OptimalBase.C 22.7 KB
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/**************************************************************************[OptimalBase.C]
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Copyright (c) 2005-2010, Niklas Een, Niklas Sorensson

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and
associated documentation files (the "Software"), to deal in the Software without restriction,
including without limitation the rights to use, copy, modify, merge, publish, distribute,
sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or
substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT
NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM,
DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT
OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
**************************************************************************************************/

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#include "Map.h"
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#include "PbSolver.h"
#include "OptimalBase.h"
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#include "Main.h"
#include "Sort.h"
#include "Debug.h"
#include <queue>
#include <utility>
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//=================================================================================================

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//int primes[] = { 2, 3, 5, 7, 11, 13, 17 };
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//int primes[] = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 };
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//int primes[] = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997 };
int primes[] = { 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997,1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069,1087,1091,1093,1097,1103,1109,1117,1123,1129,1151,1153,1163,1171,1181,1187,1193,1201,1213,1217,1223,1229,1231,1237,1249,1259,1277,1279,1283,1289,1291,1297,1301,1303,1307,1319,1321,1327,1361,1367,1373,1381,1399,1409,1423,1427,1429,1433,1439,1447,1451,1453,1459,1471,1481,1483,1487,1489,1493,1499,1511,1523,1531,1543,1549,1553,1559,1567,1571,1579,1583,1597,1601,1607,1609,1613,1619,1621,1627,1637,1657,1663,1667,1669,1693,1697,1699,1709,1721,1723,1733,1741,1747,1753,1759,1777,1783,1787,1789,1801,1811,1823,1831,1847,1861,1867,1871,1873,1877,1879,1889,1901,1907,1913,1931,1933,1949,1951,1973,1979,1987,1993,1997,1999,2003,2011,2017,2027,2029,2039,2053,2063,2069,2081,2083,2087,2089,2099,2111,2113,2129,2131,2137,2141,2143,2153,2161,2179,2203,2207,2213,2221,2237,2239,2243,2251,2267,2269,2273,2281,2287,2293,2297,2309,2311,2333,2339,2341,2347,2351,2357,2371,2377,2381,2383,2389,2393,2399,2411,2417,2423,2437,2441,2447,2459,2467,2473,2477,2503,2521,2531,2539,2543,2549,2551,2557,2579,2591,2593,2609,2617,2621,2633,2647,2657,2659,2663,2671,2677,2683,2687,2689,2693,2699,2707,2711,2713,2719,2729,2731,2741,2749,2753,2767,2777,2789,2791,2797,2801,2803,2819,2833,2837,2843,2851,2857,2861,2879,2887,2897,2903,2909,2917,2927,2939,2953,2957,2963,2969,2971,2999,3001,3011,3019,3023,3037,3041,3049,3061,3067,3079,3083,3089,3109,3119,3121,3137,3163,3167,3169,3181,3187,3191,3203,3209,3217,3221,3229,3251,3253,3257,3259,3271,3299,3301,3307,3313,3319,3323,3329,3331,3343,3347,3359,3361,3371,3373,3389,3391,3407,3413,3433,3449,3457,3461,3463,3467,3469,3491,3499,3511,3517,3527,3529,3533,3539,3541,3547,3557,3559,3571,3581,3583,3593,3607,3613,3617,3623,3631,3637,3643,3659,3671,3673,3677,3691,3697,3701,3709,3719,3727,3733,3739,3761,3767,3769,3779,3793,3797