TopCoder Statistics - Problem Statement

Problem Statement

Fox Ciel is playing a game named Bomberfox. The game is played on a rectangular grid divided into 1x1 cells. Each cell is either a wall or a floor. Initially, all the floor is colored white.

Ciel can place bombs onto floor cells of the field. When a bomb explodes, its blast spreads to four direction - up, down, left and right. In each of the four directions the blast only stops when it hits the wall. When a cell gets hit by a blast, its color turns to red. The purpose of the game is to color all floor cells red by placing as few bombs as possible.

You are given a String[] grid, which represents the grid of the game. The j-th character of the i-th element of grid is '#' if the cell in the j-th column of the i-th row is a wall, and is '.' if the cell is a floor (quotes for clarity). Your method must return the minimum required number of bombs.

In this problem, there is an additional constraint: the floor cells form a tree. A more formal specification follows: We say that two cells are adjacent when they share an edge. A path from cell A to cell B is a sequence of distinct cells such that the first cell in the sequence is cell A, the last cell is B, and each pair of consecutive cells in the sequence is adjacent. A floor-only path is a path such that all cells in it, including A and B, are floor cells. The test data for this task has the following property: For each pair of floor cells in the grid, there is exactly one floor-only path from one of them to the other.

Definition

Class:: FoxBomb
Method:: getMinimumCost
Parameters:: String[]
Returns:: int
Method signature:: int getMinimumCost(String[] grid)
(be sure your method is public)

Constraints

grid will contain between 1 and 50 elements, inclusive.
Each element of grid will contain between 1 and 50 characters, inclusive.
All elements of grid will contain the same number of characters.
Each character of grid will be either '#' or '.'.
grid will contain at least one '.' character.
Floor cells of grid will form a tree. See the statement for formal constraints.

Examples

{"#..." ,"..##" ,"#.##"}

Returns: 2

In this case, there are multiple optimal solutions. One of the optimal solution is shown below. Here, 'B' represents a cell to which Ciel should place a bomb. #.B. .B## #.##
{".#.#.#." ,"......." ,".#.#.#."}

Returns: 4

One optimal solution is shown below. .#.#.#. B.B.B.B .#.#.#.
{"######################################" ,"######################################" ,"###.....................##############" ,"###.###################.###....#...###" ,"###.###################.###.######.###" ,"###.###################.###.######.###" ,"###.###################.###.######.###" ,"###.###################.###.######.###" ,"###.###################.###.######.###" ,"###.........####........###.######.###" ,"###########.###########.###........###" ,"###########.###########.##########.###" ,"###########.###########.##########.###" ,"###########.###########.##########.###" ,"###########.###########.##########.###" ,"##..........##..........##########.###" ,"#######################............###" ,"######################################"}

Returns: 9
{".#." ,"..." ,"#.#" ,"..." ,".#."}

Returns: 5
{"."}

Returns: 1
{"."}

Returns: 1
{".."}

Returns: 1
{"." ,"."}

Returns: 1
{".................................................."}

Returns: 1
{"#########################.########################"}

Returns: 1
{"." ,"." ,"." ,"." ,"." ,"." ,"." ,"." ,"." ,"." ,"." ,"." ,"." ,"." ,"." ,"." ,"." ,"." ,"." ,"." ,"." ,"." ,"." ,"." ,"." ,"." ,"." ,"." ,"." ,"." ,"." ,"." ,"." ,"." ,"." ,"." ,"." ,"." ,"." ,"." ,"." ,"." ,"." ,"." ,"." ,"." ,"." ,"." ,"." ,"."}

Returns: 1
{"#" ,"#" ,"#" ,"#" ,"#" ,"#" ,"#" ,"#" ,"#" ,"#" ,"#" ,"#" ,"#" ,"#" ,"#" ,"#" ,"#" ,"#" ,"#" ,"#" ,"#" ,"#" ,"#" ,"#" ,"#" ,"#" ,"#" ,"#" ,"#" ,"#" ,"#" ,"#" ,"#" ,"#" ,"#" ,"#" ,"#" ,"#" ,"#" ,"#" ,"#" ,"#" ,"." ,"." ,"." ,"#" ,"#" ,"#" ,"#" ,"#"}

Returns: 1
{".." ,".#"}

Returns: 1
{"#." ,".."}

Returns: 1
{".." ,"#."}

Returns: 1
{".#" ,".."}

Returns: 1
{"....." ,".#.#."}

Returns: 3
{"....." ,".#.#." ,"..#.."}

Returns: 3
{"..#.." ,".#.#." ,"....."}

Returns: 3
{"..." ,".#." ,"..#" ,".#." ,"..."}

Returns: 3
{"..." ,".#." ,"#.." ,".#." ,"..."}

Returns: 3
{"###.#.#.###" ,"###.#.#.###" ,"###.#.#.###" ,"##.......##" ,"##.#.#.#.##" ,"#..#.#.#..#"}

Returns: 7
{"###.#.#.###" ,"##..#.#..##" ,"#.#.#.#.#.#" ,"#.........#" ,"##.#.#.#.##" ,"##.#.#.#.##" ,"##..###..##"}

