Create README.md

Miscellaneous Algorithms/Maximum Products/README.md

@@ -0,0 +1,32 @@
+# Maximum Products of two elements in an array
+
+
+
+## How Does It Work?
+
+Given the array of integers nums, you will choose two different indices i and j of that array. Return the maximum value of (nums[i]-1)*(nums[j]-1).
+
+
+## Example:
+### Example 1:
+
+Input: nums = [3,4,5,2]
+Output: 12 
+Explanation: If you choose the indices i=1 and j=2 (indexed from 0), you will get the maximum value, that is, (nums[1]-1)*(nums[2]-1) = (4-1)*(5-1) = 3*4 = 12. 
+
+### Example 2:
+Input: nums = [1,5,4,5]
+Output: 16
+Explanation: Choosing the indices i=1 and j=3 (indexed from 0), you will get the maximum value of (5-1)*(5-1) = 16.
+
+
+
+# Approach :
+1. Sort the Array : Begin by sorting the array nums in ascending order. This will arrange the numbers such that the largest numbers are at the end of the array.
+2. Identify the Two Largest Numbers : After sorting, the two largest numbers in the array will be at the last two indices. Specifically, the largest number will be at nums[nums.size() - 1] and the second largest will be at nums[nums.size() - 2].
+3. Calculate the Product : Subtract 1 from each of these two largest numbers and then calculate their product.
+
+# Complexity :
+Time complexity : O(n*log(n))
+The time complexity of this solution is O(n log n) due to the sorting operation, where n is the number of elements in the input vector.
+Space complexity : O(1)