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.
Vincoli
0 ≤ left ≤ right ≤ 10¹⁸. The range may be too large to inspect each integer individually.
Esempi
Input:
left = 10
right = 15
Output atteso:
expected = 5Input:
long long left = 10;
long long right = 15;
Output atteso:
long long expected = 5;Input:
long left = 10;
long right = 15;
Output atteso:
long expected = 5;Spiegazione
Only 11 has equal neighboring digits. The other five numbers qualify.
Input:
left = 0
right = 9
Output atteso:
expected = 10Input:
long long left = 0;
long long right = 9;
Output atteso:
long long expected = 10;Input:
long left = 0;
long right = 9;
Output atteso:
long expected = 10;Spiegazione
All ten values have just one digit and therefore no equal neighbors.
Come affrontarlo
Prova prima da solo, poi apri un suggerimento alla volta.
Suggerimento 1
Count valid numbers up to each endpoint, then subtract to get the range answer.
Suggerimento 2
Digit DP fits because validity depends on adjacent digits and whether you have started the number.
Suggerimento 3
Leading zeros need special handling so that shorter numbers are counted correctly.
Complessità attesa
O(k * 10 * states) time, O(k * states) extra space
Riferimenti
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