C++||clean and explained||using heap
Intuition\nThe intuition behind the provided code lies in its implementation of a basic trading algorithm that handles buy and sell orders efficiently. The algo
# Intuition\nThe intuition behind the provided code lies in its implementation of a basic trading algorithm that handles buy and sell orders efficiently. The algorithm uses two priority queues, one for buy orders and one for sell orders, to maintain a sorted order by price. As it iterates through each order in the input vector, it categorizes the order as a buy or sell order based on the type. For buy orders, the algorithm attempts to fulfill them by matching with existing sell orders, adjusting quantities accordingly. Similarly, for sell orders, it seeks matching buy orders. The process ensures that orders are processed in a way that maximizes fulfillment while maintaining sorted queues. The final step involves calculating the total backlogged orders by summing the remaining quantities in both the buy and sell priority queues. The algorithm optimally manages the order book, providing insights into the backlog of unfulfilled orders in a trading environment.\n\n# Approach\nThe approach of the given code is to simulate a trading system and efficiently handle buy and sell orders. Here\'s a step-by-step breakdown of the approach:\n - **Data Structures:**\n Two priority queues (buyOrders and sellOrders) are used to maintain the buy and sell orders sorted by price.\nThe min-heap property is applied to sellOrders so that the lowest price sell order is at the front.\nThe max-heap property is applied to buyOrders so that the highest price buy order is at the front.\nIterating Through Orders:\nThe code iterates through each order in the input vector, extracting relevant information such as price, quantity, and order type (buy or sell).\n- **Processing Buy Orders:**\n For buy orders, the algorithm attempts to match them with existing sell orders.\nIt iterates through the sell orders while there is quantity to be fulfilled in the buy order.\nIf a matching sell order is found (lower or equal price), it adjusts quantities accordingly and updates the sell queue.\nIf the buy order cannot be fulfilled by the existing sell orders, it is added to the buy queue.\n- **Processing Sell Orders:**\nFor sell orders, the algorithm seeks matching buy orders following a similar process as with buy orders.\nIt iterates through the buy orders while there is quantity to be fulfilled in the sell order.\nIf a matching buy order is found (higher or equal price), it adjusts quantities accordingly and updates the buy queue.\nIf the sell order cannot be fulfilled by the existing buy orders, it is added to the sell queue.\n- **Calculating Total Backlogs:**\nAfter processing all orders, the code calculates the total backlogged orders by summing the remaining quantities in both the buy and sell priority queues.\n- **Result:**\nThe final result is the total number of backlogged orders, considering a modulo operation for numerical stability.\nOverall, the approach efficiently manages and processes orders, ensuring that buy and sell orders are matched appropriately while maintaining sorted queues based on price. This algorithm provides a practical simulation of a trading system\'s order book.\n\n# Complexity\n- Time complexity:\nO(n * log(k)).\n\n- Space complexity:\nO(n).\n\n# Code\n```\nclass Solution {\npublic:\n    int getNumberOfBacklogOrders(vector<vector<int>>& orders) \n    {\n        // Priority queue for sell orders, sorted by price (min heap)\n        priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> sellOrders;\n        // Priority queue for buy orders, sorted by price (max heap)\n        priority_queue<pair<int, int>> buyOrders;\n        // Loop through each order in the input vector\n        for (const auto& order : orders)\n         {\n            // Extract order details\n            int orderPrice = order[0];\n            int orderQuantity = order[1];\n            int orderType = order[2]; // Assuming type is at index 2 in the inner vector\n            // Process buy orders\n            if (orderType == 0)\n             {\n                // If no sell orders, add the buy order to buy queue and continue to the next order\n                if (sellOrders.empty())\n                 {\n                    buyOrders.push({orderPrice, orderQuantity});\n                    continue;\n                }\n                // Process buy order against sell orders\n                while (!sellOrders.empty() && orderQuantity > 0)\n                 {\n                    int sellPrice = sellOrders.top().first;\n                    int sellQuantity = sellOrders.top().second;\n                    // Check if the sell order can be completely fulfilled\n                    if (sellPrice <= orderPrice)\n                     {\n                        sellOrders.pop();\n                        if (sellQuantity >= orderQuantity)\n                         {\n                            sellQuantity -= orderQuantity;\n                            orderQuantity = 0;\n                            // If there is remaining sell quantity, add it back to sell orders\n                            if (sellQuantity > 0) \n                            {\n                                sellOrders.push({sellPrice, sellQuantity});\n                            }\n                        } \n                        else {\n                            orderQuantity -= sellQuantity;\n                        }\n                    } \n                    else \n                    {\n                        // If the current sell order has a higher price, add the buy order to buy queue\n                        buyOrders.push({orderPrice, orderQuantity});\n                        orderQuantity = 0;\n                        break;\n                    }\n                }\n                // If there is remaining quantity for the buy order, add it to buy queue\n                if (orderQuantity > 0)\n                 {\n                    buyOrders.push({orderPrice, orderQuantity});\n                }\n            } \n            else \n            { // Process sell orders\n                // If no buy orders, add the sell order to sell queue and continue to the next order\n                if (buyOrders.empty())\n                 {\n                    sellOrders.push({orderPrice, orderQuantity});\n                    continue;\n                }\n                // Process sell order against buy orders\n                while (!buyOrders.empty() && orderQuantity > 0) \n                {\n                    int buyPrice = buyOrders.top().first;\n                    int buyQuantity = buyOrders.top().second;\n\n                    // Check if the buy order can be completely fulfilled\n                    if (buyPrice >= orderPrice) \n                    {\n                        buyOrders.pop();\n\n                        if (buyQuantity >= orderQuantity)\n                        {\n                            buyQuantity -= orderQuantity;\n                            orderQuantity = 0;\n                            // If there is remaining buy quantity, add it back to buy orders\n                            if (buyQuantity > 0) \n                            {\n                                buyOrders.push({buyPrice, buyQuantity});\n                            }\n                        } \n                        else\n                         {\n                            orderQuantity -= buyQuantity;\n                        }\n                    } \n                    else\n                     {\n                        // If the current buy order has a lower price, add the sell order to sell queue\n                        sellOrders.push({orderPrice, orderQuantity});\n                        orderQuantity = 0;\n                        break;\n                    }\n                }\n                // If there is remaining quantity for the sell order, add it to sell queue\n                if (orderQuantity > 0) \n                {\n                    sellOrders.push({orderPrice, orderQuantity});\n                }\n            }\n        }\n        // Calculate the total backlogs from remaining sell and buy orders\n        int totalBacklogs = 0;\n        const int mod = 1e9 + 7;\n        while (!sellOrders.empty()) \n        {\n            totalBacklogs = (totalBacklogs + sellOrders.top().second) % mod;\n            sellOrders.pop();\n        }\n        while (!buyOrders.empty())\n        {\n            totalBacklogs = (totalBacklogs + buyOrders.top().second) % mod;\n            buyOrders.pop();\n        }\n        // Return the final result\n        return totalBacklogs;\n    }\n};\n\n```
['Heap (Priority Queue)', 'Simulation', 'C++']