1. [LO 1, LO 2, LO 3 & LO 4, Treasure Hunter Description You are in front of a cave that has treasures. The cave can be represented in a grid which has rows numbered from 1 to , and columns numbered from 1 to . For this problem, define (x,y ) as a tile that is in the the-x row and the y-row. There is a character in each tile, which indicates the type of that tile. Tiles can be floors, walls, or treasures which are represented respectively by the characters '.' (period), '#' (hashmark), and '*' (asterisk). You can go through the floor tiles and treasures, but you can't get past the wall tiles. Initially, you are in a tile (??, Sy). You want to visit all the treasure squares, and retrieve the treasure. When you visit a treasure tile, the treasure is instantly retrieved, and the tile turns into a floor. In a move, if you are on a tile (?,y), then you can move to the right tile above (?-1,y), right (?,y + 1), down (? + 1, ), and left (?, 1) of the current tile. The tile you visit must not be off the grid, and must not be a wall tile. Determine the minimum number of steps you can take to retrieve all the treasures. Input Format The first line contains 3 integers, N, M, and T. The second line contains 2 integers, Sx and Sy. It is guaranteed that this tile is a floor tile. The next N lines contain M characters. The characters in the i-th row and j-th column represent the tile type. Guaranteed that there are exactly T characters '*' in the grid. Output Format A line containing the minimum number of steps to retrieve all treasures. If you cannot retrieve all the treasures, remove 1. Example Input and Output Input Example Output Example 1 6 5 1 3 **.*** 7 5 5 2 2 1 ##### ....# #.#*# #*..# ##### 6 5 7 4 1 2 #.##### #*...*# #..#### ##.#..# #.....# #*.#.*# ####### 19 3 5 2 1 2 #.### #*#*# ##### -1 Explanation Example In the first sample test case, you can perform the following sequence of steps: 1. walk left towards (1, 2) and pick up the treasure, 2. walk left towards (1,1) and pick up the treasure, 3. walk right towards (1, 2), 4. walk right towards (1, 3), 5. walk to the right towards (1, 4) and pick up the treasure, 6. walk right towards (1,5) and pick up the treasure, and 7. Walk to the right towards (1, 6) and pick up the treasure. Task You are asked to create an algorithm that can solve a given problem. Provide an analysis of why your algorithm is correct, and write down the time complexity of your algorithm. Note that you are not asked to program, but you may attach your code as supporting evidence for your algorithm. NOTE LO1: Explain fundamental concept of analysis arithms. LO2: Apply algorithm techniques and methods. LO3: Solve a problem using specific algorithm. LO4: Compare several algorithm design methods. Please answer the bottom question, and please don't reject. I need it in 60-90 minutes, thanks
1. [LO 1, LO 2, LO 3 & LO 4, Treasure Hunter Description
You are in front of a cave that has treasures. The cave can be represented in a grid which has rows numbered from 1 to , and columns numbered from 1 to . For this problem, define (x,y ) as a tile that is in the the-x row and the y-row. There is a character in each tile, which indicates the type of that tile. Tiles can be floors, walls, or treasures which are represented respectively by the characters '.' (period), '#' (hashmark), and '*' (asterisk). You can go through the floor tiles and treasures, but you can't get past the wall tiles.
Initially, you are in a tile (??, Sy). You want to visit all the treasure squares, and retrieve the treasure. When you visit a treasure tile, the treasure is instantly retrieved, and the tile turns into a floor.
In a move, if you are on a tile (?,y), then you can move to the right tile above (?-1,y), right (?,y + 1), down (? + 1, ), and left (?, 1) of the current tile. The tile you visit must not be off the grid, and must not be a wall tile.
Determine the minimum number of steps you can take to retrieve all the treasures.
Input Format
The first line contains 3 integers, N, M, and T.
The second line contains 2 integers, Sx and Sy. It is guaranteed that this tile is a floor tile.
The next N lines contain M characters. The characters in the i-th row and j-th column represent the tile type. Guaranteed that there are exactly T characters '*' in the grid.
Output Format
A line containing the minimum number of steps to retrieve all treasures. If you cannot retrieve all the treasures, remove 1.
Example Input and Output
|
Input Example |
Output Example |
|
1 6 5 1 3 **.*** |
7 |
|
5 5 2 2 1 ##### ....# #.#*# #*..# ##### |
6 |
|
5 7 4 1 2 #.##### #*...*# #..#### ##.#..# #.....# #*.#.*# ####### |
19 |
|
3 5 2 1 2 #.### #*#*# ##### |
-1 |
Explanation Example
In the first sample test case, you can perform the following sequence of steps:
1. walk left towards (1, 2) and pick up the treasure,
2. walk left towards (1,1) and pick up the treasure,
3. walk right towards (1, 2),
4. walk right towards (1, 3),
5. walk to the right towards (1, 4) and pick up the treasure,
6. walk right towards (1,5) and pick up the treasure, and
7. Walk to the right towards (1, 6) and pick up the treasure.
Task
You are asked to create an
NOTE
LO1: Explain fundamental concept of analysis arithms.
LO2: Apply algorithm techniques and methods.
LO3: Solve a problem using specific algorithm.
LO4: Compare several algorithm design methods.
Please answer the bottom question, and please don't reject. I need it in 60-90 minutes, thanks
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