disjoint_sparse_table_example.cc

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/*
Aleph_w
 
  Data structures & Algorithms
  version 2.0.0b
  https://github.com/lrleon/Aleph-w
 
  This file is part of Aleph-w library
 
  Copyright (c) 2002-2026 Leandro Rabindranath Leon
 
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  of this software and associated documentation files (the "Software"), to deal
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*/
 
# include <cstdio>
# include <iostream>
# include <iomanip>
# include <numeric>
# include <cassert>
 
# include <tpl_disjoint_sparse_table.H>
 
using namespace std;
using namespace Aleph;
 
// =====================================================================
// SCENARIO 1 — Sales Analytics (range sum)
// =====================================================================
 
void scenario_sales_analytics()
{
  cout << "============================================================\n";
  cout << " SCENARIO 1: Sales Analytics (Sum_Disjoint_Sparse_Table)\n";
  cout << "============================================================\n\n";
 
  // Daily revenue (thousands of dollars) for 15 days
  const vector<int> revenue =
    {120, 95, 140, 88, 175, 63, 210, 155, 102, 180,
     135, 90, 200, 110, 165};
 
  Sum_Disjoint_Sparse_Table<int> sales(revenue);
 
  cout << "Daily revenue ($ thousands):\n\n";
  cout << "  Day  Revenue\n";
  cout << "  ---  -------\n";
  for (size_t i = 0; i < revenue.size(); ++i)
    cout << "   " << setw(2) << i << "    $" << setw(3) << revenue[i]
         << "K\n";
 
  cout << "\nTable info: " << sales.size() << " elements, "
       << sales.num_levels() << " levels\n";
 
  cout << "\nRange sum queries:\n\n";
  cout << "  Range       Total     Description\n";
  cout << "  ----------  --------  ----------------------------\n";
 
  struct Query { size_t l, r; const char * desc; };
  Query queries[] = {
    {0,  4, "Week 1 (Mon-Fri)"},
    {5,  9, "Week 2 (Mon-Fri)"},
    {10, 14, "Week 3 (Mon-Fri)"},
    {0, 14, "Entire period"},
    {3,  7, "Mid-period slice"},
    {6,  6, "Day 6 alone"},
  };
 
  for (const auto & q : queries)
    {
      int total = sales.query(q.l, q.r);
      cout << "  [" << setw(2) << q.l << ", " << setw(2) << q.r << "]"
           << "    $" << setw(4) << total << "K  " << q.desc << "\n";
    }
 
  // Brute-force verification
  int bf = 0;
  for (size_t i = 0; i <= 14; ++i) bf += revenue[i];
  assert(sales.query(0, 14) == bf);
  cout << "\n  ✓ Brute-force verification passed for full range\n";
  cout << endl;
}
 
// =====================================================================
// SCENARIO 2 — Probability Chains (range product)
// =====================================================================
 
void scenario_probability()
{
  cout << "============================================================\n";
  cout << " SCENARIO 2: Reliability Analysis (Product_Disjoint_Sparse_Table)\n";
  cout << "============================================================\n\n";
 
  // Component reliabilities (probability of working)
  const vector<double> reliability =
    {0.99, 0.95, 0.98, 0.97, 0.93, 0.96, 0.99, 0.94, 0.98, 0.97};
 
  const vector<string> names =
    {"Power", "CPU", "Memory", "Disk", "Network",
     "Cooling", "PSU", "GPU", "SSD", "Bus"};
 
  Product_Disjoint_Sparse_Table<double> rel_table(reliability);
 
  cout << "Component reliabilities:\n\n";
  cout << "  #   Component   Reliability\n";
  cout << "  --  ----------  -----------\n";
  for (size_t i = 0; i < reliability.size(); ++i)
    cout << "  " << setw(2) << i << "  " << setw(10) << left
         << names[i] << right << "  " << fixed << setprecision(4)
         << reliability[i] << "\n";
 
  cout << "\nSubsystem reliability queries (product of individual):\n\n";
  cout << "  Range       Reliability  Description\n";
  cout << "  ----------  -----------  ----------------------\n";
 
  struct Query { size_t l, r; const char * desc; };
  Query queries[] = {
    {0,  2, "Core compute (Power-Memory)"},
    {3,  5, "Storage+Net (Disk-Cooling)"},
    {6,  9, "Expansion (PSU-Bus)"},
    {0,  9, "Full system"},
    {1,  4, "CPU through Network"},
    {7,  7, "GPU alone"},
  };
 
  for (const auto & q : queries)
    {
      double p = rel_table.query(q.l, q.r);
      cout << "  [" << setw(2) << q.l << ", " << setw(2) << q.r << "]"
           << "    " << fixed << setprecision(6) << p
           << "     " << q.desc << "\n";
    }
 
