Fruit Into Baskets

You are visiting a farm that has a single row of fruit trees arranged from left to right. The trees are represented by an integer array fruits where fruits[i] is the type of fruit the ith tree produces.

You want to collect as much fruit as possible. However, the owner has some strict rules that you must follow:

• You only have two baskets, and each basket can only hold a single type of fruit. There is no limit on the amount of fruit each basket can hold.
• Starting from any tree of your choice, you must pick exactly one fruit from every tree (including the start tree) while moving to the right. The picked fruits must fit in one of your baskets.
• Once you reach a tree with fruit that cannot fit in your baskets, you must stop.

Given the integer array fruits, return the maximum number of fruits you can pick.

Example 1:

Input: fruits = [1,2,1] Output: 3 Explanation: We can pick from all 3 trees.

Example 2:

Input: fruits = [0,1,2,2] Output: 3 Explanation: We can pick from trees [1,2,2]. If we had started at the first tree, we would only pick from trees [0,1].

Example 3:

Input: fruits = [1,2,3,2,2] Output: 4 Explanation: We can pick from trees [2,3,2,2]. If we had started at the first tree, we would only pick from trees [1,2].

Constraints:

• 1 <= fruits.length <= 105
• 0 <= fruits[i] < fruits.length

Approach: Sliding Window with at Most Two Distinct Types

Algorithm

1. Use a sliding window defined by left and right pointers
2. Maintain a frequency map of the fruit types within the window
3. Expand the right pointer, adding each fruit to the map
4. If the map has more than two types, shrink from the left until only two types remain
5. Track the maximum window size seen

Time & Space Complexity

• Time Complexity: O(n) - each element enters and leaves the window once
• Space Complexity: O(1) - the frequency map holds at most a constant number of distinct types

Java Implementation

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

public class FruitIntoBaskets {

    /**
     * Return the maximum number of fruits you can pick with two baskets.
     * @param fruits Fruit type at each tree
     * @return Maximum number of pickable fruits
     */
    public static int totalFruit(int[] fruits) {
        Map<Integer, Integer> basket = new HashMap<>();
        int left = 0;
        int maxPicked = 0;

        for (int right = 0; right < fruits.length; right++) {
            basket.put(fruits[right], basket.getOrDefault(fruits[right], 0) + 1);

            while (basket.size() > 2) {
                int leftFruit = fruits[left];
                basket.put(leftFruit, basket.get(leftFruit) - 1);
                if (basket.get(leftFruit) == 0) {
                    basket.remove(leftFruit);
                }
                left++;
            }

            maxPicked = Math.max(maxPicked, right - left + 1);
        }

        return maxPicked;
    }

    // Test method
    public static void main(String[] args) {
        int[] fruits1 = {1, 2, 1};
        System.out.println("Input: fruits = [1,2,1]");
        System.out.println("Output: " + totalFruit(fruits1)); // Expected: 3

        int[] fruits2 = {0, 1, 2, 2};
        System.out.println("Input: fruits = [0,1,2,2]");
        System.out.println("Output: " + totalFruit(fruits2)); // Expected: 3

        int[] fruits3 = {1, 2, 3, 2, 2};
        System.out.println("Input: fruits = [1,2,3,2,2]");
        System.out.println("Output: " + totalFruit(fruits3)); // Expected: 4
    }
}

Example Walkthrough

For fruits = [1, 2, 3, 2, 2]:

1. right=0 fruit 1: window {1:1}, size 1
2. right=1 fruit 2: window {1:1, 2:1}, size 2
3. right=2 fruit 3: window {1:1, 2:1, 3:1} > 2, shrink. Remove left fruit 1, left=1. Window {2:1, 3:1}, size 2
4. right=3 fruit 2: window {2:2, 3:1}, size 3
5. right=4 fruit 2: window {2:3, 3:1}, size 4

Answer: 4.

Key Points

1. Two-Basket Constraint: The window may contain at most two distinct fruit types
2. Shrink on Violation: When a third type appears, move left until the window is valid again
3. Longest Substring Variant: This is “Longest Substring with At Most Two Distinct Characters” applied to an integer array
4. O(n) Time: Each fruit is added and removed at most once
5. Start Anywhere: The sliding window naturally tries every possible start