C# Solution for Maximise Happiness of Selected Children Problem
Intuition\n Describe your first thoughts on how to solve this problem. \nThe solution aims to maximize the total sum of happiness values by selecting children i
# Intuition\n<!-- Describe your first thoughts on how to solve this problem. -->\nThe solution aims to maximize the total sum of happiness values by selecting children in each round based on their happiness values. It iterates through the sorted array and selects the maximum happiness value that hasn\u2019t been fully selected yet.\n\n# Approach\n<!-- Describe your approach to solving the problem. -->\n1.\tSort the happiness array in descending order to prioritize selecting children with higher happiness values first.\n2.\tIterate through the sorted array for each selection round (up to k rounds or the length of the array).\n3.\tFor each round, pick the ith biggest happiness score and subtract the number of rounds passed from it. If the result is positive, add it to the total sum of happiness and increment the rounds.\n4.\tReturn the total sum of happiness achieved.\n\n# Complexity\n- Time complexity:\n<!-- Add your time complexity here, e.g. $$O(n)$$ -->\n\u2022\tSorting the array takes O(nlogn) time.\n\u2022\tThe iteration through the array for each selection round takes O(n) time.\n\u2022\tOverall, the time complexity is O(nlogn), dominated by the sorting operation.\n\n- Space complexity:\n<!-- Add your space complexity here, e.g. $$O(n)$$ -->\nThe space complexity is O(1) as the algorithm uses only a constant amount of extra space for variables regardless of the input size.\n\n# Code\n```\npublic class Solution {\n    public long MaximumHappinessSum(int[] happiness, int k) {\n        Array.Sort(happiness, (a, b) => b - a); // Sort in descending order\n        \n        int rounds = 0;\n        long totalHappySum = 0;\n        \n        for (int i = 0; i < k && i < happiness.Length; i++) {\n            int selected = happiness[i] - rounds;\n            if (selected > 0) {\n                totalHappySum += selected;\n                rounds++;\n            }\n        }\n        \n        return totalHappySum;\n    }\n}\n```
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