,3803,3821,3823,3833,3847,3851,3853,3863,3877,3881,3889,3907,3911,3917,3919,3923,3929,3931,3943,3947,3967,3989,4001,4003,4007,4013,4019,4021,4027,4049,4051,4057,4073,4079,4091,4093,4099,4111,4127,4129,4133,4139,4153,4157,4159,4177,4201,4211,4217,4219,4229,4231,4241,4243,4253,4259,4261,4271,4273,4283,4289,4297,4327,4337,4339,4349,4357,4363,4373,4391,4397,4409,4421,4423,4441,4447,4451,4457,4463,4481,4483,4493,4507,4513,4517,4519,4523,4547,4549,4561,4567,4583,4591,4597,4603,4621,4637,4639,4643,4649,4651,4657,4663,4673,4679,4691,4703,4721,4723,4729,4733,4751,4759,4783,4787,4789,4793,4799,4801,4813,4817,4831,4861,4871,4877,4889,4903,4909,4919,4931,4933,4937,4943,4951,4957,4967,4969,4973,4987,4993,4999,5003,5009,5011,5021,5023,5039,5051,5059,5077,5081,5087,5099,5101,5107,5113,5119,5147,5153,5167,5171,5179,5189,5197,5209,5227,5231,5233,5237,5261,5273,5279,5281,5297,5303,5309,5323,5333,5347,5351,5381,5387,5393,5399,5407,5413,5417,5419,5431,5437,5441,5443,5449,5471,5477,5479,5483,5501,5503,5507,5519,5521,5527,5531,5557,5563,5569,5573,5581,5591,5623,5639,5641,5647,5651,5653,5657,5659,5669,5683,5689,5693,5701,5711,5717,5737,5741,5743,5749,5779,5783,5791,5801,5807,5813,5821,5827,5839,5843,5849,5851,5857,5861,5867,5869,5879,5881,5897,5903,5923,5927,5939,5953,5981,5987,6007,6011,6029,6037,6043,6047,6053,6067,6073,6079,6089,6091,6101,6113,6121,6131,6133,6143,6151,6163,6173,6197,6199,6203,6211,6217,6221,6229,6247,6257,6263,6269,6271,6277,6287,6299,6301,6311,6317,6323,6329,6337,6343,6353,6359,6361,6367,6373,6379,6389,6397,6421,6427,6449,6451,6469,6473,6481,6491,6521,6529,6547,6551,6553,6563,6569,6571,6577,6581,6599,6607,6619,6637,6653,6659,6661,6673,6679,6689,6691,6701,6703,6709,6719,6733,6737,6761,6763,6779,6781,6791,6793,6803,6823,6827,6829,6833,6841,6857,6863,6869,6871,6883,6899,6907,6911,6917,6947,6949,6959,6961,6967,6971,6977,6983,6991,6997,7001,7013,7019,7027,7039,7043,7057,7069,7079,7103,7109,7121,7127,7129,7151,7159,7177,7187,7193,7207,7211,7213,7219,7229,7237,7243,7247,7253,7283,7297,7307,7309,7321,7331,7333,7349,7351,7369,7393,7411,7417,7433,7451,7457,7459,7477,7481,7487,7489,7499,7507,7517,7523,7529,7537,7541,7547,7549,7559,7561,7573,7577,7583,7589,7591,7603,7607,7621,7639,7643,7649,7669,7673,7681,7687,7691,7699,7703,7717,7723,7727,7741,7753,7757,7759,7789,7793,7817,7823,7829,7841,7853,7867,7873,7877,7879,7883,7901,7907,7919,7927,7933,7937,7949,7951,7963,7993,8009,8011,8017,8039,8053,8059,8069,8081,8087,8089,8093,8101,8111,8117,8123,8147,8161,8167,8171,8179,8191,8209,8219,8221,8231,8233,8237,8243,8263,8269,8273,8287,8291,8293,8297,8311,8317,8329,8353,8363,8369,8377,8387,8389,8419,8423,8429,8431,8443,8447,8461,8467,8501,8513,8521,8527,8537,8539,8543,8563,8573,8581,8597,8599,8609,8623,8627,8629,8641,8647,8663,8669,8677,8681,8689,8693,8699,8707,8713,8719,8731,8737,8741,8747,8753,8761,8779,8783,8803,8807,8819,8821,8831,8837,8839,8849,8861,8863,8867,8887,8893,8923,8929,8933,8941,8951,8963,8969,8971,8999,9001,9007,9011,9013,9029,9041,9043,9049,9059,9067,9091,9103,9109,9127,9133,9137,9151,9157,9161,9173,9181,9187,9199,9203,9209,9221,9227,9239,9241,9257,9277,9281,9283,9293,9311,9319,9323,9337,9341,9343,9349,9371,9377,9391,9397,9403,9413,9419,9421,9431,9433,9437,9439,9461,9463,9467,9473,9479,9491,9497,9511,9521,9533,9539,9547,9551,9587,9601,9613,9619,9623,9629,9631,9643,9649,9661,9677,9679,9689,9697,9719,9721,9733,9739,9743,9749,9767,9769,9781,9787,9791,9803,9811,9817,9829,9833,9839,9851,9857,9859,9871,9883,9887,9901,9907,9923,9929,9931,9941,9949,9967,9973 };
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#define ExpensiveBigConstants

