point[1]))
+
+            if char not in minLens:
+                minLens[char] = size
+            elif size < minLens[char]:
+                secondMin = min(minLens[char], secondMin)
+                minLens[char] = size
+            else:
+                secondMin = min(size, secondMin)
+
+        count = 0
+        for len in minLens.values():
+            if len < secondMin:
+                count += 1
+
+        return count
+```
+
+#### C++
+
+```c++
+class Solution {
+public:
+    int maxPointsInsideSquare(vector<vector<int>>& points, string s) {
+        unordered_map<char, int> minLens;
+        int secondMin = INT_MAX, count = 0;
+
+        for(size_t i = 0; i < points.size(); ++i) {
+            int len = max(abs(points[i][0]), abs(points[i][1]));
+            char c = s[i];
+
+            if(minLens.find(c) == minLens.end()) {
+                minLens[c] = len;
+            } else if(len < minLens[c]) {
+                secondMin = min(secondMin, minLens[c]); 
+                minLens[c] = len;
+            } else {
+                secondMin = min(secondMin, len);
+            }
+        }
+
+        for(auto& pair : minLens) {
+            if(pair.second < secondMin) {
+                count++;
+            }
+        }
+
+        return count;
+    }
+};
+```
+
+#### Java
+```java
+class Solution {
+    public int maxPointsInsideSquare(int[][] points, String s) {
+        HashMap<Character, Integer> minLens = new HashMap<>();
+        int secondMin = Integer.MAX_VALUE, count = 0;
+
+        for (int i = 0; i < points.length; ++i) {
+            int len = Math.max(Math.abs(points[i][0]), Math.abs(points[i][1]));
+            char c = s.charAt(i);
+
+            if (!minLens.containsKey(c)) {
+                minLens.put(c, len);
+            } else if (len < minLens.get(c)) {
+                secondMin = Math.min(minLens.get(c), secondMin);
+                minLens.put(c, len);
+            } else {
+                secondMin = Math.min(len, secondMin);
+            }
+        }   
+
+        for(int len : minLens.values()) {
+            if(len < secondMin) {
+                count++;
+            } 
+        }
+
+        return count;
+    }
+}
+```
+
+### Conclusion
+The solutions provided utilize sorting and a sliding window approach to efficiently determine the 
+maximum number of points that can be inside a square of side length K. These solutions ensure 
+correctness and handle edge cases within the given constraints effectively.