  // Brute-force verification of full system
  double bf = 1.0;
  for (double r : reliability) bf *= r;
  double computed = rel_table.query(0, 9);
  assert(abs(computed - bf) < 1e-12);
  cout << "\n  ✓ Full system reliability = " << fixed << setprecision(6)
       << computed << " — verified\n";
  cout << endl;
}
 
// =====================================================================
// SCENARIO 3 — XOR Checksums (custom associative op)
// =====================================================================
 
struct Xor_Op
{
  constexpr unsigned operator()(unsigned a, unsigned b) const noexcept
  {
    return a ^ b;
  }
};
 
void scenario_xor_checksum()
{
  cout << "============================================================\n";
  cout << " SCENARIO 3: XOR Checksums (Gen_Disjoint_Sparse_Table)\n";
  cout << "============================================================\n\n";
 
  const vector<unsigned> data =
    {0xA3, 0x5F, 0x12, 0xB7, 0x8C, 0xE1, 0x3D, 0x74, 0x9A, 0x06};
 
  Gen_Disjoint_Sparse_Table<unsigned, Xor_Op> xor_tbl(data);
 
  cout << "Data blocks (hex):\n\n";
  cout << "  Index  Value\n";
  cout << "  -----  -----\n";
  for (size_t i = 0; i < data.size(); ++i)
    cout << "     " << i << "   0x" << hex << uppercase
         << setw(2) << setfill('0') << data[i]
         << setfill(' ') << dec << "\n";
 
  cout << "\nTable info: " << xor_tbl.size() << " elements, "
       << xor_tbl.num_levels() << " levels\n";
 
  cout << "\nRange XOR queries:\n\n";
  cout << "  Range     XOR     Values\n";
  cout << "  --------  ------  ------\n";
 
  struct Query { size_t l, r; };
  Query queries[] = {{0, 2}, {0, 9}, {3, 5}, {1, 4}, {6, 9}, {4, 4}, {0, 5}};
 
  for (const auto & q : queries)
    {
      unsigned result = xor_tbl.query(q.l, q.r);
 
      cout << "  [" << q.l << ", " << q.r << "]   0x"
           << hex << uppercase << setw(2) << setfill('0') << result
           << setfill(' ') << dec << "    {";
 
      for (size_t i = q.l; i <= q.r; ++i)
        {
          if (i > q.l) cout << ", ";
          cout << "0x" << hex << uppercase << setw(2) << setfill('0')
               << data[i] << setfill(' ') << dec;
        }
      cout << "}\n";
    }
 
  // Brute-force verification
  bool all_ok = true;
  for (const auto & q : queries)
    {
      unsigned bf = 0;
      for (size_t i = q.l; i <= q.r; ++i) bf ^= data[i];
      if (xor_tbl.query(q.l, q.r) != bf)
        all_ok = false;
    }
  assert(all_ok);
  cout << "\n  ✓ All XOR queries verified against brute-force\n";
  cout << endl;
}
 
// =====================================================================
// SCENARIO 5 — Construction from different containers
// =====================================================================
 
void scenario_construction()
{
  cout << "============================================================\n";
  cout << " SCENARIO 5: Construction from different containers\n";
  cout << "============================================================\n\n";
 
  const vector<int> raw = {5, 3, 7, 1, 9, 2, 8, 4, 6};
 
  // From Array<int>
  Array<int> arr(raw.size());
  for (size_t i = 0; i < raw.size(); ++i)
    arr.append(raw[i]);
  Sum_Disjoint_Sparse_Table<int> from_arr(arr);
 
  // From std::vector<int>
  Sum_Disjoint_Sparse_Table<int> from_vec(raw);
 
  // From DynList<int>
  DynList<int> dl;
  for (size_t i = 0; i < raw.size(); ++i)
    dl.append(raw[i]);
  Sum_Disjoint_Sparse_Table<int> from_dl(dl);
 
  // From initializer_list
  Sum_Disjoint_Sparse_Table<int> from_il = {5, 3, 7, 1, 9, 2, 8, 4, 6};
 
  int expected = 0;
  for (int v : raw) expected += v;
 
  cout << "From Array<int>:   sum[0,8] = " << from_arr.query(0, 8) << "\n";
  cout << "From vector<int>:  sum[0,8] = " << from_vec.query(0, 8) << "\n";
  cout << "From DynList<int>: sum[0,8] = " << from_dl.query(0, 8) << "\n";
  cout << "From init-list:    sum[0,8] = " << from_il.query(0, 8) << "\n";
 
  assert(from_arr.query(0, 8) == expected);
  assert(from_vec.query(0, 8) == expected);
  assert(from_dl.query(0, 8) == expected);
  assert(from_il.query(0, 8) == expected);
 
  // Reconstruct values
  auto vals = from_vec.values();
  cout << "\nReconstructed values: ";
  for (size_t i = 0; i < vals.size(); ++i)
    {
      if (i > 0) cout << ", ";
      cout << vals(i);
    }
  cout << "\n";
 
