LeetCode 351. Android Unlock Patterns（安卓解锁）

原题网址：https://leetcode.com/problems/android-unlock-patterns/

Given an Android 3x3 key lock screen and two integers m and n, where 1 ≤ m ≤ n ≤ 9, count the total number of unlock patterns of the Android lock
screen, which consist of minimum of m keys and maximum n keys.

Rules for a valid pattern:

Each pattern must connect at least m keys and at most n keys.
All the keys must be distinct.
If the line connecting two consecutive keys in the pattern passes through any other keys, the other keys must have previously selected in the pattern. No jumps through non selected key is allowed.
The order of keys used matters.



Explanation:

| 1 | 2 | 3 |
| 4 | 5 | 6 |
| 7 | 8 | 9 |

Invalid move:

4 - 1 - 3 - 6

Line 1 - 3 passes through key 2 which had not been selected in the pattern.

Invalid move:

4 - 1 - 9 - 2

Line 1 - 9 passes through key 5 which had not been selected in the pattern.

Valid move:

2 - 4 - 1 - 3 - 6

Line 1 - 3 is valid because it passes through key 2, which had been selected in the pattern

Valid move:

6 - 5 - 4 - 1 - 9 - 2

Line 1 - 9 is valid because it passes through key 5, which had been selected in the pattern.

Example:

Given m = 1, n = 1, return 9.
方法：深度优先搜索。

public class Solution {
private int patterns;
private boolean valid(boolean[] keypad, int from, int to) {
if (from==to) return false;
int i=Math.min(from, to), j=Math.max(from,to);
if ((i==1 && j==9) || (i==3 && j==7)) return keypad[5] && !keypad[to];
if ((i==1 || i==4 || i==7) && i+2==j) return keypad[i+1] && !keypad[to];
if (i<=3 && i+6==j) return keypad[i+3] && !keypad[to];
return !keypad[to];
}
private void find(boolean[] keypad, int from, int step, int m, int n) {
if (step == n) {
patterns ++;
return;
}
if (step >= m) patterns ++;
for(int i=1; i<=9; i++) {
if (valid(keypad, from, i)) {
keypad[i] = true;
find(keypad, i, step+1, m, n);
keypad[i] = false;
}
}
}
public int numberOfPatterns(int m, int n) {
boolean[] keypad = new boolean[10];
for(int i=1; i<=9; i++) {
keypad[i] = true;
find(keypad, i, 1, m, n);
keypad[i] = false;
}
return patterns;
}
}