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Problem of the day

Given a rod of length ‘N’ units. The rod can be cut into different sizes and each size has a cost associated with it. Determine the maximum cost obtained by cutting the rod and selling its pieces.

```
1. The sizes will range from 1 to ‘N’ and will be integers.
2. The sum of the pieces cut should be equal to ‘N’.
3. Consider 1-based indexing.
```

Detailed explanation

```
1 <= T <= 50
1 <= N <= 100
1 <= A[i] <= 100
Where ‘T’ is the total number of test cases, ‘N’ denotes the length of the rod, and A[i] is the cost of sub-length.
Time limit: 1 sec.
```

```
2
5
2 5 7 8 10
8
3 5 8 9 10 17 17 20
```

```
12
24
```

```
Test case 1:
All possible partitions are:
1,1,1,1,1 max_cost=(2+2+2+2+2)=10
1,1,1,2 max_cost=(2+2+2+5)=11
1,1,3 max_cost=(2+2+7)=11
1,4 max_cost=(2+8)=10
5 max_cost=(10)=10
2,3 max_cost=(5+7)=12
1,2,2 max _cost=(1+5+5)=12
Clearly, if we cut the rod into lengths 1,2,2, or 2,3, we get the maximum cost which is 12.
Test case 2:
Possible partitions are:
1,1,1,1,1,1,1,1 max_cost=(3+3+3+3+3+3+3+3)=24
1,1,1,1,1,1,2 max_cost=(3+3+3+3+3+3+5)=23
1,1,1,1,2,2 max_cost=(3+3+3+3+5+5)=22
and so on….
If we cut the rod into 8 pieces of length 1, for each piece 3 adds up to the cost. Hence for 8 pieces, we get 8*3 = 24.
```

```
1
6
3 5 6 7 10 12
```

```
18
```