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void optimizeBase(vec<Int>& seq, int carry_ins, vec<Int>& rhs, int dcost, vec<int>& base, int& cost_bestfound, vec<int>& base_bestfound, OptBaseT obt)
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{
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    if (dcost >= cost_bestfound)
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        return;
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#ifdef DEBUG
    /**/static int depth = 0;
#endif
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    // "Base case" -- don't split further, build sorting network for current sequence:
    int final_cost = 0;
    for (int i = 0; i < seq.size(); i++){
        if (seq[i] > INT_MAX)
            goto TooBig;
      #ifdef ExpensiveBigConstants
        final_cost += toint(seq[i]);
      #else
        int c; for (c = 1; c*c < seq[i]; c++);
        final_cost += c;
      #endif
        if (final_cost < 0)
            goto TooBig;
    }
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#ifdef DEBUG
    if(opt_verbosity >=2) {
      for (int n = depth; n != 0; n--) reportf("  "); reportf("dcost=%d,final_cost(msd)=%d,h=%d cost_bestfound=%d  Best_base:", dcost, final_cost, seq.size(),cost_bestfound);
    }
#endif
    if (dcost + seq.size() > cost_bestfound){   //cost_alpha = dcost + seq.size(), final_cost = dcost + SUM of seqs
#ifdef DEBUG
      if(opt_verbosity >=2) reportf("Pruned.\n");
#endif
      return;
    }
    if (dcost + final_cost < cost_bestfound){
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        base.copyTo(base_bestfound);
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        cost_bestfound = dcost + final_cost;
#ifdef DEBUG
	if(opt_verbosity >=2)
	  for (int j = 0; j < base_bestfound.size(); j++)
	    reportf(" %d", base_bestfound[j]);
#endif
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    }
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#ifdef DEBUG
    if(opt_verbosity >=2) reportf("\n");
#endif
    
 TooBig:;
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    // <<== could count 1:s here for efficiency

    vec<Int> new_seq;
    vec<Int> new_rhs;
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#ifdef DEBUG
    if(opt_verbosity >=2) {
      reportf("\nbase: ");
      dump(base);
    }
    
#endif
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#ifdef PickSmallest
    int p = -1;
    for (int i = 0; i < seq.size(); i++)
        if (seq[i] > 1){ p = seq[i]; break; }
    if (p != -1){
#else
    for (int i = 0; i < (int)elemsof(primes); i++){
        int p    = primes[i];
#endif
        int rest = carry_ins;   // Sum of all the remainders.
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        Int div;
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#ifdef DEBUG
	if(opt_verbosity >=2) {
	  for (int n = depth; n != 0; n--) reportf("  "); reportf("prime=%d   carry_ins=%d  New seq:", p, rest);
	}
#endif
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        for (int j = 0; j < seq.size(); j++){
            rest += toint(seq[j] % Int(p));
            div = seq[j] / Int(p);
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            if (div > 0){
#ifdef DEBUG
	      if(opt_verbosity >=2) reportf(" %d", toint(div));
#endif
	      new_seq.push(div);
	    }
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        }
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#ifdef DEBUG
	if(opt_verbosity >=2) {
        /**/reportf("  ");
        /**/for (int n = depth; n != 0; n--) reportf("  "); reportf("rest(current carry*p)=%d\n", rest);
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        //**/for (int n = depth; n != 0; n--) reportf("  "); reportf("New rhs:");
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	}
#endif
      
