The Column for Letter "E"
Now that we've filled in the column for the letter B, let's move on to the column for the letter E from the string best.
Calculating the Costs
Starting with E and T, we again find that the two letters are different, so the edit cost is 1. Here are the calculations for the cell:
- From Above: (1 + 1 = 2)
- From the Left: (2 + 1 = 3)
- From the Diagonal: (1 + 1 = 2)
The minimum of these is 2, so we place it in the cell where E intersects with T.
Next, we move to E and e. The two letters are the same, so the edit cost is 0. The calculations for this cell are:
- From Above: (2 + 1 = 3)
- From the Left: (1 + 1 = 2)
- From the Diagonal: (0 + 1 = 1)
The minimum is 1, so we place it in the cell where E intersects with e.
The Updated Matrix
Here's how our matrix looks after filling in the "E" column:
| b | E | s | t | ||
|---|---|---|---|---|---|
| 0 | 1 | 2 | 3 | 4 | |
| T | 1 | 1 | 2 | ||
| e | 2 | 2 | 1 | ||
| s | 3 | 3 | 2 | ||
| t | 4 | 4 | 3 |
We've successfully filled in the second column for the letter E. As before, we'd continue this process for the remaining columns to complete the matrix and find the total edit distance.
