# 1011. Capacity To Ship Packages Within D Days

## Description

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

The ith 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 days days.

Example 1:

Input: weights = [1,2,3,4,5,6,7,8,9,10], days = 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], days = 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], days = 4
Output: 3
Explanation:
1st day: 1
2nd day: 2
3rd day: 3
4th day: 1, 1


Constraints:

• 1 <= days <= weights.length <= 5 * 104
• 1 <= weights[i] <= 500

## Solutions

Binary search.

• class Solution {
public int shipWithinDays(int[] weights, int days) {
int left = 0, right = 0;
for (int w : weights) {
left = Math.max(left, w);
right += w;
}
while (left < right) {
int mid = (left + right) >> 1;
if (check(mid, weights, days)) {
right = mid;
} else {
left = mid + 1;
}
}
return left;
}

private boolean check(int mx, int[] weights, int days) {
int ws = 0, cnt = 1;
for (int w : weights) {
ws += w;
if (ws > mx) {
ws = w;
++cnt;
}
}
return cnt <= days;
}
}

• class Solution {
public:
int shipWithinDays(vector<int>& weights, int days) {
int left = 0, right = 0;
for (auto& w : weights) {
left = max(left, w);
right += w;
}
auto check = [&](int mx) {
int ws = 0, cnt = 1;
for (auto& w : weights) {
ws += w;
if (ws > mx) {
ws = w;
++cnt;
}
}
return cnt <= days;
};
while (left < right) {
int mid = (left + right) >> 1;
if (check(mid)) {
right = mid;
} else {
left = mid + 1;
}
}
return left;
}
};

• class Solution:
def shipWithinDays(self, weights: List[int], days: int) -> int:
def check(mx):
ws, cnt = 0, 1
for w in weights:
ws += w
if ws > mx:
cnt += 1
ws = w
return cnt <= days

left, right = max(weights), sum(weights) + 1
return left + bisect_left(range(left, right), True, key=check)


• func shipWithinDays(weights []int, days int) int {
var left, right int
for _, w := range weights {
if left < w {
left = w
}
right += w
}
return left + sort.Search(right, func(mx int) bool {
mx += left
ws, cnt := 0, 1
for _, w := range weights {
ws += w
if ws > mx {
ws = w
cnt++
}
}
return cnt <= days
})
}

• function shipWithinDays(weights: number[], days: number): number {
let left = 0;
let right = 0;
for (const w of weights) {
left = Math.max(left, w);
right += w;
}
const check = (mx: number) => {
let ws = 0;
let cnt = 1;
for (const w of weights) {
ws += w;
if (ws > mx) {
ws = w;
++cnt;
}
}
return cnt <= days;
};
while (left < right) {
const mid = (left + right) >> 1;
if (check(mid)) {
right = mid;
} else {
left = mid + 1;
}
}
return left;
}