如何为LeetCode最小加油次数问题设计递归解决方案？已实现递归代码但无法通过全部测试用例求助

Let's break down the issues in your current code and fix them step by step—since you specified you only care about the recursive approach, I'll keep that front and center.

Key Issues in Your Code #

• Incorrect Memoization Key: Your memo only uses target and currentFuel, but it's missing the start index. The state of our recursion depends on which stations we've already passed, so omitting start leads to caching wrong results for different scenarios.
• Confusing Distance Calculation: The initialDistance logic overcomplicates tracking fuel consumption to reach a station, leading to miscalculations of remaining fuel and target distance.
• Unnecessary Target Adjustment: The way you modify target in recursive calls adds confusion; we can simplify how we track remaining distance to the end.

Corrected Recursive Code #

import java.util.HashMap;
import java.util.Map;

class Solution {
    private static int totalTarget;

    private static int helper(int remainingDistance, int currentFuel, int startIdx, int[][] stations, Map<String, Integer> memo) {
        // If current fuel is enough to reach the end, no stops needed
        if (currentFuel >= remainingDistance) {
            return 0;
        }
        // No stations left to check, can't reach the end
        if (startIdx == stations.length) {
            return -1;
        }

        // Unique key for memo: includes all state variables
        String memoKey = remainingDistance + "," + currentFuel + "," + startIdx;
        if (memo.containsKey(memoKey)) {
            return memo.get(memoKey);
        }

        int minStops = Integer.MAX_VALUE;
        // Farthest we can go right now without refueling
        int maxReachable = (totalTarget - remainingDistance) + currentFuel;

        for (int i = startIdx; i < stations.length; i++) {
            int stationPos = stations[i][0];
            // Stations are sorted—if this one is out of reach, the rest are too
            if (stationPos > maxReachable) {
                break;
            }
            // Fuel needed to drive from current position to this station
            int fuelToStation = stationPos - (totalTarget - remainingDistance);
            // Fuel left after arriving at the station
            int fuelAfterArrival = currentFuel - fuelToStation;
            // Remaining distance from this station to the end
            int newRemaining = totalTarget - stationPos;

            // Recurse: we choose to refuel here, so add 1 to stop count
            int recursiveResult = helper(newRemaining, fuelAfterArrival + stations[i][1], i + 1, stations, memo);
            if (recursiveResult != -1) {
                minStops = Math.min(minStops, 1 + recursiveResult);
            }
        }

        // If no valid refuel path found, return -1; else return the minimum stops
        int finalResult = (minStops == Integer.MAX_VALUE) ? -1 : minStops;
        memo.put(memoKey, finalResult);
        return finalResult;
    }

    public static int minRefuelStopsBruteForce(int target, int startFuel, int[][] stations) {
        totalTarget = target;
        // Quick edge case: no stops needed at all
        if (startFuel >= target) {
            return 0;
        }
        return helper(target, startFuel, 0, stations, new HashMap<>());
    }
}

What Changed? #

1. Memoization Fix: Added startIdx to the memo key to ensure we cache results for the exact state (remaining distance, current fuel, and which stations are still available to choose from).
2. Simplified Distance Tracking: We track remainingDistance as the direct distance left to the end. Our current position is calculated as totalTarget - remainingDistance, making it easy to compute fuel needed to reach any station.
3. Early Loop Exit: Since stations are sorted by position, once we hit a station we can't reach, we break the loop early to save unnecessary computations.
4. Clearer Recursive Flow: When refueling at a station, we pass the new remaining distance (from the station to the end) and updated fuel (after driving to the station plus refueling).

Testing Tips #

Make sure to test edge cases like:

• No stations available (check if start fuel covers the target)
• All stations are unnecessary (start fuel is enough to reach the end)
• Needing to refuel at every station to reach the end
• A station that sits exactly at the maximum reachable distance with current fuel

内容的提问来源于stack exchange，提问作者IkhideIfidon