# Weightlifting solution codejam 2022 Round 1A

## Weightlifting solution codejam

### Problem

You are following a prescribed training for weightlifting. The training consists of a series of exercises that you must do in order. Each exercise requires a specific set of weights to be placed on a machine. There are WW types of different weights. For example, an exercise may require 33 weights of type A and 11 weight of type B, while the next requires 22 weights each of types A, C, and D.

The weights are placed on the machine as a stack. Formally, with a single operation, you can either add a new weight of any type to the top of the stack, or remove the weight that is currently at the top of the stack. You can load the weights for each exercise onto the machine’s stack in any order. So, if you place the weight of type B at the bottom in the first exercise of the example above, you will have to take all the weights off before putting on the weights for the second exercise. On the other hand, if you place the weight of type B third from the bottom, you can leave two of the weights of type A on the bottom of the stack to be part of the next exercise’s set, saving you some time. Given the amount of weights of each type needed for each exercise, find the minimum number of operations needed to do them all. You must complete the exercises in the order given. The machine stack starts out empty, and you must leave it empty after you finish with all your exercises.

## Weightlifting solution codejam

The first line of the input gives the number of test cases, TTTT test cases follow. Each test case starts with a line containing 22 integers EE and WW: the number of exercises and the number of types of weights. Weight types are numbered between 11 and WW. Then, EE lines follow. The ii-th of these lines contains WW integers Xi,1,Xi,2,,Xi,WXi,1,Xi,2,…,Xi,W representing that the ii-th exercise requires exactly Xi,jXi,j weights of type jj.

### Output

For each test case, output one line containing Case #xx: yy, where xx is the test case number (starting from 1) and yy is the minimum number of machine stack operations needed to run through all your exercises.

## Weightlifting solution codejam

Time limit: 20 seconds. Memory limit: 1 GB. 1T1001≤T≤100. 1Xi,1+Xi,2++Xi,W1≤Xi,1+Xi,2+⋯+Xi,W, for all ii. (Each exercise requires at least one weight.)

#### Test Set 1 (Visible Verdict)

1E101≤E≤10. 1W31≤W≤3. 0Xi,j30≤Xi,j≤3, for all i,ji,j.

#### Test Set 2 (Hidden Verdict)

1E1001≤E≤100. 1W1001≤W≤100. 0Xi,j1000≤Xi,j≤100, for all i,ji,j.

## Weightlifting solution codejam

Sample Input
3
3 1
1
2
1
2 3
1 2 1
2 1 2
3 3
3 1 1
3 3 3
2 3 3

Sample Output
Case #1: 4
Case #2: 12
Case #3: 20

In Sample Case #1, there is only one type of weight. The first exercise needs 11 weight, the second needs 22 weights, and the third needs 11 weight. You can complete the exercise in 44 operations as follows:
1. Add a weight onto the stack. You do the first exercise.
2. Add a weight onto the stack. You do the second exercise.
3. Remove a weight from the top of the stack. You do the third exercise.
4. Remove a weight from the top of the stack. Now the stack becomes empty.
In Sample Case #2, one way to complete the exercises in 1212 operations is as follows:
1. Add a weight of type 22.
2. Add a weight of type 33.
3. Add a weight of type 11.
4. Add a weight of type 22. Now the stack contains weights of types 2,3,1,22,3,1,2 from bottom to top. You do the first exercise.
5. Remove a weight of type 22 from the top of the stack.
6. Add a weight of type 33.
7. Add a weight of type 11. Now the stack contains weights of types 2,3,1,3,12,3,1,3,1 from bottom to top. You do the second exercise.
8. Remove a weight of type 11 from the top of the stack.
9. Remove a weight of type 33 from the top of the stack.
10. Remove a weight of type 11 from the top of the stack.
11. Remove a weight of type 33 from the top of the stack.
12. Remove a weight of type 22 from the top of the stack. Now the stack becomes empty.