Maximum Fruits Harvested After at Most K Steps

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Problem Statement

Fruits are available at some positions on an infinite x-axis. You are given a 2D integer array fruits where fruits[i] = [position _i , amount _i ] depicts amount _i fruits at the position position _i . fruits is already sorted by position _i in ascending order , and each position _i is unique .

You are also given an integer startPos and an integer k . Initially, you are at the position startPos . From any position, you can either walk to the left or right . It takes one step to move one unit on the x-axis, and you can walk at most k steps in total. For every position you reach, you harvest all the fruits at that position, and the fruits will disappear from that position.

Return the maximum total number of fruits you can harvest .

Examples

Example 1

Input: fruits = [[2,8],[6,3],[8,6]], startPos = 5, k = 4
Output: 9
The optimal way is to:
- Move right to position 6 and harvest 3 fruits
- Move right to position 8 and harvest 6 fruits
You moved 3 steps and harvested 3 + 6 = 9 fruits in total.

Example 2

Input: fruits = [[0,9],[4,1],[5,7],[6,2],[7,4],[10,9]], startPos = 5, k = 4
Output: 14
You can move at most k = 4 steps, so you cannot reach position 0 nor 10.
The optimal way is to:
- Harvest the 7 fruits at the starting position 5
- Move left to position 4 and harvest 1 fruit
- Move right to position 6 and harvest 2 fruits
- Move right to position 7 and harvest 4 fruits
You moved 1 + 3 = 4 steps and harvested 7 + 1 + 2 + 4 = 14 fruits in total.

Example 3

Input: fruits = [[0,3],[6,4],[8,5]], startPos = 3, k = 2
Output: 0
You can move at most k = 2 steps and cannot reach any position with fruits.

Constraints

1 <= fruits.length <= 10 ^5

fruits[i].length == 2

0 <= startPos, position _i <= 2 * 10 ^5

position _i-1 < position _i for any i > 0 ( 0-indexed )

1 <= amount _i <= 10 ^4

0 <= k <= 2 * 10 ^5

😤

Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicBinary Search