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        base.push(p);
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#ifdef DEBUG
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        /**/depth++;
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#endif
        optimizeBase(new_seq, rest/p, new_rhs, dcost+(obt == obt_comb ? rest : 0), base, cost_bestfound, base_bestfound, obt);
#ifdef DEBUG
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        /**/depth--;
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#endif
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        base.pop();

        new_seq.clear();
        new_rhs.clear();
    }
}

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class CompareDist {
public:
  template <class T>
  bool operator()(Pair<int,T > x, Pair<int, T > y) {
    return x.fst > y.fst;
  }
};

// Pair<int, contener > means that <costA, <<base, B>, carry_ins> >
typedef Pair<Pair<std::vector<int>, Int >, int> container;
inline int              getCostA(Pair<int,container> d) {return d.fst;}
inline std::vector<int> getBase (Pair<int,container> d) {return d.snd.fst.fst;}
inline Int              getB    (Pair<int,container> d) {return d.snd.fst.snd;}
inline int              getCarry(Pair<int,container> d) {return d.snd.snd;}
      // combination of vec with priority_queue does not work.
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// B = b1 * ... * bn for base=<b1,...,bn>
// Case obt_digit:
//   final_cost =  sum of all digits
//   dcost = final_cost - sum of most significant digits
//   costA = dcost + num of msds ,

// Case obt_carry:
//   final_cost =  sum of all digits and carries
//   dcost = final_cost - sum of msignificant digits
//   costA = dcost + num of msds ,

// Case obt_kind:
//   final_cost =  sum of cost_weighted_sort(digits) for each significance
//   dcost = final_cost - sum of cost_weighted_sort(most significant digits)
//   costA = dcost 
 
void optimizeBaseBB(const vec<Int>& seq, std::vector<int>& base_bestfound, OptBaseT obt)
{

  std::priority_queue<Pair<int, container>, std::vector<Pair<int, container> >, CompareDist > Q;
  int cost_bestfound = INT_MAX;
  std::vector<int> initBase;

  Int sum_msb = 0, div, B;
  
  for (int i = 0; i < seq.size(); i++)
    sum_msb += seq[i];

  if(obt == obt_kind)
    cost_bestfound = seq.size() + CountKind_Sort(seq);
  else
    if (sum_msb < INT_MAX) cost_bestfound = toint(sum_msb);

  Q.push( Pair_new((int)seq.size()+(obt==obt_kind ? 1 : 0), Pair_new(Pair_new(initBase,1), 0)) );

#ifdef DEBUG
  if(opt_verbosity >=2){
    reportf("-1: Q.size()=%d, getCostA(Q.top())=%d, cost_bestfound=%d\n",Q.size(), getCostA(Q.top()), cost_bestfound);
  }
#endif
  
  while( Q.size() != 0 && getCostA(Q.top()) < cost_bestfound ) {
    Pair<int, container> cBase = Q.top();  Q.pop();
    int seq_len = 0, new_seq_len = 0;

    B = getB(cBase);

    for (int j = 0; j < seq.size(); j++){
      div = seq[j] / B ;
      if (div > 0) seq_len++;
    }
    
#ifdef DEBUG
    if(opt_verbosity >=2){
      reportf("O: costA=%d, carry_ins=%d, cost_bestfound=%d\n   base:", getCostA(cBase), getCarry(cBase), cost_bestfound);
      for (int i = 0; i < (int)getBase(cBase).size(); i++)
	reportf(" %d", getBase(cBase)[i]);
      reportf("\n");
    }
    //    if(opt_verbosity >=2){
    //      reportf("   Seq:");
    //      for (int i = 0; i < (int)getSeq(cBase).size(); i++)
    //	reportf(" "),dump(getSeq(cBase)[i]);
    //      reportf("\n");
    //}
#endif

    for (int i = 0; i < (int)elemsof(primes); i++){
      int p = primes[i];

