Easy Explained Solution with comments||C++||Java
Approach\n here are the key points explaining the code:\n\nClass and Comparator Function:\n\nThe Solution class contains the logic to maximize capital after sel
# Approach\n here are the key points explaining the code:\n\nClass and Comparator Function:\n\nThe Solution class contains the logic to maximize capital after selecting projects.\nA static comparator function cmp sorts pairs of capital and profits.\nSorts primarily by ascending capital.\nIf capitals are equal, sorts by descending profit.\nInput Parameters for findMaximizedCapital:\n\nk: Maximum number of projects to select.\nw: Initial capital.\nprofits: Vector of project profits.\ncapital: Vector of capital required for each project.\nSetup and Population of Vector:\n\nn: Number of projects.\nA vector v is created to store pairs of capital and profits.\nThe vector v is populated by iterating through profits and capital.\nSorting:\n\nThe vector v is sorted using the custom comparator cmp.\nPriority Queue (Max-Heap):\n\nA max-heap pq is initialized to store profits of feasible projects.\nj is used to track the current position in the sorted vector v.\nMain Loop:\n\nIterates k times to select up to k projects.\nInner While Loop:\nAdds projects to the max-heap if their capital requirement is \u2264 current capital w.\nMax-Heap Operation:\nIf the max-heap is not empty, the project with the highest profit is selected.\nThe profit is added to w, and the project is removed from the heap.\nBreak Condition:\nIf the max-heap is empty, no more feasible projects can be selected, and the loop breaks.\nReturn Statement:\n\nReturns the final capital w after selecting up to k projects.\nMain Function:\n\nDemonstrates the usage of findMaximizedCapital.\nDefines example vectors profits and capital.\nCalls the function with example parameters.\nPrints the result, showing the maximum capital after selecting projects.\nThis breakdown highlights the structure and logic of the code step-by-step.\n\n# Complexity\n\n- Time complexity:\n\nThe space complexity is O(n), primarily due to the storage of pairs in a vector and elements in a priority queue.\n\n- Space complexity:\n\nThe overall time complexity is O(n log n), dominated by the sorting step. The detailed breakdown is:\nCreating pairs: O(n)\nSorting the pairs: O(n log n)\nInserting and managing elements in the priority queue: O(n log n)\nSelecting up to k projects: O(k log n)\nGiven that k is typically much smaller than n, the dominant term remains O(n log n).\n\n# Code\n```\nclass Solution {\n    // Comparator function to sort pairs based on capital in ascending order\n    // If capital is the same, sort based on profits in descending order\n    static bool cmp(pair<int,int>&a, pair<int,int>&b) {\n        if (a.first < b.first) {\n            return true;\n        } else if (a.first == b.first && a.second > b.second) {\n            return true;\n        }\n        return false;\n    }\npublic:\n    // Function to find the maximized capital after selecting k projects\n    int findMaximizedCapital(int k, int w, vector<int>& profits, vector<int>& capital) {\n        int n = profits.size();  // Get the number of projects\n        vector<pair<int, int>> v;  // Vector to store pairs of capital and profits\n        \n        // Populate the vector with pairs of capital and profits\n        for (int i = 0; i < n; i++) {\n            v.push_back({capital[i], profits[i]});\n        }\n        \n        // Sort the vector based on capital (ascending) and profits (descending)\n        sort(v.begin(), v.end(), cmp);\n        \n        // Max-heap (priority queue) to store the profits of feasible projects\n        priority_queue<int> pq;\n        int j = 0;  // Index to track the position in the sorted vector\n        \n        // Iterate k times to select k projects\n        for (int i = 0; i < k; i++) {\n            // Add all feasible projects to the max-heap\n            while (j < n && v[j].first <= w) {\n                pq.push(v[j].second);\n                j++;\n            }\n            \n            // If the max-heap is not empty, add the maximum profit project to w\n            if (!pq.empty()) {\n                w += pq.top();\n                pq.pop();\n            } else {\n                // Break if no more feasible projects can be selected\n                break;\n            }\n        }\n\n        // Return the maximized capital after selecting k projects\n        return w;\n    }\n};\n```
['Array', 'Greedy', 'Sorting', 'Heap (Priority Queue)', 'C++']