# Progress: TFR Scrapped, Contour Introduced

Hmm, after running some numbers using the TFR strategy on a field with 10 columns, the (max) number of states is 1.099511628 x 10^12 (2^40). Which is way too much. This could be done with TTR strategy, giving only 1048576 (2^20) states. This wouldn’t work well with L pieces and straight pieces.

TFR could still be used if nothing else is available with a small amount of state space reduction. By removing any bottom rows from the 4 rows that aren’t required, the state space can be something else. For example:
``` 01111111    00000000 11110111 = 00000000 11110111 =/ 00000000 10101111    01111111 `````` 00010000    00000000 00110000 = 00000000 11101111 =/ 00010000 10100110    00110000 ```

However, even this won’t be enough to sufficiently reduce the state space.

Another strategy to take is using the contour method as seen here. The values will be all integers between (and including) {-3,…,3}. The contours are measured in relation to the current elevation of the preceding block. So the first column is taken as the base at the highest block and then numbers from {-3,…,3} are used to represent the differences in height of the blocks. Any difference outside the set is truncated to -3 or 3.
This method will give a maximum of 40353607 (7^9) states with 10 columns (9 = 10 -1). 7 is the number of possible values.

This strategy should be implemented before TFR strategy due to it’s higher chance of success.

The contour strategy would also benefit from state space reduction which will be looked at later.