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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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 | #include <bits/stdc++.h>
using namespace std;
vector<vector<pair<int,int>>> g; // adjacency list: (to, weight)
int startNode, sinkNode;
vector<int> suf; // suf[k] = node id for "k bits remaining", suf[0] = sink
int newNode() {
g.push_back({});
return (int)g.size() - 1;
}
void addEdge(int u, int v, int w) {
g[u].push_back({v, w});
}
// Ensure suf[k] exists for k >= 1, with edges to suf[k-1]
int getSuf(int k) {
while ((int)suf.size() <= k) {
int idx = (int)suf.size(); // new index
int node = newNode();
suf.push_back(node);
int child = suf[idx - 1];
addEdge(node, child, 0);
addEdge(node, child, 1);
}
return suf[k];
}
// Convert x to D-bit binary (MSB at index 0)
vector<int> getBits(int x, int D) {
vector<int> bits(D);
for (int i = D - 1; i >= 0; --i) {
bits[i] = x & 1;
x >>= 1;
}
return bits;
}
// Build DP for lower bound only, length D >= 2
int buildLowerBound(int D, const vector<int>& Lbits) {
vector<int> node(D);
for (int pos = 1; pos <= D - 1; ++pos) {
node[pos] = newNode();
}
for (int pos = 1; pos <= D - 1; ++pos) {
int u = node[pos];
int rem = D - pos - 1;
int Lnext = Lbits[pos];
// Option 1: b = Lnext (stay equal)
int v1 = (rem == 0) ? sinkNode : node[pos + 1];
addEdge(u, v1, Lnext);
// Option 2: if Lnext == 0, b = 1 (become greater -> unconstrained)
if (Lnext == 0) {
int v2 = (rem == 0) ? sinkNode : getSuf(rem);
addEdge(u, v2, 1);
}
}
return node[1];
}
// Build DP for upper bound only, length D >= 2
int buildUpperBound(int D, const vector<int>& Rbits) {
vector<int> node(D);
for (int pos = 1; pos <= D - 1; ++pos) {
node[pos] = newNode();
}
for (int pos = 1; pos <= D - 1; ++pos) {
int u = node[pos];
int rem = D - pos - 1;
int Rnext = Rbits[pos];
if (Rnext == 1) {
// b = 1 (stay equal)
int v1 = (rem == 0) ? sinkNode : node[pos + 1];
addEdge(u, v1, 1);
// b = 0 (become smaller -> unconstrained)
int v0 = (rem == 0) ? sinkNode : getSuf(rem);
addEdge(u, v0, 0);
} else { // Rnext == 0
// only b = 0 allowed (stay equal)
int v0 = (rem == 0) ? sinkNode : node[pos + 1];
addEdge(u, v0, 0);
}
}
return node[1];
}
// Build DP for both lower and upper bounds, length D >= 2
int buildBothBounds(int D, const vector<int>& Lbits, const vector<int>& Rbits) {
vector<array<int,4>> node(D); // node[pos][mask], mask: bit0=tl, bit1=tr
int entry = newNode();
node[1][3] = entry; // tl = 1, tr = 1
for (int pos = 1; pos <= D - 1; ++pos) {
for (int mask = 0; mask < 4; ++mask) {
int u = node[pos][mask];
if (!u) continue;
bool tl = mask & 1;
bool tr = mask & 2;
int rem = D - pos - 1;
for (int b = 0; b <= 1; ++b) {
if (tl && b < Lbits[pos]) continue;
if (tr && b > Rbits[pos]) continue;
bool newtl = tl && (b == Lbits[pos]);
bool newtr = tr && (b == Rbits[pos]);
if (rem == 0) {
addEdge(u, sinkNode, b);
} else {
if (!newtl && !newtr) {
int v = getSuf(rem);
addEdge(u, v, b);
} else {
int newMask = (newtl ? 1 : 0) + (newtr ? 2 : 0);
int &v = node[pos + 1][newMask];
if (!v) v = newNode();
addEdge(u, v, b);
}
}
}
}
}
return entry;
}
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int L, R;
if (!(cin >> L >> R)) return 0;
g.clear();
g.push_back({}); // dummy index 0
// Create start node (index 1)
startNode = newNode();
// Create sink node (index 2)
sinkNode = newNode();
// Initialize suf[0] = sink; others created lazily
suf.clear();
suf.push_back(sinkNode);
int lenL = 32 - __builtin_clz(L);
int lenR = 32 - __builtin_clz(R);
if (lenL == lenR) {
int D = lenL;
if (D == 1) {
// Only number is 1
addEdge(startNode, sinkNode, 1);
} else {
vector<int> Lbits = getBits(L, D);
vector<int> Rbits = getBits(R, D);
int entry = buildBothBounds(D, Lbits, Rbits);
addEdge(startNode, entry, 1);
}
} else { // lenL < lenR
int D1 = lenL;
int D2 = lenR;
int entryL = -1, entryR = -1;
// Lower-bound part for length D1
if (D1 == 1) {
// Only number of length 1 in this range is 1
// We'll add edge start->sink with weight 1 later
} else {
vector<int> Lbits = getBits(L, D1);
entryL = buildLowerBound(D1, Lbits);
}
// Upper-bound part for length D2 (D2 >= 2 here)
vector<int> Rbits = getBits(R, D2);
entryR = buildUpperBound(D2, Rbits);
// Connect start node
if (D1 == 1) {
// length 1 number: 1
addEdge(startNode, sinkNode, 1);
} else {
addEdge(startNode, entryL, 1);
}
// Middle lengths: lenL+1 .. lenR-1
for (int d = lenL + 1; d <= lenR - 1; ++d) {
int k = d - 1; // bits remaining after first '1'
int sufNode = getSuf(k);
addEdge(startNode, sufNode, 1);
}
// Upper-bound length D2
addEdge(startNode, entryR, 1);
}
int n = (int)g.size() - 1;
cout << n << "\n";
for (int i = 1; i <= n; ++i) {
int k = (int)g[i].size();
cout << k;
for (auto &e : g[i]) {
cout << " " << e.first << " " << e.second;
}
cout << "\n";
}
return 0;
} |