C# Priority Queue-Based Solution
Intuition\n Describe your first thoughts on how to solve this problem. \nTo solve the problem of processing orders and managing the backlog, we can use two prio
# Intuition\n<!-- Describe your first thoughts on how to solve this problem. -->\nTo solve the problem of processing orders and managing the backlog, we can use two priority queues (heaps) to efficiently match buy and sell orders:\n\nBuy Orders: We need a max-heap to store the buy orders because we want to match the highest-priced buy order first.\nSell Orders: We need a min-heap to store the sell orders because we want to match the lowest-priced sell order first.\n___\n\n# Approach\n<!-- Describe your approach to solving the problem. -->Priority Queues:\n\nbuyBacklog: A max-heap stores buy orders with the highest prices at the top.\nsellBacklog: A min-heap stores sell orders with the lowest prices at the top.\nOrder Matching:\n\nFor buy orders, we check if they can be matched with the smallest sell order in the sellBacklog.\nFor sell orders, we check if they can be matched with the largest buy order in the buyBacklog.\nMatching continues until either the current order is exhausted or no more valid matches exist.\nHandling Remaining Orders:\n\nIf there are any unprocessed orders after matching, they are added to their respective backlogs (buy or sell).\n\nTotal Backlog Calculation:\nAfter processing all orders, we sum the remaining orders in both backlogs and return the result modulo 10^9 + 7.\n___\n\n# Complexity\n- Time complexity:\n<!-- Add your time complexity here, e.g. $$O(n)$$ -->O(n log n), where \'n\' is the number of orders.\n____\n\n- Space complexity:\n<!-- Add your space complexity here, e.g. $$O(n)$$ -->O(n), due to the space used by the priority queues for storing and buying sell orders.\n___\n\n# Code\n```csharp []\nusing System;\nusing System.Collections.Generic;\n\npublic class Solution {\n    private const int MOD = 1000000007;\n\n    public int GetNumberOfBacklogOrders(int[][] orders) {\n        // Max-heap for buy orders (store negative price to simulate max-heap using PriorityQueue)\n        PriorityQueue<(int price, int amount), int> buyBacklog = new PriorityQueue<(int price, int amount), int>(Comparer<int>.Create((x, y) => y.CompareTo(x)));\n        \n        // Min-heap for sell orders\n        PriorityQueue<(int price, int amount), int> sellBacklog = new PriorityQueue<(int price, int amount), int>();\n        \n        foreach (var order in orders) {\n            int price = order[0];\n            int amount = order[1];\n            int orderType = order[2];\n            \n            if (orderType == 0) {\n                // Buy order\n                while (amount > 0 && sellBacklog.Count > 0 && sellBacklog.Peek().price <= price) {\n                    var sellOrder = sellBacklog.Dequeue();\n                    int sellAmount = Math.Min(amount, sellOrder.amount);\n                    amount -= sellAmount;\n                    sellOrder.amount -= sellAmount;\n                    \n                    if (sellOrder.amount > 0) {\n                        sellBacklog.Enqueue(sellOrder, sellOrder.price);\n                    }\n                }\n                if (amount > 0) {\n                    buyBacklog.Enqueue((price, amount), price);\n                }\n            } else {\n                // Sell order\n                while (amount > 0 && buyBacklog.Count > 0 && buyBacklog.Peek().price >= price) {\n                    var buyOrder = buyBacklog.Dequeue();\n                    int buyAmount = Math.Min(amount, buyOrder.amount);\n                    amount -= buyAmount;\n                    buyOrder.amount -= buyAmount;\n                    \n                    if (buyOrder.amount > 0) {\n                        buyBacklog.Enqueue(buyOrder, buyOrder.price);\n                    }\n                }\n                if (amount > 0) {\n                    sellBacklog.Enqueue((price, amount), price);\n                }\n            }\n        }\n\n        // Calculate total backlog orders\n        long totalOrders = 0;\n        while (buyBacklog.Count > 0) {\n            totalOrders = (totalOrders + buyBacklog.Dequeue().amount) % MOD;\n        }\n        while (sellBacklog.Count > 0) {\n            totalOrders = (totalOrders + sellBacklog.Dequeue().amount) % MOD;\n        }\n\n        return (int)totalOrders;\n    }\n}\n```
['Array', 'Heap (Priority Queue)', 'Simulation', 'C#']