      if (seq[seq.size()-1] / B < (Int)p) break;
      
      int rest = (obt == obt_comb ? getCarry(cBase) : 0);  //, seq_shrink = 0;
      vec<int> rest_seq;
      // int rest = 0, seq_shrink = 0;
      int digit;
      vec<Int> new_seq;
      std::vector<int> new_base = getBase(cBase);
      sum_msb = 0; new_seq_len = 0;
      for (int j = 0; j < seq.size(); j++){
        digit = toint(seq[j]/B % Int(p));
	if (digit > 0){
	  rest += digit;
	  rest_seq.push(digit);
	}
	div = seq[j] / B / Int(p);
	if (div > 0){
	  sum_msb += div;
	  new_seq.push(div);
	  new_seq_len++;
	}
      }

      int new_costA;
      if(obt == obt_kind){
	sort(rest_seq);
	new_costA = getCostA(cBase) + CountKind_Sort(rest_seq) + rest_seq.size() - seq_len + new_seq_len;
	//reportf("old_constA=%d, kind-rest=%d, size-rest=%d, seq_len=%d, new_seq_len=%d\n", getCostA(cBase), CountKind_Sort(rest_seq), rest_seq.size(), seq_len, new_seq_len);
      } else {
	new_costA = getCostA(cBase) + rest - seq_len + new_seq_len;
	//reportf("old_constA=%d, rest=%d, seq_len=%d, new_seq_len=%d\n", getCostA(cBase), rest, seq_len, new_seq_len);
      }

#ifdef DEBUG
      if(opt_verbosity >=2){
	reportf("prime=%d, rest=%d, New seq:", p, rest);
	for (int j = 0; j < new_seq.size(); j++)
	  reportf(" %d", toint(new_seq[j]));
	reportf("\n");
	reportf("1: new_costA=%d\n", new_costA);
      }
#endif
      

      
      if (new_costA <= cost_bestfound) {
	new_base.push_back(p);

#ifdef DEBUG
	if(opt_verbosity >=2){
	  reportf("2: new_base:");
	  for(int j = 0; j < (int)new_base.size(); j++)
	    reportf(" %d", new_base[j]);
	  reportf("  new_costA=%d, new_carry=%d, cand_cost_bestfound=%d\n", new_costA, rest/p, new_costA - new_seq.size() + toint(sum_msb));
	}
#endif
	  
	Q.push(Pair_new(new_costA, Pair_new(Pair_new(new_base, B*p), rest/p )));

	int new_cost; 
	if(obt == obt_kind){
	  sortUnique(new_seq);
	  new_cost = new_costA - 1 + new_seq.size();
	} else
	  new_cost = new_costA - new_seq.size() + toint(sum_msb);
	if (sum_msb < INT_MAX && new_cost < cost_bestfound) {
	  base_bestfound = new_base, cost_bestfound = new_cost;
#ifdef DEBUG
	  if(opt_verbosity >=2){
	    reportf("  cost_bestfound=%d\n", cost_bestfound);
	  }
#endif
	}
      }
    }
  }
}


// Using Pair<int, Int> for <costA, B>
// Using Map<Int, Pair<int, Pair<vec<int>, int> > >
//      for <B,        costA,    base,     carry_ins>
typedef Pair<int, Pair<std::vector<int>, int> > container2;
inline int      getCostA(container2 d) {return d.fst;}
inline std::vector<int>
                getBase (Pair<int, Pair<std::vector<int >, int> > d) {return d.snd.fst;}
inline int      getCarry(container2 d) {return d.snd.snd;}


 void optimizeBaseHashBB(const vec<Int>& seq, std::vector<int>& base_bestfound, OptBaseT obt)
{

  std::priority_queue<Pair<int, Int>, std::vector<Pair<int, Int> >, CompareDist > Q;
   Map<Int, container2> memo;

  int cost_bestfound = INT_MAX;
  std::vector<int> initBase;
  