  // Cross-validate a sub-range
  for (size_t l = 0; l < raw.size(); ++l)
    for (size_t r = l; r < raw.size(); ++r)
      assert(from_arr.query(l, r) == from_vec.query(l, r));
 
  cout << "\n  ✓ All construction methods produce identical results\n";
  cout << endl;
}
 
// =====================================================================
// SCENARIO 4 — Parlay Betting (range product of odds)
// =====================================================================
 
void scenario_parlay_betting()
{
  cout << "============================================================\n";
  cout << " SCENARIO 4: Parlay Betting (Product_Disjoint_Sparse_Table)\n";
  cout << "============================================================\n\n";
 
  // A Saturday match card: 12 events with decimal odds
  // Decimal odds already include the stake: payout = stake × odds
  struct Match { const char * event; double odds; };
  Match card[] = {
    {"Arsenal vs Chelsea",        1.85},  //  0
    {"Real Madrid vs Barcelona",  2.10},  //  1
    {"Bayern vs Dortmund",        1.55},  //  2
    {"PSG vs Lyon",               1.40},  //  3
    {"Juventus vs Inter",         2.25},  //  4
    {"Liverpool vs Man City",     3.10},  //  5
    {"Ajax vs Feyenoord",         1.90},  //  6
    {"Benfica vs Porto",          2.05},  //  7
    {"Milan vs Napoli",           1.75},  //  8
    {"Atletico vs Sevilla",       1.60},  //  9
    {"Tottenham vs Man United",   2.40},  // 10
    {"Celtic vs Rangers",         1.95},  // 11
  };
 
  const size_t N = sizeof(card) / sizeof(card[0]);
 
  vector<double> odds(N);
  for (size_t i = 0; i < N; ++i)
    odds[i] = card[i].odds;
 
  Product_Disjoint_Sparse_Table<double> parlay(odds);
 
  cout << "Saturday Match Card:\n\n";
  cout << "  #   Match                        Odds\n";
  cout << "  --  ---------------------------  ----\n";
  for (size_t i = 0; i < N; ++i)
    cout << "  " << setw(2) << i << "  " << setw(27) << left
         << card[i].event << right << "  " << fixed << setprecision(2)
         << card[i].odds << "\n";
 
  cout << "\nTable info: " << parlay.size() << " events, "
       << parlay.num_levels() << " levels\n";
 
  // Parlay queries: what is the combined multiplier for a range?
  cout << "\nParlay (accumulator) queries — combined payout multiplier:\n\n";
  cout << "  Parlay          Combined   $10 Bet\n";
  cout << "  Range   Legs    Multiplier  Payout\n";
  cout << "  ------  ------  ----------  --------\n";
 
  struct PQuery { size_t l, r; const char * desc; };
  PQuery queries[] = {
    {0,  1, nullptr},   // double
    {0,  2, nullptr},   // treble
    {0,  4, nullptr},   // 5-fold
    {5,  8, nullptr},   // 4-fold mid-card
    {0, 11, nullptr},   // full card 12-fold
    {3,  3, nullptr},   // single
    {9, 11, nullptr},   // last 3
  };
 
  for (const auto & q : queries)
    {
      double mult = parlay.query(q.l, q.r);
      size_t legs = q.r - q.l + 1;
      double payout = 10.0 * mult;
 
      cout << "  [" << setw(2) << q.l << "," << setw(2) << q.r << "]"
           << "  " << setw(2) << legs << "-fold"
           << "  " << setw(10) << fixed << setprecision(2) << mult
           << "  $" << setw(7) << fixed << setprecision(2) << payout
           << "\n";
    }
 
  // Brute-force verification
  double bf_full = 1.0;
  for (size_t i = 0; i < N; ++i) bf_full *= odds[i];
  double computed_full = parlay.query(0, N - 1);
  assert(abs(computed_full - bf_full) < 1e-6);
 
  cout << "\n  Full-card 12-fold parlay: $10 bet pays $"
       << fixed << setprecision(2) << 10.0 * computed_full << "\n";
 
  // Show why classical Sparse Table can't do this:
  // product is NOT idempotent: 2.0 * 2.0 = 4.0 ≠ 2.0
  cout << "\n  Note: product is NOT idempotent (odds × odds ≠ odds),\n"
       << "  so a classical Sparse Table cannot handle parlay queries.\n"
       << "  The Disjoint Sparse Table handles them in O(1).\n";
 
  cout << "\n  ✓ Full-card parlay verified against brute-force\n";
  cout << endl;
}
 
// =====================================================================
// SCENARIO 5 — Construction from different containers
// =====================================================================
 
int main()
{
  scenario_sales_analytics();
  scenario_probability();
  scenario_xor_checksum();
  scenario_parlay_betting();
  scenario_construction();
 
  return 0;
}