Java - Maximum sum in path through a 2D array

Question

Basically I have a problem that goes something similar to this:

There is a garden of strawberry plants represented by a 2D, square array. Each plant(each element) h

Answer 1

You can solve this with DP tabulation method, with which you can save space from O(m*n) to just O(n). With DP Memorization, you need m*n matrix to store intermediate values. Following is my Python code. Hope it can help.

def max_path(field):
    dp = [sum(field[0][:i]) for i in range(1, len(field[0]) + 1)]
    for i in range(1, len(field)):
        for j in range(len(dp)):
            dp[j] = min(dp[j], dp[j - 1] if j > 0 else float('inf')) + field[i][j]
    return dp[-1]