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 do it using memoization. Here is Java-like pseudodoce (memo, R, and C are assumed to be instance variables available to the max method).

int R = 10, C = 20;
int memo[][] = new int[R][C];
for (int r=0 ; r != R ; r++)
    for (int c = 0 ; c != C ; c++)
        memo[r][c] = -1;
int res = max(0, 0, field);

int max(int r, int c, int[][] field) {
    if (memo[r][c] != -1) return memo[r][c];
    int down = 0; right = 0;
    if (r != R) down = max(r+1, c, field);
    if (c != C) right = max(r, c+1, field);
    return memo[r][c] = (field[r][c] + Math.max(down, right));
}