python coding test course, game development

Today, we will solve an algorithm problem for game development using Python. In this tutorial, we will enhance our problem-solving skills through algorithm problems and learn various techniques and concepts that can be applied to real game development.

Problem Description

Problem: “Strange Grid” Game

A grid-shaped game board is given, where each cell contains an integer. In the game, the player starts from outside the boundary of the board and can move up to 3 cells. However, the score that the player can move is calculated as the sum of the values of each cell. The player must choose moves in such a way that they ultimately have a score of 0 or more. Find the possible maximum score while visiting all the cells of the game board.

Input

        First line: Size of the grid N (1 ≤ N ≤ 10)
        Next N lines: Each element of the grid (−100 ≤ element ≤ 100)

Output

        Maximum achievable score

Example Input

Example Output

Problem Analysis

This problem requires using the ‘DFS (Depth First Search)’ technique to explore all possible paths and find the maximum score among them. First, we need to define the moving paths for each cell in the grid. According to the given rules, let us explore all possible paths from the starting point to find the highest total score.

Problem Solving Process

1. Set Up Basic Structure

To solve the problem, we will implement DFS using a recursive function. The recursive function will explore all possible paths from the current position. Here is the basic framework.

def dfs(x, y, score):
    # Function to explore all possible paths from the current position and return the maximum score
    pass

2. Implement Path Exploration Logic

Now, we should be able to calculate the positions when moving up, down, left, and right from each cell. To do this, we will use a direction array. We can use the following direction array to explore paths.

dx = [0, 1, 0, -1] # Left and Right
dy = [1, 0, -1, 0] # Up and Down

3. Implement Recursive Function

Now let’s recursively move within the DFS function and calculate the scores. We will check the possibility of movement based on the size of the grid and the current score, and set the boundary condition.

def dfs(x, y, score, visited):
    if x < 0 or x >= N or y < 0 or y >= N or visited[x][y]:
        return score
    
    visited[x][y] = True
    score += grid[x][y] # Add the score of the current position to the current score.
    
    max_score = score
    for i in range(4):
        new_x = x + dx[i]
        new_y = y + dy[i]
        max_score = max(max_score, dfs(new_x, new_y, score, visited))
    
    visited[x][y] = False # Backtracking
    return max_score

4. Implement Main Function

To start exploring all paths, we need to define the main function. In this function, we will read the grid input and start DFS exploration. Finally, we output the maximum score.

def main():
    global grid, N
    N = int(input())
    grid = [list(map(int, input().split())) for _ in range(N)]
    
    visited = [[False]*N for _ in range(N)]
    max_total_score = 0
    
    # Start DFS from all positions.
    for i in range(N):
        for j in range(N):
            max_total_score = max(max_total_score, dfs(i, j, 0, visited))
    
    print(max_total_score)

5. Full Code

The complete code that integrates all parts is as follows.

def dfs(x, y, score, visited):
    if x < 0 or x >= N or y < 0 or y >= N or visited[x][y]:
        return score
    
    visited[x][y] = True
    score += grid[x][y]
    
    max_score = score
    for i in range(4):
        new_x = x + dx[i]
        new_y = y + dy[i]
        max_score = max(max_score, dfs(new_x, new_y, score, visited))
    
    visited[x][y] = False
    return max_score

def main():
    global grid, N
    N = int(input())
    grid = [list(map(int, input().split())) for _ in range(N)]
    
    visited = [[False]*N for _ in range(N)]
    max_total_score = 0
    
    for i in range(N):
        for j in range(N):
            max_total_score = max(max_total_score, dfs(i, j, 0, visited))
    
    print(max_total_score)

if __name__ == "__main__":
    main()

Conclusion

Through this problem, we learned how to utilize DFS to explore paths and maximize points in a game environment. By solving coding problems through algorithms, we can enhance our effectiveness as game developers.

Additional Learning Resources

Referencing the following materials can provide deeper learning: