TheTower | Topcoder Archive

Problem Statement

N checkers are placed on an infinitely large board. The i-th checker is in the cell at row x[i], column y[i]. There can be more than one checker in the same cell. A move consists of taking one checker and moving it one cell up, down, left or right.

Return a int[] containing exactly N elements, where the i-th element (0-based) is the minimum number of moves necessary to end up with at least i+1 checkers in the same cell.

Definition

Class:: TheTower
Method:: count
Parameters:: int[], int[]
Returns:: int[]
Method signature:: int[] count(int[] x, int[] y)
(be sure your method is public)

Constraints

x will contain between 1 and 50 elements, inclusive.
y will contain the same number of elements as x.
Each element of x will be between 1 and 1,000,000, inclusive.
Each element of y will be between 1 and 1,000,000, inclusive.

Examples

```
{1, 2, 4, 9}
```
```
{1, 1, 1, 1}
```
```
Returns: {0, 1, 3, 10 }
```
Here is one possible way to get the minimal number of moves: for 1 checker: do nothing for 2 checkers: put the first two checkers at cell (1, 1) for 3 checkers: put the first three checkers at cell (2, 1) for 4 checkers: put all the checkers at cell (3, 1)
```
{15, 15, 14, 16}
```
```
{14, 16, 15, 15}
```
```
Returns: {0, 2, 3, 4 }
```
Whenever we need to have more than one checker in a single cell, we can put them in cell (15, 15).
```
{4, 4}
```
```
{7, 7}
```
```
Returns: {0, 0 }
```
They are already at the same cell.

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