Create solution for Leetcode 0302

Author: SanskarSinghiit

dsa-solutions/lc-solutions/0300-0399/0302-smallest-rectangle-enclosing-black-pixels.md

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+---
+id: smallest-rectangle-enclosing-black-pixels
+title: Smallest Rectangle Enclosing Black Pixels
+sidebar_label: 0302-Smallest-Rectangle-Enclosing-Black-Pixels
+tags: [Binary Search, Matrix, Array, Hard]
+description: Given an image represented by a binary matrix where 0 is a white pixel and 1 is a black pixel, return the area of the smallest rectangle that encloses all black pixels. The black pixels are connected, and the rectangle must be axis-aligned.
+
+---
+
+## Problem Statement
+
+You are given an `m x n` binary matrix `image` where `0` represents a white pixel and `1` represents a black pixel. The black pixels are connected, i.e., there is only one black region. Pixels are connected horizontally and vertically. 
+
+Given the location `(x, y)` of one of the black pixels, return the area of the smallest (axis-aligned) rectangle that encloses all black pixels.
+
+**You must write an algorithm with less than O(mn) runtime complexity.**
+
+### Examples
+
+**Example 1:**
+
+```plaintext
+Input: image = [["0","0","1","0"],["0","1","1","0"],["0","1","0","0"]], x = 0, y = 2
+Output: 6
+```
+
+**Example 2:**
+
+```plaintext
+Input: image = [["1"]], x = 0, y = 0
+Output: 1
+```
+### Constraints
+- m == image.length
+- n == image[i].length
+- 1 <= m, n <= 100
+- image[i][j] is either '0' or '1'.
+- 0 <= x < m
+- 0 <= y < n
+- image[x][y] == '1'
+- The black pixels in the image only form one component.
+- At most 104 calls will be made to `add` and `find`.
+
+## Solution
+
+### Approach 
+
+We use binary search to find the left, right, top, and bottom edges of the rectangle that encloses all the black pixels.
+
+#### Algorithm
+
+`Binary Search` to hold remainder.
+
+- Horizontal Search: Find the top and bottom boundaries of the rectangle by searching for rows that contain black pixels.
+- Vertical Search: Find the left and right boundaries of the rectangle by searching for columns that contain black pixels.
+
+#### Implementation
+
+## (Java)
+
+```Java
+public class Smallest_Rectangle_Enclosing_Black_Pixels {
+
+    public class Solution_BinarySearch {
+        public int minArea(char[][] image, int x, int y) {
+            if (image == null || image.length == 0) {
+                return 0;
+            }
+
+            int m = image.length;
+            int n = image[0].length;
+
+            int up = binarySearch(image, true, 0, x, 0, n, true);
+            int down = binarySearch(image, true, x + 1, m, 0, n, false);
+            int left = binarySearch(image, false, 0, y, up, down, true);
+            int right = binarySearch(image, false, y + 1, n, up, down, false);
+
+            return (right - left) * (down - up);
+        }
+
+        int binarySearch(char[][] image, boolean isHorizontal, int i, int j, int low, int high, boolean opt) {
+            while (i < j) {
+                int k = low;
+                int mid = (i + j) / 2;
+
+                while (k < high && (isHorizontal ? image[mid][k] : image[k][mid]) == '0') {
+                    ++k;
+                }
+
+                if (k < high == opt) {
+                    j = mid;
+                } else {
+                    i = mid + 1;
+                }
+            }
+
+            return i;
+        }
+    }
+
+    class Solution_BruteForce {
+        public int minArea(char[][] image, int x, int y) {
+            int rows = image.length, columns = image[0].length;
+            int top = x, bottom = x, left = y, right = y;
+            int[][] directions = { {-1, 0}, {1, 0}, {0, -1}, {0, 1} };
+            image[x][y] = '2';
+            Queue<int[]> queue = new LinkedList<>();
+            queue.offer(new int[]{x, y});
+            while (!queue.isEmpty()) {
+                int[] cell = queue.poll();
+                int row = cell[0], column = cell[1];
+                for (int[] direction : directions) {
+                    int newRow = row + direction[0], newColumn = column + direction[1];
+                    if (newRow >= 0 && newRow < rows && newColumn >= 0 && newColumn < columns && image[newRow][newColumn] == '1') {
+                        image[newRow][newColumn] = '2';
+                        top = Math.min(top, newRow);
+                        bottom = Math.max(bottom, newRow);
+                        left = Math.min(left, newColumn);
+                        right = Math.max(right, newColumn);
+                        queue.offer(new int[]{newRow, newColumn});
+                    }
+                }
+            }
+            return (bottom - top + 1) * (right - left + 1);
+        }
+    }
+}
+
+```
+
+## (C++) 
+``` C++
+C++
+class TwoSum {
+    Map<Integer,Boolean> map;
+    List<Integer> list;
+    int low = Integer.MAX_VALUE;
+    int high = Integer.MIN_VALUE;
+    /** Initialize your data structure here. */
+    public TwoSum() {
+        map = new HashMap<>();
+        list = new LinkedList<>();
+    }
+
+    /** Add the number to an internal data structure..*/
+    public void add(int number) {
+        if(map.containsKey(number)){
+            map.put(number,true);
+        }else{
+            map.put(number,false);
+            list.add(number);
+            low = Math.min(low,number);
+            high = Math.max(high,number);
+        }
+    }
+
+    /** Find if there exists any pair of numbers which sum is equal 
+     * to the value. */
+    public boolean find(int value) {
+        if(value < 2* low || value > 2*high) return false;
+        for(int num : list){
+            int target = value - num;
+            if(map.containsKey(target)){
+                if(num != target) return true;
+                else if(map.get(target)) return true;
+            }
+        }
+        return false;
+    }
+}
+
+```
+
+### Complexity Analysis
+
+- **Time Complexity**: $O(\log m \cdot n + \log n \cdot m)$, where $m$ is the number of rows and $n$ is the number of columns.
+    
+- **Space complexity**: $O(1)$, as we are using a constant amount of extra space for variables and no additional data structures.