/*
Rozwiazanie na podstawie artykulu i kodu stad:
https://www.geeksforgeeks.org/number-of-integers-in-a-range-l-r-which-are-divisible-by-exactly-k-of-its-digits/
*/
#include <bits/stdc++.h>
using namespace std;
typedef long long int LL;
const int LCM = 2520;
const int MAX_MASK = (1 << 9) + 1;
const int MAX_LEN = 19;
LL l, r;
LL states[MAX_LEN][2][LCM][MAX_MASK];
vector<int> digits;
LL dp(const int idx, const int canZero, const int tight, const int rem, const int mask)
{
LL& res = states[idx][tight][rem][mask];
if(res != -1)
{
return res;
}
res = 0;
if(idx == digits.size())
{
int usedDigsCount = 0, divisibleByDigsCount = 0;
for(int d = 1; d < 10; ++d)
{
if(mask & (1 << (d-1)))
{
++usedDigsCount;
if(rem % d == 0)
{
++divisibleByDigsCount;
}
}
}
if(usedDigsCount == divisibleByDigsCount && usedDigsCount > 0)
{
res = 1;
}
}
else
{
for(int d = (canZero ? 0 : 1); d < 10; ++d)
{
if(tight && d > digits[idx])
{
continue;
}
const int newTight = ((tight == 1) ? (d == digits[idx]) : 0);
const int newRem = (10*rem + d) % LCM;
const int newCanZero = (canZero && (d == 0));
int newMask = mask;
if(d != 0)
{
newMask = (mask | (1 << (d-1)));
}
res += dp(idx+1, newCanZero, newTight, newRem, newMask);
}
}
return res;
}
LL findCount(LL x)
{
digits.clear();
while(x > 0)
{
digits.push_back(x%10);
x /= 10;
}
reverse(digits.begin(), digits.end());
memset(states, -1, sizeof(states));
return dp(0, 1, 1, 0, 0);
}
int main()
{
ios_base::sync_with_stdio(0);
cin >> l >> r;
cout << findCount(r) - findCount(l-1) << endl;
return 0;
}
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 | /* Rozwiazanie na podstawie artykulu i kodu stad: https://www.geeksforgeeks.org/number-of-integers-in-a-range-l-r-which-are-divisible-by-exactly-k-of-its-digits/ */ #include <bits/stdc++.h> using namespace std; typedef long long int LL; const int LCM = 2520; const int MAX_MASK = (1 << 9) + 1; const int MAX_LEN = 19; LL l, r; LL states[MAX_LEN][2][LCM][MAX_MASK]; vector<int> digits; LL dp(const int idx, const int canZero, const int tight, const int rem, const int mask) { LL& res = states[idx][tight][rem][mask]; if(res != -1) { return res; } res = 0; if(idx == digits.size()) { int usedDigsCount = 0, divisibleByDigsCount = 0; for(int d = 1; d < 10; ++d) { if(mask & (1 << (d-1))) { ++usedDigsCount; if(rem % d == 0) { ++divisibleByDigsCount; } } } if(usedDigsCount == divisibleByDigsCount && usedDigsCount > 0) { res = 1; } } else { for(int d = (canZero ? 0 : 1); d < 10; ++d) { if(tight && d > digits[idx]) { continue; } const int newTight = ((tight == 1) ? (d == digits[idx]) : 0); const int newRem = (10*rem + d) % LCM; const int newCanZero = (canZero && (d == 0)); int newMask = mask; if(d != 0) { newMask = (mask | (1 << (d-1))); } res += dp(idx+1, newCanZero, newTight, newRem, newMask); } } return res; } LL findCount(LL x) { digits.clear(); while(x > 0) { digits.push_back(x%10); x /= 10; } reverse(digits.begin(), digits.end()); memset(states, -1, sizeof(states)); return dp(0, 1, 1, 0, 0); } int main() { ios_base::sync_with_stdio(0); cin >> l >> r; cout << findCount(r) - findCount(l-1) << endl; return 0; } |
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