1) Create a memo grid that will be used to build the solution -
int[][] memo = new int[m][n];2) Fill the first Row and Columns of the memo matrix :
for(int i = 1; i < m; i++){
memo[i][0] = memo[i-1][0] + grid[i][0];
}
for(int j = 1; j < n; j++){
memo[0][j] = memo[0][j-1] + grid[0][j];
}3) Traverse over
memo and use the information of the cells in the previous row / col to fill the current cell :
for(int i = 1; i < m; i++){
for(int j = 1; j < n; j++){
memo[i][j] = grid[i][j] + Math.max(memo[i-1][j], memo[i][j-1]);
}
}4) Return the value stored in the last cell :
return memo[m-1][n-1];
