• Source 
    1. // ideone.com/ysdd6b
    2. #include <iostream>
    3. #include <algorithm>
    4. #include <cmath>
    5. #include <functional>
    6. #include <numeric>
    7. #include <vector>
    8. #include <boost/multiprecision/cpp_int.hpp>
    9.  
    10. using namespace std;
    11.  
    12. using BigInt = boost::multiprecision::int128_t;
    13.  
    14. const int N = 36;
    15. const int W = N * (1 - 1 / log10(16)) + 1;
    16.  
    17. BigInt a[N], d[N], h[N], ax[N][10], smin[N][10], smax[N][10];
    18. int x[N], q, w;
    19. vector<BigInt> X;
    20.  
    21. BigInt toBigInt()
    22. {
    23.     return inner_product(x, x + N, d, (BigInt)0);
    24. }
    25.  
    26. void solve(int p = 0, BigInt s = 0, int t = 0)
    27. {
    28.     int i, j;
    29.     bool isExtraEnd = w == 0 && p == q - 1;
    30.  
    31.     if (a[p] >= 0) {
    32.         i = lower_bound(smax[p], smax[p] + 10, s) - smax[p];
    33.         j = upper_bound(smin[p], smin[p] + 10, s) - smin[p];
    34.     } else {
    35.         i = lower_bound(smin[p], smin[p] + 10, s, greater<BigInt>()) - smin[p];
    36.         j = upper_bound(smax[p], smax[p] + 10, s, greater<BigInt>()) - smax[p];
    37.     }
    38.  
    39.     for (x[p] = i; x[p] < j; x[p]++) {
    40.         if (isExtraEnd && (t + x[p]) % 3) continue;
    41.         if (p == N - 1) {
    42.             X.push_back(toBigInt());
    43.         } else {
    44.             solve(p + 1, s - ax[p][x[p]], t + x[p]);
    45.         }
    46.     }
    47. }
    48.  
    49. int main(void)
    50. {
    51.     int i, j;
    52.  
    53.     for (i = N - 1; i >= 0; i--) {
    54.         d[i] = i + 1 < N ? 10 * d[i + 1] : (BigInt)1;
    55.         h[i] = i + 1 < N ? 16 * h[i + 1] : (BigInt)1;
    56.     }
    57.  
    58.     for (w = 0; w <= W; w++) {
    59.         for (i = 0; i < N; i++) a[i] = (i + w < N ? h[i + w] : 0) - d[i];
    60.         for (i = 0; i < N; i++) for (j = 0; j < 10; j++) ax[i][j] = a[i] * j;
    61.  
    62.         for (i = N - 1; i >= 0; i--) {
    63.             for (j = 0; j < 10; j++) {
    64.                 if (a[i + 1] >= 0) {
    65.                     smin[i][j] = (i + 1 < N ? smin[i + 1][0] : 0) + ax[i][j];
    66.                     smax[i][j] = (i + 1 < N ? smax[i + 1][9] : 0) + ax[i][j];
    67.                 } else {
    68.                     smin[i][j] = (i + 1 < N ? smin[i + 1][9] : 0) + ax[i][j];
    69.                     smax[i][j] = (i + 1 < N ? smax[i + 1][0] : 0) + ax[i][j];
    70.                 }
    71.             }
    72.         }
    73.  
    74.         for (q = 0; q < N; q++) {
    75.             if (q > 0) {
    76.                 a[q - 1] = -d[q - 1];
    77.                 for (j = 0; j < 10; j++) ax[q - 1][j] = a[q - 1] * j;
    78.  
    79.                 for (i = q - 1; i >= 0; i--) {
    80.                     for (j = 0; j < 10; j++) {
    81.                         if (a[i + 1] >= 0) {
    82.                             smin[i][j] = smin[i + 1][0] + ax[i][j];
    83.                             smax[i][j] = smax[i + 1][9] + ax[i][j];
    84.                         } else {
    85.                             smin[i][j] = smin[i + 1][9] + ax[i][j];
    86.                             smax[i][j] = smax[i + 1][0] + ax[i][j];
    87.                         }
    88.                     }
    89.                 }
    90.             }
    91.             solve();
    92.         }
    93.     }
    94.  
    95.     sort(X.begin(), X.end());
    96.     X.erase(unique(X.begin(), X.end()), X.end());
    97.  
    98.     for (auto x : X) cout << x << endl;
    99.     cout << endl << X.size() << endl;
    100.  
    101.     return 0;
    102. }