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Formatted question description: https://leetcode.ca/all/2106.html

# 2106. Maximum Fruits Harvested After at Most K Steps (Hard)

Fruits are available at some positions on an infinite x-axis. You are given a 2D integer array `fruits`

where `fruits[i] = [position`

depicts _{i}, amount_{i}]`amount`

fruits at the position _{i}`position`

. _{i}`fruits`

is already **sorted** by `position`

in _{i}**ascending order**, and each `position`

is _{i}**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*.

**Example 1:**

Input:fruits = [[2,8],[6,3],[8,6]], startPos = 5, k = 4Output:9Explanation: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 = 4Output:14Explanation: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 = 2Output:0Explanation: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`

for any_{i-1}< position_{i}`i > 0`

(**0-indexed**)`1 <= amount`

_{i}<= 10^{4}`0 <= k <= 2 * 10`

^{5}

**Similar Questions**:

## Solution 1. Sliding Window

```
// OJ: https://leetcode.com/problems/maximum-fruits-harvested-after-at-most-k-steps/
// Time: O(N)
// Space: O(1)
class Solution {
public:
int maxTotalFruits(vector<vector<int>>& A, int start, int k) {
int N = A.size(), i = 0, sum = 0;
for (; i < N && A[i][0] <= start; ++i);
int j = i;
while (j < N && A[j][0] - start <= k) sum += A[j++][1];
--j;
int ans = sum;
while (i > 0) {
--i;
sum += A[i][1];
while (j >= i && A[j][0] - start + A[j][0] - A[i][0] > k) {
sum -= A[j--][1];
}
if (j < i) continue;
if (A[j][0] < start) break;
ans = max(ans, sum);
}
i = N - 1;
sum = 0;
for (; i >= 0 && A[i][0] >= start; --i);
j = i;
while (j >= 0 && start - A[j][0] <= k) sum += A[j--][1];
++j;
ans = max(ans, sum);
while (i < N - 1) {
++i;
sum += A[i][1];
while (j <= i && start - A[j][0] + A[i][0] - A[j][0] > k) {
sum -= A[j++][1];
}
if (j > i) continue;
if (A[j][0] > start) break;
ans = max(ans, sum);
}
return ans;
}
};
```

## Solution 2. Sliding Window

Note: when comparing 2 vectors, the result is determined in the following order:

- The first place where the values differ between the two arrays.
- If we’ve exhausted one array and still can’t have a difference, the array with longer length is greater.

In the following code, we use `{start - k}`

in the binary search. It is always smaller than a position with the same `x`

value `{start - k, amount}`

. So using `upper_bound`

or `lower_bound`

makes no difference.

`(start - A[i][0]) + (A[j][0] - A[i][0])`

is the steps needed to go left first then right.

`(A[j][0] - A[i][0]) + (A[j][0] - start)`

is the steps needed to go right first then left.

```
// OJ: https://leetcode.com/problems/maximum-fruits-harvested-after-at-most-k-steps/
// Time: O(N)
// Space: O(1)
// Ref: https://leetcode.com/problems/maximum-fruits-harvested-after-at-most-k-steps/discuss/1624215/(Strange)-Sliding-Window
class Solution {
public:
int maxTotalFruits(vector<vector<int>>& A, int start, int k) {
int i = upper_bound(begin(A), end(A), vector<int>{start - k}) - begin(A), sum = 0, ans = 0, N = A.size();
for (int j = i; j < N && A[j][0] <= start + k; ++j) {
sum += A[j][1];
while (min(start - 2 * A[i][0] + A[j][0], 2 * A[j][0] - A[i][0] - start) > k) sum -= A[i++][1];
ans = max(ans, sum);
}
return ans;
}
};
```