Given an array, task is to compute the sum of all possible maximum area rectangle which can be formed from the array elements. Also, you can reduce the elements of the array by at most 1.

Examples :

Input :a = {10, 10, 10, 10, 11, 10, 11, 10} Output : 210Explanation :We can form two rectangles one square (10 * 10) and one (11 * 10). Hence, total area = 100 + 110 = 210. Input : a = { 3, 4, 5, 6 } Output : 15 Explanation : We can reduce 4 to 3 and 6 to 5 so that we got rectangle of (3 * 5). Hence area = 15. Input : a = { 3, 2, 5, 2 } Output : 0

**Naive Approach : **Check for all possible four elements of the array and then whichever can form a rectangle. In these rectangles, separate all those rectangles which are of maximum area formed by these elements. After getting the rectangles and their areas, sum them all to get our desired solution.

**Efficient Approach :** To get the maximum area rectangle, first sort the elements of the array in non-increasing array. After sorting, start the procedure to select the elements of the array. Here, selection of two elements of array (as length of rectangle) is possible if elements of array are equal *(a[i] == a[i+1])* or if length of smaller element a[i+1] is one less than a[i] (*in this case we have our length a[i+1] because a[i] is decreased by 1*). One flag variable is maintained to check that *whether we get length and breadth both.* After getting length, set the flag variable, now calculate the breadth in the same way as we have done for length and sum the area of rectangle. After getting length and breadth both, again set the flag variable false so that we will now search for a new rectangle. This process is repeated and lastly, final sum of area is returned.

**Below is C++ implementation of the above approach.**

// CPP code to find sum of all // area rectangle possible #include <bits/stdc++.h> using namespace std; // Function to find area of rectangles int MaxTotalRectangleArea(int a[], int n) { // sorting the array in // descending order sort(a, a + n, greater<int>()); // store the final sum of // all the rectangles area // possible int sum = 0; bool flag = false; // temporary variable to store // the length of rectangle int len; for (int i = 0; i < n; i++) { // Selecting the length of rectangle // so that difference between any // two number is 1 only. Here length // is selected so flag is set if ((a[i] == a[i + 1] || a[i] - a[i + 1] == 1) && (!flag)) { // flag is set means // we have got length of // rectangle flag = true; // length is set to // a[i+1] so that if // a[i+1] is less than a[i] // by 1 then also we have // the correct chice for length len = a[i + 1]; // incrementing the counter one // time more as we have considered // a[i+1] element also so. i++; } // Selecting the width of rectangle // so that difference between any // two number is 1 only. Here width // is selected so now flag is again // unset for next rectangle else if ((a[i] == a[i + 1] || a[i] - a[i + 1] == 1) && (flag)) { // area is calculated for // rectangle sum = sum + a[i + 1] * len; // flag is set false // for another rectangle // which we can get from // elements in array flag = false; // incrementing the counter one // time more as we have considered // a[i+1] element also so. i++; } } return sum; } // Driver code int main() { int a[] = { 10, 10, 10, 10, 11, 10, 11, 10, 9, 9, 8, 8 }; int n = sizeof(a) / sizeof(a[0]); cout << MaxTotalRectangleArea(a, n); return 0; }

Time Complexity: **O(nlog(n))**

Auxiliary Space: **O(1)**

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