Create main.cpp

Author: JawadSher

24 - Dynamic Programming Problems/39 - Max Rectangle/main.cpp

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+class Solution {
+    // Function to find the index of the next smaller element for each element in the array
+    private:
+        vector<int> nextSmallerElementIndexes(vector<int> arr, int n){
+            stack<int> st;  // Stack to store indices
+            vector<int> ans(n);  // Vector to store the result
+    
+            st.push(-1);  // Push -1 as the base value for comparison
+    
+            for(int i = n-1; i >= 0; i--){  // Traverse the array from right to left
+                int current = arr[i];  // Current element
+                
+                // Pop elements from the stack until a smaller element is found
+                while(st.top() != -1 && arr[st.top()] >= current){
+                    st.pop();
+                }
+    
+                ans[i] = st.top();  // Store the index of the next smaller element
+                st.push(i);  // Push current index to the stack
+            }
+    
+            return ans;
+        }
+        
+        // Function to find the index of the previous smaller element for each element in the array
+        vector<int> prevSmallerElementIndexes(vector<int> arr, int n){
+            stack<int> st;  // Stack to store indices
+            vector<int> ans(n);  // Vector to store the result
+    
+            st.push(-1);  // Push -1 as the base value for comparison
+    
+            for(int i = 0; i < n; i++){  // Traverse the array from left to right
+                int current = arr[i];  // Current element
+    
+                // Pop elements from the stack until a smaller element is found
+                while(st.top() != -1 && arr[st.top()] >= current){
+                    st.pop();
+                }
+    
+                ans[i] = st.top();  // Store the index of the previous smaller element
+                st.push(i);  // Push current index to the stack
+            }
+    
+            return ans;
+        }
+        
+        // Function to calculate the largest rectangular area that can be formed from the histogram
+        int largestRectangleArea(vector<int>& heights) {
+            int n = heights.size();  // Get the number of bars in the histogram
+        
+            // Get the next smaller element indexes for each bar
+            vector<int> next(n);
+            next = nextSmallerElementIndexes(heights, n);
+        
+            // Get the previous smaller element indexes for each bar
+            vector<int> prev(n);
+            prev = prevSmallerElementIndexes(heights, n);
+        
+            int area = INT_MIN;  // Initialize area to the minimum possible value
+        
+            for(int i = 0; i < n; i++){
+                int l = heights[i];  // Height of the current bar
+        
+                // If no next smaller element exists, set it to n (end of the histogram)
+                if(next[i] == -1) next[i] = n;
+        
+                // Width is the distance between the previous and next smaller elements
+                int b = next[i] - prev[i] - 1;
+                
+                // Calculate the area for the current bar and update the maximum area
+                int newArea = l * b;
+                area = max(area, newArea);
+            }
+        
+            return area;  // Return the maximum area found
+        }
+        
+    public:
+        // Function to calculate the maximum area of a rectangle in a 2D matrix
+        int maxArea(vector<vector<int>> &mat) {
+            vector<int> height(mat[0].size(), 0);  // Initialize height array with 0s (one for each column)
+            int maxi = INT_MIN;  // Variable to store the maximum area
+        
+            for(int i = 0; i < mat.size(); i++){  // Traverse each row of the matrix
+                for(int j = 0; j < height.size(); j++){  // Traverse each column in the row
+                    if(mat[i][j] == 1) height[j]++;  // If the element is 1, increment the height
+                    else height[j] = 0;  // If the element is 0, reset the height
+                }
+                
+                // Calculate the maximum area for the current row using the histogram approach
+                maxi = max(maxi, largestRectangleArea(height));
+            }
+            
+            return maxi;  // Return the maximum area found
+        }
+};