# 1011. Capacity To Ship Packages Within D Days (Medium)

https://leetcode.com/problems/capacity-to-ship-packages-within-d-days/

A conveyor belt has packages that must be shipped from one port to another within `D` days.

The `i`-th package on the conveyor belt has a weight of `weights[i]`.  Each day, we load the ship with packages on the conveyor belt (in the order given by `weights`). We may not load more weight than the maximum weight capacity of the ship.

Return the least weight capacity of the ship that will result in all the packages on the conveyor belt being shipped within `D` days.

Example 1:

```Input: weights = [1,2,3,4,5,6,7,8,9,10], D = 5
Output: 15
Explanation:
A ship capacity of 15 is the minimum to ship all the packages in 5 days like this:
1st day: 1, 2, 3, 4, 5
2nd day: 6, 7
3rd day: 8
4th day: 9
5th day: 10

Note that the cargo must be shipped in the order given, so using a ship of capacity 14 and splitting the packages into parts like (2, 3, 4, 5), (1, 6, 7), (8), (9), (10) is not allowed.
```

Example 2:

```Input: weights = [3,2,2,4,1,4], D = 3
Output: 6
Explanation:
A ship capacity of 6 is the minimum to ship all the packages in 3 days like this:
1st day: 3, 2
2nd day: 2, 4
3rd day: 1, 4
```

Example 3:

```Input: weights = [1,2,3,1,1], D = 4
Output: 3
Explanation:
1st day: 1
2nd day: 2
3rd day: 3
4th day: 1, 1
```

Note:

1. `1 <= D <= weights.length <= 50000`
2. `1 <= weights[i] <= 500`

## Solutions

``````class Solution {

// This problem states that the packages need to be loaded in the order given by weights.
// This policy reduce the complexity of delivering the cargos. Assume there is no such
// restriction, for goods weight [3, 5, 6, 7, 14] and daily limit is 18, the shortest time is 2 days.
// On 1st day, [5,6,7]; On 2nd day, [3,14]. Suppose we consider the problem restriction,
// it will be at least 3 days.

public int shipWithinDays(int[] weights, int D) {
int max = 0;
int sum = 0;
for (int weight : weights) {
sum += weight;
if (weight > max) {
max = weight;
}
}

// since problem subjects to 1<=D<=weights.length, the least weight capacity of ship is max(weights)
int least = max;
int most = sum + 1;

while (least < most) {
int mid = (int) ((least * 1l + most * 1l) / 2);
int day = getDays(weights, mid);
if (day <= D) {
most = mid;
} else {
least = mid + 1;
}
}

return least;
}

private int getDays(int[] weights, int limit) {
int sum = 0;
int day = 1;
for (int weight : weights) {
if (sum + weight > limit) {
day++;
sum = weight;
} else {
sum += weight;
}
}

return day;
}
}
``````