Returns: 9
{"########..##########" ,"#########.......####" ,"####......##########" ,"#########..........." ,"..........##########" ,"#########..#########" ,"#######...##########" ,"#########.......####" ,"###.......##########" ,"#########.......####" ,"#######...##########"}

Returns: 11
{"######.####" ,"###.#..####" ,"###...#.###" ,"##.##...###" ,"##....##.##" ,"#.###....##" ,"#.....###.#" ,".####.....#" ,"......####." ,"#####......"}

Returns: 9
{".#####....." ,"....#..###." ,"###...#.###" ,"...##...##." ,".#....##..." ,"#.###....##" ,"#.....###.#" ,".####.....#" ,"......####." ,"#####......"}

Returns: 13
{"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"#########################.########################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################"}

Returns: 1
{"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################" ,"#########################.########################"}

Returns: 1
{"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,".................................................." ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################" ,"##################################################"}

Returns: 1
{"...#...#...#...#...#...#...#...#...#...#...#...#.." ,".#...#...#...#...#...#...#...#...#...#...#...#...#" ,".#################################################" ,".#...#...#...#...#...#...#...#...#...#...#...#...#" ,"...#...#...#...#...#...#...#...#...#...#...#...#.." ,"#################################################." ,"...#...#...#...#...#...#...#...#...#...#...#...#.." ,".#...#...#...#...#...#...#...#...#...#...#...#...#" ,".#################################################" ,".#...#...#...#...#...#...#...#...#...#...#...#...#" ,"...#...#...#...#...#...#...#...#...#...#...#...#.." ,"#################################################." ,"...#...#...#...#...#...#...#...#...#...#...#...#.." ,".#...#...#...#...#...#...#...#...#...#...#...#...#" ,".#################################################" ,".#...#...#...#...#...#...#...#...#...#...#...#...#" ,"...#...#...#...#...#...#...#...#...#...#...#...#.." ,"#################################################." ,"...#...#...#...#...#...#...#...#...#...#...#...#.." ,".#...#...#...#...#...#...#...#...#...#...#...#...#" ,".#################################################" ,".#...#...#...#...#...#...#...#...#...#...#...#...#" ,"...#...#...#...#...#...#...#...#...#...#...#...#.." ,"#################################################." ,"...#...#...#...#...#...#...#...#...#...#...#...#.." ,".#...#...#...#...#...#...#...#...#...#...#...#...#" ,".#################################################" ,".#...#...#...#...#...#...#...#...#...#...#...#...#" ,"...#...#...#...#...#...#...#...#...#...#...#...#.." ,"#################################################." ,"...#...#...#...#...#...#...#...#...#...#...#...#.." ,".#...#...#...#...#...#...#...#...#...#...#...#...#" ,".#################################################" ,".#...#...#...#...#...#...#...#...#...#...#...#...#" ,"...#...#...#...#...#...#...#...#...#...#...#...#.." ,"#################################################." ,"...#...#...#...#...#...#...#...#...#...#...#...#.." ,".#...#...#...#...#...#...#...#...#...#...#...#...#" ,".#################################################" ,".#...#...#...#...#...#...#...#...#...#...#...#...#" ,"...#...#...#...#...#...#...#...#...#...#...#...#.." ,"#################################################." ,"...#...#...#...#...#...#...#...#...#...#...#...#.." ,".#...#...#...#...#...#...#...#...#...#...#...#...#" ,".#################################################" ,".#...#...#...#...#...#...#...#...#...#...#...#...#" ,"...#...#...#...#...#...#...#...#...#...#...#...#.." ,"#################################################." ,"...#...#...#...#...#...#...#...#...#...#...#...#.." ,".#...#...#...#...#...#...#...#...#...#...#...#...#"}

Returns: 417
{"#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#." ,"#................................................." ,"..#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#." ,".#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#" ,".................................................#" ,".#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.." ,"#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#." ,"#................................................." ,"..#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#." ,".#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#" ,".................................................#" ,".#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.." ,"#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#." ,"#................................................." ,"..#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#." ,".#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#" ,".................................................#" ,".#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.." ,"#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#." ,"#................................................." ,"..#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#." ,".#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#" ,".................................................#" ,".#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.." ,"#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#." ,"#................................................." ,"..#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#." ,".#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#" ,".................................................#" ,".#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.." ,"#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#." ,"#................................................." ,"..#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#." ,".#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#" ,".................................................#" ,".#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.." ,"#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#." ,"#................................................." ,"..#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#." ,".#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#" ,".................................................#" ,".#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.." ,"#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#." ,"#................................................." ,"..#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#." ,".#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#" ,".................................................#" ,".#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.." ,"#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#." ,".................................................."}