  Int sum_msb = 0, div, B;
  
  for (int i = 0; i < seq.size(); i++)
    sum_msb += seq[i];

  if(obt == obt_kind)
    //    cost_bestfound = seq.size() + CountKind_Sort(seq);
    cost_bestfound = count_weighted_sort(seq);
  else
    if (sum_msb < INT_MAX) cost_bestfound = toint(sum_msb);

  //  Q.push( Pair_new((int)seq.size()+(obt==obt_kind ? 1 : 0), 1) );
  Q.push( Pair_new( (obt==obt_kind ? 0 : (int)seq.size()), 1) );
  //  memo.set( 1, Pair_new((int)seq.size()+(obt==obt_kind ? 1 : 0), Pair_new(initBase, 0)) );
  memo.set( 1, Pair_new( (obt==obt_kind ? 0 : (int)seq.size()), Pair_new(initBase, 0)) );

#ifdef DEBUG
  if(opt_verbosity >=2){
    reportf("-1: Q.size()=%d, getCostA(Q.top())=%d, cost_bestfound=%d\n",Q.size(), Q.top().fst, cost_bestfound);
  }
#endif

  while( Q.size() != 0 && Q.top().fst < cost_bestfound ) {
    int costA = Q.top().fst;
    B = Q.top().snd;  Q.pop();
    container2 cBase;
    if (!memo.peek(B, cBase)) assert(false);

    if (getCostA(cBase) != costA) continue;
    
    int seq_len = 0, new_seq_len = 0;
    
    for (int j = 0; j < seq.size(); j++){
      div = seq[j] / B ;
      if (div > 0) seq_len++;
    }

#ifdef DEBUG
    if(opt_verbosity >=2){
      reportf("O: costA=%d, carry_ins=%d, cost_bestfound=%d\n   base:", costA, getCarry(cBase), cost_bestfound);
      for (int i = 0; i < (int)getBase(cBase).size(); i++)
	reportf(" %d", getBase(cBase)[i]);
      reportf("\n");
    }
    //    if(opt_verbosity >=2){
    //      reportf("   Seq:");
    //      for (int i = 0; i < (int)getSeq(cBase).size(); i++)
    //	reportf(" "),dump(getSeq(cBase)[i]);
    //      reportf("\n");
    //}
#endif

    for (int i = 0; i < (int)elemsof(primes); i++){
      int p = primes[i];
      
      if (seq[seq.size()-1] / B < (Int)p) break;
      
      int rest = (obt == obt_comb ? getCarry(cBase) : 0);  //, seq_shrink = 0;
      vec<int> rest_seq;
      // int rest = 0, seq_shrink = 0;
      int digit;
      vec<Int> new_seq;
      std::vector<int> new_base = getBase(cBase);
      sum_msb = 0; new_seq_len = 0;
      for (int j = 0; j < seq.size(); j++){
        digit = toint(seq[j]/B % Int(p));
	if (digit > 0){
	  rest += digit;
	  rest_seq.push(digit);
	}
	div = seq[j] / B / Int(p);
	if (div > 0){
	  sum_msb += div;
	  new_seq.push(div);
	  new_seq_len++;
	}
      }

      int new_costA;
      if(obt == obt_kind){
       	sort(rest_seq);
	//	new_costA = costA + CountKind_Sort(rest_seq) + rest_seq.size() - seq_len + new_seq_len;
	new_costA = costA + count_weighted_sort(rest_seq);
	//reportf("old_constA=%d, kind-rest=%d, size-rest=%d, seq_len=%d, new_seq_len=%d\n", getCostA(cBase), CountKind_Sort(rest_seq), rest_seq.size(), seq_len, new_seq_len);
      } else {
	new_costA = costA + rest - seq_len + new_seq_len;
	//reportf("old_constA=%d, rest=%d, seq_len=%d, new_seq_len=%d\n", getCostA(cBase), rest, seq_len, new_seq_len);
      }

