File size: 4,230 Bytes
1fd0050 | 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 | #include <bits/stdc++.h>
using namespace std;
int main() {
// For S = 2^30 - 2 (worst case: k = 2^31 - 3)
long long S = (1LL << 30) - 2;
int best_cost = 999;
int best_m = -1;
for (int m = 1; m <= 500; m++) {
long long T = S + m;
if (T & 1) continue; // T must be even
if (T < 2LL * m) continue;
// Get bits of T at positions >= 1
vector<int> bits;
int sum_bits = 0;
for (int b = 1; b <= 40; b++) {
if ((T >> b) & 1) {
bits.push_back(b);
sum_bits += b;
}
}
int pc = bits.size();
if (pc > m) continue;
// Need m - pc splits
int splits = m - pc;
// Simulate splitting (smallest >= 2 first)
multiset<int> exps(bits.begin(), bits.end());
int cost = sum_bits;
bool valid = true;
for (int s = 0; s < splits; s++) {
auto it = exps.lower_bound(2);
if (it == exps.end()) { valid = false; break; }
int d = *it;
exps.erase(it);
exps.insert(d - 1);
exps.insert(d - 1);
cost += (d - 2);
}
if (!valid) continue;
int total = cost + 1;
if (total < best_cost) {
best_cost = total;
best_m = m;
}
}
cout << "Best cost: " << best_cost << " with m = " << best_m << endl;
// Also check what happens for k = 2^31 - 1
S = (1LL << 30) - 1;
best_cost = 999;
for (int m = 1; m <= 500; m++) {
long long T = S + m;
if (T & 1) continue;
if (T < 2LL * m) continue;
vector<int> bits;
int sum_bits = 0;
for (int b = 1; b <= 40; b++) {
if ((T >> b) & 1) {
bits.push_back(b);
sum_bits += b;
}
}
int pc = bits.size();
if (pc > m) continue;
int splits = m - pc;
multiset<int> exps(bits.begin(), bits.end());
int cost = sum_bits;
bool valid = true;
for (int s = 0; s < splits; s++) {
auto it = exps.lower_bound(2);
if (it == exps.end()) { valid = false; break; }
int d = *it;
exps.erase(it);
exps.insert(d - 1);
exps.insert(d - 1);
cost += (d - 2);
}
if (!valid) continue;
int total = cost + 1;
if (total < best_cost) {
best_cost = total;
best_m = m;
}
}
cout << "For 2^31-1: Best cost: " << best_cost << " with m = " << best_m << endl;
// Find the WORST case S in [0, 2^30-1]
// Test a range of difficult S values
int worst_cost = 0;
long long worst_S = 0;
for (long long s = (1LL << 30) - 100; s <= (1LL << 30) - 1; s++) {
int bc = 999;
for (int m = 1; m <= 100; m++) {
long long T = s + m;
if (T & 1) continue;
if (T < 2LL * m) continue;
vector<int> bits;
int sb = 0;
for (int b = 1; b <= 40; b++) {
if ((T >> b) & 1) { bits.push_back(b); sb += b; }
}
int pc = bits.size();
if (pc > m) continue;
int sp = m - pc;
multiset<int> exps(bits.begin(), bits.end());
int cost = sb;
bool valid = true;
for (int ss = 0; ss < sp; ss++) {
auto it = exps.lower_bound(2);
if (it == exps.end()) { valid = false; break; }
int d = *it;
exps.erase(it);
exps.insert(d-1);
exps.insert(d-1);
cost += (d-2);
}
if (!valid) continue;
int total = cost + 1;
if (total < bc) bc = total;
}
if (bc > worst_cost) {
worst_cost = bc;
worst_S = s;
}
}
cout << "Worst case near 2^30: S = " << worst_S << " cost = " << worst_cost << endl;
return 0;
}
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