2862. Maximum Element-Sum of a Complete Subset of Indices

Author: sergeyleschev

2501-3000/2862. Maximum Element-Sum of a Complete Subset of Indices.swift

@@ -3,8 +3,27 @@ class Solution {
     // Solution by Sergey Leschev
     // 2862. Maximum Element-Sum of a Complete Subset of Indices
 
+    // Intuition
+    // A set of numbers is considered complete if the product of every pair of its elements is a perfect square. 
+    // In this problem, we are given an array of integers and are tasked with finding the maximum possible sum of elements in a complete subset of indices.
+
+    // Approach
+    // To tackle this problem, we start by determining the "key" for each index in the array. 
+    // This key is found by iteratively dividing the index by all possible square numbers until we can no longer do so. 
+    // For example, the key of index 1 is 1, the key of index 18 is 2, and the key of index 24 is 6. In a complete set, all indices share the same key.
+
+    // We maintain a dictionary count to keep track of the sum of elements associated with each key. 
+    // For each index i in the array, we find its key x, accumulate A[i] to count[x], and update our result res as the maximum between its current value and count[x]. 
+    // Finally, we return res as our result, which represents the maximum possible sum of a complete subset of indices in the given array.
+
+    // By using this approach, we can efficiently determine the maximum element-sum for a complete subset of indices, 
+    // ensuring the product of their elements is always a perfect square.
+
     // Time complexity: O(n)
     // Space complexity: O(n)
+    // The process to determine each key has a time complexity of O(sqrt(n)). 
+    // However, by precalculating all the keys, the final solution becomes O(n). 
+    // In fact, the complexity can be simplified to O(n) due to the sum of a convergent series (1 + 1/4 + 1/9 + ...).
 
     func maximumSum(_ nums: [Int]) -> Int {
         var count = [Int: Int]()