351. Android Unlock Patterns π
Description
Android devices have a special lock screen with a 3 x 3
grid of dots. Users can set an "unlock pattern" by connecting the dots in a specific sequence, forming a series of joined line segments where each segment's endpoints are two consecutive dots in the sequence. A sequence of k
dots is a valid unlock pattern if both of the following are true:
- All the dots in the sequence are distinct.
- If the line segment connecting two consecutive dots in the sequence passes through the center of any other dot, the other dot must have previously appeared in the sequence. No jumps through the center non-selected dots are allowed.
- For example, connecting dots
2
and9
without dots5
or6
appearing beforehand is valid because the line from dot2
to dot9
does not pass through the center of either dot5
or6
. - However, connecting dots
1
and3
without dot2
appearing beforehand is invalid because the line from dot1
to dot3
passes through the center of dot2
.
- For example, connecting dots
Here are some example valid and invalid unlock patterns:
- The 1st pattern
[4,1,3,6]
is invalid because the line connecting dots1
and3
pass through dot2
, but dot2
did not previously appear in the sequence. - The 2nd pattern
[4,1,9,2]
is invalid because the line connecting dots1
and9
pass through dot5
, but dot5
did not previously appear in the sequence. - The 3rd pattern
[2,4,1,3,6]
is valid because it follows the conditions. The line connecting dots1
and3
meets the condition because dot2
previously appeared in the sequence. - The 4th pattern
[6,5,4,1,9,2]
is valid because it follows the conditions. The line connecting dots1
and9
meets the condition because dot5
previously appeared in the sequence.
Given two integers m
and n
, return the number of unique and valid unlock patterns of the Android grid lock screen that consist of at least m
keys and at most n
keys.
Two unlock patterns are considered unique if there is a dot in one sequence that is not in the other, or the order of the dots is different.
Example 1:
Input: m = 1, n = 1 Output: 9
Example 2:
Input: m = 1, n = 2 Output: 65
Constraints:
1 <= m, n <= 9
Solutions
Solution 1
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