X is a good number if after rotating each digit individually by 180 degrees, we get a valid number that is different from X. Each digit must be rotated - we cannot choose to leave it alone.
A number is valid if each digit remains a digit after rotation. 0, 1, and 8 rotate to themselves; 2 and 5 rotate to each other; 6 and 9 rotate to each other, and the rest of the numbers do not rotate to any other number and become invalid.
Now given a positive number
N
, how many numbers X from 1
to N
are good?Example: Input: 10 Output: 4 Explanation: There are four good numbers in the range [1, 10] : 2, 5, 6, 9. Note that 1 and 10 are not good numbers, since they remain unchanged after rotating.
Note:
- N will be in range
[1, 10000]
.
Solution:
The problem can be solved by using dp.
dp[i] = 0 means the number i is not good
dp[i] = 1 means the number is rotated to itself.
dp[i] = 2 means the number is rotated to the different number, so it's a good number.
Code (Java):
class Solution { public int rotatedDigits(int N) { int[] dp = new int[N + 1]; int count = 0; for (int i = 0; i <= N; i++) { if (i < 10) { if (i == 0 || i == 1 || i == 8) { dp[i] = 1; } else if (i == 2 || i == 5 || i == 6 || i == 9) { dp[i] = 2; count++; } } else { int a = dp[i / 10]; int b = dp[i % 10]; if (a == 1 && b == 1) { dp[i] = 1; } else if ((a == 1 && b == 2) || (a == 2 && b >= 1)) { dp[i] = 2; count++; } } } return count; } }
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