Problem
Count integers from left through right, including both endpoints, that have no equal neighboring digits. Use their usual decimal writing with no leading zeroes. Zero and all other single-digit numbers qualify.
Implement counting_numbers(left, right).
Input
left: The first allowed value.
right: The last allowed value.
Output
Return how many values satisfy the rule.
Constraints
0 ≤ left ≤ right ≤ 10¹⁸. The range may be too large to inspect each integer individually.
Examples
Input:
left = 10
right = 15
Expected output:
expected = 5Input:
long long left = 10;
long long right = 15;
Expected output:
long long expected = 5;Input:
long left = 10;
long right = 15;
Expected output:
long expected = 5;Explanation
Only 11 has equal neighboring digits. The other five numbers qualify.
Input:
left = 0
right = 9
Expected output:
expected = 10Input:
long long left = 0;
long long right = 9;
Expected output:
long long expected = 10;Input:
long left = 0;
long right = 9;
Expected output:
long expected = 10;Explanation
All ten values have just one digit and therefore no equal neighbors.
How to approach it
Try on your own first, then open one hint at a time.
Hint 1
Count valid numbers up to each endpoint, then subtract to get the range answer.
Hint 2
Digit DP fits because validity depends on adjacent digits and whether you have started the number.
Hint 3
Leading zeros need special handling so that shorter numbers are counted correctly.
Expected complexity
O(k * 10 * states) time, O(k * states) extra space
References
This challenge is adapted for CodeUtility. Follow the statement and constraints above.