C# Recursive DP solution
\n\n# Approach\n Describe your approach to solving the problem. The solution uses dynamic programming and recursion to count all possible routes from the start 
\n\n# Approach\n<!-- Describe your approach to solving the problem. -->The solution uses dynamic programming and recursion to count all possible routes from the start to the finish city within the given fuel constraint. The CountRoutes method initializes the DP array and calls the recursive helper method CountRoutesRecursive to calculate the count.\n___\n\n# Complexity\n- Time complexity:\n<!-- Add your time complexity here, e.g. $$O(n)$$ -->The time complexity of the solution is O(n * fuel^2), where n is the number of cities (length of the locations array) and fuel is the initial amount of fuel. This is because for each city, we iterate over all other cities and for each city, we iterate over the fuel range. So, the overall time complexity is proportional to n * fuel^2.\n___\n\n- Space complexity:\n<!-- Add your space complexity here, e.g. $$O(n)$$ -->The space complexity of the solution is O(n * fuel) because we use a 2D DP array of size n * fuel to store the intermediate results. Each cell in the DP array represents the number of routes from a city with a certain amount of fuel to the finish city. Hence, the space complexity is proportional to n * fuel.\n\n# Code\n```\nusing System;\n\npublic class Solution {\n    private const int MOD = 1000000007;\n    \n    public int CountRoutes(int[] locations, int start, int finish, int fuel) {\n        int[,] dp = new int[locations.Length, fuel + 1];\n        for (int i = 0; i < locations.Length; i++) {\n            for (int j = 0; j <= fuel; j++) {\n                dp[i, j] = -1; // Initialize with -1 indicating unvisited state\n            }\n        }\n        \n        return CountRoutesRecursive(locations, start, finish, fuel, dp);\n    }\n    \n    private int CountRoutesRecursive(int[] locations, int curr, int finish, int fuel, int[,] dp) {\n        if (dp[curr, fuel] != -1) {\n            return dp[curr, fuel];\n        }\n        \n        int count = 0;\n        if (curr == finish) {\n            count = 1; // Reached the finish city\n        }\n        \n        for (int i = 0; i < locations.Length; i++) {\n            if (i != curr) {\n                int distance = Math.Abs(locations[curr] - locations[i]);\n                if (fuel >= distance) {\n                    count = (count + CountRoutesRecursive(locations, i, finish, fuel - distance, dp)) % MOD;\n                }\n            }\n        }\n        \n        dp[curr, fuel] = count;\n        return count;\n    }\n}\n\n```
['C#']