Contents

**Fill The Truck Maximum Units on a Truck Solution**

You are assigned to put some amount of boxes onto **one truck**. You are given a 2D array boxTypes, where boxTypes[i] = [numberOfBoxes_{i}, numberOfUnitsPerBox_{i}]:

- numberOfBoxes
_{i}is the number of boxes of type i. - numberOfUnitsPerBox
_{i}is the number of units in each box of the type i.

You are also given an integer truckSize, which is the **maximum** number of **boxes** that can be put on the truck. You can choose any boxes to put on the truck as long as the number of boxes does not exceed truckSize.

Return *the **maximum** total number of **units** that can be put on the truck.*

**Example 1:**

**Input:** boxTypes = [[1,3],[2,2],[3,1]], truckSize = 4

**Output:** 8

**Explanation:** There are:

- 1 box of the first type that contains 3 units.
- 2 boxes of the second type that contain 2 units each.
- 3 boxes of the third type that contain 1 unit each.

You can take all the boxes of the first and second types, and one box of the third type. The total number of units will be = (1 * 3) + (2 * 2) + (1 * 1) = 8.

**Example 2:**

**Input:** boxTypes = [[5,10],[2,5],[4,7],[3,9]], truckSize = 10

**Output:** 91

**Constraints:**

- 1 <= boxTypes.length <= 1000
- 1 <= numberOfBoxes
_{i}, numberOfUnitsPerBox_{i}<= 1000 - 1 <= truckSize <= 10
^{6}

**SOLUTION**

**Simple Sort Solution**

For this problem, we simply need to prioritize the more valuable boxes first. To do this, we should **sort** the boxtypes array (**B**) in descending order by the number of units per box (**B[i][1]**).

Then we can iterate through **B** and at each step, we should add as many of the **boxes** as we can, until we reach the truck size (**T**). We should add the number of **boxes** added multiplied by the units per box to our answer (**ans**), and decrease **T** by the same number of **boxes**.

Once the truck is full (**T == 0**), or once the iteration is done, we should **return ans**.

*Time Complexity: O(N log N)**where**N**is the length of**B**, for the sort**Space Complexity: O(1)*

** Program:** Fill The Truck Maximum Units on a Truck Solution in C++

```
class Solution {
public:
int maximumUnits(vector<vector<int>>& B, int T) {
sort(B.begin(), B.end(), [](auto& a, auto& b) { return b[1] < a[1];});
int ans = 0;
for (auto& b : B) {
int count = min(b[0], T);
ans += count * b[1], T -= count;
if (!T) return ans;
}
return ans;
}
};
```

** Program: ** Fill The Truck Maximum Units on a Truck Solution in Python

```
class Solution:
def maximumUnits(self, B: List[List[int]], T: int) -> int:
B.sort(key=lambda x: x[1], reverse=True)
ans = 0
for b,n in B:
boxes = min(b, T)
ans += boxes * n
T -= boxes
if T == 0: return ans
return ans
```

** Program: ** Fill The Truck Maximum Units on a Truck Solution in Java

```
class Solution {
public int maximumUnits(int[][] B, int T) {
Arrays.sort(B, (a,b) -> b[1] - a[1]);
int ans = 0;
for (int[] b : B) {
int count = Math.min(b[0], T);
ans += count * b[1];
T -= count;
if (T == 0) return ans;
}
return ans;
}
}
```

**Program**** :** Fill The Truck Maximum Units on a Truck Solution in JavaScript

```
var maximumUnits = function(B, T) {
B.sort((a,b) => b[1] - a[1])
let ans = 0
for (let i = 0; T && i < B.length; i++) {
let count = Math.min(B[i][0], T)
ans += count * B[i][1], T -= count
}
return ans
};
```

**Greedily Select Max Units/Box Ratio**

The given constraints for numberOfUnitsPerBox are small enough that we can use an approach similar to counting sort to reduce the time complexity to O(N).

Here, we can declare an array *freq* of size=1000 (which is maximum number of units per box) where *freq[i]* will denote the number of boxes that can hold *i* number of units. We can iterate through the given *boxTypes* array and populate the freq array. Then we can iterate over the freq array and greedily choose starting from i=1000 till we run out of *truckSize* or pick all available boxes.

*Time Complexity :***O(N)**

*Space Complexity :***O(1)**

** Program**: Maximum Units on a Truck Solution in C++

```
int maximumUnits(vector<vector<int>>& boxTypes, int truckSize) {
int freq[1001]{0}, maxUnits = 0; // freq[i] = number of boxes that can hold i units
for(auto& box : boxTypes) freq[box[1]] += box[0];
// greedily choose starting from max units till either truckSize runs out or you choose all boxes
for(int units = 1000; truckSize > 0 && ~units; --units) {
maxUnits += min(truckSize, freq[units]) * units;
truckSize -= freq[units];
}
return maxUnits;
}
```

** Program**:

**Maximum Units on a Truck Solution in Python**

```
def maximumUnits(self, boxTypes: List[List[int]], truckSize: int) -> int:
freq, max_units = [0]*1001, 0
for box in boxTypes:
freq[box[1]] += box[0]
for units in range(1000,0,-1):
if truckSize < 0: break
max_units += min(truckSize, freq[units]) * units
truckSize -= freq[units]
return max_units
```

** Program Java**: Maximum Units on a Truck Solution in Java

```
class Solution {
public int maximumUnits(int[][] boxTypes, int truckSize) {
Arrays.sort(boxTypes,(a,b)->(b[1]-a[1]));
int i=0;
int ans=0;
while(i<boxTypes.length && truckSize>0){
if(truckSize-boxTypes[i][0]>=0){
truckSize-=boxTypes[i][0];
ans+=boxTypes[i][0]*boxTypes[i][1];}else{
ans+=boxTypes[i][1]*truckSize;
truckSize=0;
}
System.out.println(ans);
i++;
}
return ans;
}
}
```

**Bucket Sort Solution**

This time we will store info into sizeBucket, an array of 1001 elements (to cover all the provided range) all set to 0 and that we will populate while also storing the extremes of said range in minBucket and maxBucket, increasing each bucket of size boxType[1] by boxType[0] (how many we have) as we go. Be sure to add, not to assign here, since we do not know if we would be given multiple entries of the same size.

Once done, we can loop through the boxes we bucket-sorted going from maxBucket to minBucket (included) and following a logic specular to the previous one.

This bucket sorting version, which despite using buckets, turns out to be even more efficient in terms of space too:

** Program:** Fill The Truck Maximum Units on a Truck Solution in C++

```
class Solution {
public:
int maximumUnits(vector<vector<int>>& boxes, int truckSize) {
// support variables
int res = 0, sizeBucket[1001] = {}, maxBucket = INT_MIN, minBucket = INT_MAX;
// bucket sorting tthe boxes and recording the bucket range
for (auto &boxType: boxes) {
maxBucket = max(maxBucket, boxType[1]);
minBucket = min(minBucket, boxType[1]);
sizeBucket[boxType[1]] += boxType[0];
}
// carrying as many larger sized boxes as we can first
for (int i = maxBucket, size, currBatch; i >= minBucket; i--) {
size = sizeBucket[i];
if (!size) continue;
currBatch = min(size, truckSize);
truckSize -= currBatch;
res += currBatch * i;
if (!truckSize) break;
}
return res;
}
};
```

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