Problema
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.
Restrições
0 ≤ left ≤ right ≤ 10¹⁸. The range may be too large to inspect each integer individually.
Exemplos
Entrada:
left = 10
right = 15
Saída esperada:
expected = 5Entrada:
long long left = 10;
long long right = 15;
Saída esperada:
long long expected = 5;Entrada:
long left = 10;
long right = 15;
Saída esperada:
long expected = 5;Explicação
Only 11 has equal neighboring digits. The other five numbers qualify.
Entrada:
left = 0
right = 9
Saída esperada:
expected = 10Entrada:
long long left = 0;
long long right = 9;
Saída esperada:
long long expected = 10;Entrada:
long left = 0;
long right = 9;
Saída esperada:
long expected = 10;Explicação
All ten values have just one digit and therefore no equal neighbors.
Como abordar
Tente sozinho primeiro e depois abra uma dica de cada vez.
Dica 1
Count valid numbers up to each endpoint, then subtract to get the range answer.
Dica 2
Digit DP fits because validity depends on adjacent digits and whether you have started the number.
Dica 3
Leading zeros need special handling so that shorter numbers are counted correctly.
Complexidade esperada
O(k * 10 * states) time, O(k * states) extra space
Referências
Este desafio foi adaptado para o CodeUtility. Siga o enunciado e as restrições acima.