Returns: 425
{".#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#" ,"..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#.." ,"#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#." ,".#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..." ,"..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..##." ,"#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#." ,".#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..." ,"..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..##." ,"#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#." ,".#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..." ,"..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..##." ,"#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#...." ,".#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#.#." ,"..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..##." ,"#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#...." ,".#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#.#." ,"..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..##." ,"#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#." ,".#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..." ,"..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..##." ,"#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#...." ,".#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#.#." ,"..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..##." ,"#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#...." ,".#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#.#." ,"..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..##." ,"#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#." ,".#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..." ,"..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..##." ,"#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#." ,".#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..." ,"..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..##." ,"#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#...." ,".#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#.#." ,"..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..##." ,"#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#...." ,".#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#.#." ,"..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..##." ,"#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#...." ,".#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#.#." ,"..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..##." ,"#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#...." ,".#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#.#." ,"..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..##." ,"#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#." ,".#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..." ,"..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..##." ,"#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#..#." ,".#.##.##.##.##.##.##.##.##.##.##.##.##.##.##.##..." ,"................................................#."}

Returns: 530
{".#","..",".#",".."}

Returns: 2
{"######","######","######","######","##.###","#...#.","..#..."}

Returns: 3
{"..........","###.#.##.#","...#...#..",".#.#.##.#.",".#..##....","..#.#..##.","#.#.#.###.","..##..##..",".#.#.#...#",".....#.#.."}

Returns: 16
{"..###....#....","#..#..##...##.","##...###.##.#.","#..##.#..#....","..#...#.#..#.#",".#..#.#..#.##.",".#.#...#..#...","..#..#.#.#..#.","#...#..#...##.","####..#.#.#...","#..#.#...##.#.","##..#..#.#..#.","###...#....#.."}

Returns: 29
{"....#..##....#....",".##..#....##..#.#.","#..#..#.##.#.#..#.","##.##...#....##.#.","#....#.##.###....#","..##..#...#...##..",".#..#...#.#.#...#.","..#.######...###..","#.#.....#..##....#","..##.##...##..##..",".#...#####...#.#.#","..#.#.#...#.#..#..","#.#.....#.#..#..#.","#.#.###.###.#..#..","...#...#.....#..#.",".#...#...#.#..#..."}

Returns: 46
{"#.........#.#.......#.","..###.#.##....#.#.#.#.",".#....#....###.###..#.","##.#.#.##.#..#..#..#..","....#...#.##..#..#...#",".##.#.#.#...#..#..##..","...#..#..##.##..#...#.",".##..#.#.##..##...#.#.",".##.##.#...#..#.#..#..","....#...##..##..##.#.#",".####.#...#...#..#.#..","......#.##.##.##.#...#",".#.#.#.#....#..###.#..","#...#....##..#....#.#.","..##..###..#.#.##.#.#.",".###.#..##.#..#...#...","..#..#.#...##...##..##",".##.#..#.#...###.#.#..","#....#....##.........#"}

Returns: 63
{".......#...#...#.",".###.#.###...##..",".#.##......#....#",".#....#####.#.#..",".#.###.......#.#.",".#...#.##.###..#.",".#####.#.#....#..",".......#...##.#.#","#######.#.#.###.#","................."}

Returns: 21
{".................#..#..",".#.#.#.#.###.#.#..#...#","#.#.#.##.#..#.#..#..#.#",".........#.#...#..#.#..",".########..#.#.#.#...#.",".#......#.##.#.#..#.##.",".####.#......#.#.#..#..",".....#.###.#.#.#.#.#..#",".#.#.#....#.#..#.#.#.#.","#.##.#.##....#...#.#.#.",".....#.#####..##...#.#.",".###.#..#..#.#..####.#.",".#.#.##.#.##...##....#.",".#....#.#.#.###...####.","..#.###.#.....#.##.....","#.###...#.##.##....###.","......##...#....#.#...."}

Returns: 53
{"..........##.#...............",".####.###....#.#####.##.####.",".#...#....####.....#...#.....",".#.##..###.....####.##..####.",".#..#.##...####........#....#",".#.##.#..##...#.##.#.#.#.##..",".#.....#.#..#.#.#.#..###.#.#.",".#######.#.####.#.#.#......#.","...........##...#...#.######.",".#.#.######...##.###..#......","#.#.##......##......#.#.####.",".......####..#.##.#.#.#.#....",".#.####...#.#..#.#..#.#..#.#.","..#....#.##..#...#.##.#.#.##.",".#..##......#.##.#.#..#.#...#",".###.#######.....#.#.#...##..","...........#.#.###.#.#.##.##.",".######.##...##....#.#.......",".#.....##.#.#.#.#.#..#.#####.",".##.##.....#..#.#.#.#.##....#","....#.####...#..#.#.#....##..","#.##......##.#.#.##.#.#.#...#",".#.#.##.##.#.#.......#..#.##.","......#.......#.#.##...#....."}

Returns: 86
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Returns: 119
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Returns: 345
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Returns: 311
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Returns: 2
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Returns: 19
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Returns: 2
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Returns: 2
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Returns: 1
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Returns: 4
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Returns: 30
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Returns: 393
{"###.#", ".#..#", "...#.", "##...", "...##", ".#...", "####." }

Returns: 5
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Returns: 400
{"#####", ".....", "#.#.#", "..###" }

Returns: 2

Statistics

Problem Statement for "FoxBomb"

Problem Statement

Definition

Constraints

Examples