There is a simple rule of thumb for the number of cartographers: there are as many cartographers as there are file sections. File splitting depends on the size of the block into which you split HDFS files (64 MB, 128 MB, 256 MB depending on your configuration), note that FileInput formats are considered, but can determine their own behavior.
Partitions are important because they are tied to the physical location of the data in the cluster; Hadoop brings the code into the data, not the data into the code.
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