Beats 100% on runtime, 85% on memory [EXPLAINED]
Intuition\nThe problem involves finding all possible routes from a starting city to a destination city with a limited amount of fuel. You can move between citie
# Intuition\nThe problem involves finding all possible routes from a starting city to a destination city with a limited amount of fuel. You can move between cities based on their distances and need to account for the fuel consumed for each move. The key insight is that a city can be revisited multiple times, allowing for various paths to be explored.\n\n# Approach\nUse Depth-First Search (DFS) with memoization to explore all routes from the starting city to the destination, keeping track of the remaining fuel and counting valid routes.\n\n# Complexity\n- Time complexity:\nO(N x F2) \n\n- Space complexity:\nO(N x F)\n\n# Code\n```typescript []\n/**\n * @param {number[]} locations - The positions of the cities.\n * @param {number} start - The starting city index.\n * @param {number} finish - The destination city index.\n * @param {number} fuel - The initial amount of fuel.\n * @return {number} - The number of possible routes to reach the destination city.\n */\nconst countRoutes = function(locations: number[], start: number, finish: number, fuel: number): number {\n    const MOD = 1000000007; // Modulo value to prevent overflow\n    const cache: number[][] = Array.from({ length: locations.length }, () => Array(fuel + 1).fill(-1)); // Cache for memoization\n\n    // Depth-First Search (DFS) function to explore routes\n    const DFS = (current: number, destination: number, remainingFuel: number): number => {\n        // Return cached result if already computed\n        if (cache[current][remainingFuel] !== -1) return cache[current][remainingFuel];\n\n        const distanceToDestination = Math.abs(locations[destination] - locations[current]); // Distance to the destination city\n        \n        // If the fuel needed to reach the destination exceeds available fuel, return 0\n        if (distanceToDestination > remainingFuel) {\n            cache[current][remainingFuel] = 0;\n            return 0;\n        }\n\n        let totalRoutes = (current === destination) ? 1 : 0; // Count this route if at destination\n\n        // Explore all possible cities to move to\n        for (let nextCity = 0; nextCity < locations.length; nextCity++) {\n            if (nextCity !== current) { // Avoid moving to the same city\n                const fuelCost = Math.abs(locations[nextCity] - locations[current]); // Cost to move to the next city\n                if (fuelCost <= remainingFuel) { // If enough fuel is available\n                    totalRoutes = (totalRoutes + DFS(nextCity, destination, remainingFuel - fuelCost)) % MOD; // Explore further\n                }\n            }\n        }\n\n        cache[current][remainingFuel] = totalRoutes; // Store the result in cache\n        return totalRoutes; // Return the total routes found\n    };\n\n    return DFS(start, finish, fuel); // Start DFS from the initial city\n};\n\n\n\n```
['TypeScript']