Add max_Rectangle implementation in cpp

CPP/algorithms/arrays/max_Rectangle.cpp

@@ -0,0 +1,72 @@
+#include <iostream>
+#include <vector>
+#include <stack>
+#include <algorithm>
+using namespace std;
+
+// Function to calculate the largest rectangle area in a histogram
+int largestRectangleArea(vector<int>& heights) {
+    stack<int> st;
+    int maxArea = 0;
+    int n = heights.size();
+
+    for (int i = 0; i <= n; i++) {
+        while (!st.empty() && (i == n || heights[st.top()] >= heights[i])) {
+            int height = heights[st.top()];
+            st.pop();
+            int width = st.empty() ? i : i - st.top() - 1;
+            maxArea = max(maxArea, height * width);
+        }
+        st.push(i);
+    }
+
+    return maxArea;
+}
+
+// Function to find the maximum rectangle area in a binary matrix
+int maxRectangle(vector<vector<int>>& mat) {
+    if (mat.empty()) return 0;
+
+    int maxArea = 0;
+    int rows = mat.size();
+    int cols = mat[0].size();
+    vector<int> heights(cols, 0);
+
+    for (int i = 0; i < rows; i++) {
+        for (int j = 0; j < cols; j++) {
+            heights[j] = mat[i][j] == 0 ? 0 : heights[j] + 1;
+        }
+        maxArea = max(maxArea, largestRectangleArea(heights));
+    }
+
+    return maxArea;
+}
+
+int main() {
+    vector<vector<int>> mat = {
+        {1, 0, 1, 0, 0},
+        {1, 0, 1, 1, 1},
+        {1, 1, 1, 1, 1},
+        {1, 0, 0, 1, 0}
+    };
+
+    cout << "Maximum rectangle area: " << maxRectangle(mat) << endl;
+
+    return 0;
+}
+
+/*
+ * Algorithm Explanation:
+ * - largestRectangleArea function computes the largest rectangular area in a histogram using a stack.
+ *   For each bar, it finds the largest rectangle that can be formed with that bar as the shortest.
+ * 
+ * - maxRectangle function finds the largest rectangle in a binary matrix. It converts each row into
+ *   a histogram of heights and calculates the maximum rectangle area by calling largestRectangleArea.
+ *
+ * Time Complexity:
+ * - largestRectangleArea: O(n), where n is the number of columns.
+ * - maxRectangle: O(rows * cols), where rows and cols are the dimensions of the matrix.
+ *
+ * Space Complexity:
+ * - O(cols), where cols is the number of columns in the matrix due to the heights array.
+ */