#ifdef DEBUG
      if(opt_verbosity >=2){
	reportf("prime=%d, rest=%d, New seq:", p, rest);
	for (int j = 0; j < new_seq.size(); j++)
	  reportf(" %d", toint(new_seq[j]));
	reportf("\n");
	reportf("1: new_costA=%d\n", new_costA);
      }
#endif

      
      if (new_costA <= cost_bestfound) {
	new_base.push_back(p);

#ifdef DEBUG
	if(opt_verbosity >=2){
	  reportf("2: new_base:");
	  for(int j = 0; j < (int)new_base.size(); j++)
	    reportf(" %d", new_base[j]);
	  reportf("  new_costA=%d, new_carry=%d, cand_cost_bestfound=%d\n", new_costA, rest/p, new_costA - new_seq.size() + toint(sum_msb));
	}
#endif
	container2 ncbase;
        if (!memo.peek(B*p, ncbase)) {
	  Q.push(Pair_new(new_costA, B*p));
	  memo.set(B*p, Pair_new(new_costA, Pair_new(new_base, rest/p )));
	} else if (new_costA < getCostA(ncbase)) {
	  Q.push(Pair_new(new_costA, B*p));
	  memo.remove(B*p);
	  memo.set(B*p, Pair_new(new_costA, Pair_new(new_base, rest/p )));
	} // else nothing to do.
	
	int new_cost = INT_MAX; 
	if(obt == obt_kind){
	  //	  sortUnique(new_seq);
	  //	  new_cost = new_costA - 1 + new_seq.size();
	  new_cost = new_costA + count_weighted_sort(new_seq);
	} else {
	  Int nc = (Int)new_costA - (Int)new_seq.size() + sum_msb;
	  if (nc < INT_MAX) new_cost = toint(nc);
	}
	if (new_cost < cost_bestfound) {
	  base_bestfound = new_base, cost_bestfound = new_cost;
#ifdef DEBUG
	  if(opt_verbosity >=2){
	    reportf("  cost_bestfound=%d\n", cost_bestfound);
	  }
#endif
	}
      }
    }
  }
}

void optimizeBase(vec<Int>& seq, vec<Int>& rhs, int& cost_bestfound, vec<int>& base_bestfound, OptBaseT obt)
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{
    vec<int>    base;
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    double start_time = cpuTime();

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    cost_bestfound = INT_MAX;
    base_bestfound.clear();
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    if (opt_opt_base_method == 0) {
#ifdef DEBUG
      if(opt_verbosity >=2) reportf("Optimized base by heuristic\n");
#endif
      optimizeBase(seq, 0, rhs, 0, base, cost_bestfound, base_bestfound, obt);
    } else {
      //**/ seq.clear(); seq.push(5); seq.push(6); seq.push(7);
    
#ifdef DEBUG
    if(opt_verbosity >=1)  reportf("optimizeBase(Seq:");
#endif
    std::vector<Int> vseq; std::vector<int> vbase;
    for (int i = 0; i < seq.size(); i++) {
#ifdef DEBUG
      if(opt_verbosity >=1) reportf(" "),dump(seq[i]);
#endif
      vseq.push_back(seq[i]);
    }
#ifdef DEBUG
      if(opt_verbosity >=1) reportf("\n");
#endif

      if(opt_opt_base_method == 1) {
#ifdef DEBUG
      if(opt_verbosity >=2) reportf("Optimized base by branch and bound\n");
#endif
	optimizeBaseBB(seq, vbase, obt);
      } else {
#ifdef DEBUG
      if(opt_verbosity >=2) reportf("Optimized base by modulo equivalence\n");
#endif
	optimizeBaseHashBB(seq, vbase, obt);
      }

#ifdef DEBUG
      if(opt_verbosity >=1) reportf("Base:");
#endif
    base_bestfound.clear();
    for (int i = 0; i < (int)vbase.size(); i++) {
#ifdef DEBUG
      if(opt_verbosity >=1) reportf(" %d", vbase[i]);
#endif
      base_bestfound.push(vbase[i]);
    }
#ifdef DEBUG
      if(opt_verbosity >=1) reportf("\n");
#endif

    }    

    stats_opt_base_calc_time += (cpuTime() - start_time);
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}