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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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 | #include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
// Structure to represent an edge in the DAG
struct Edge {
int to;
int w;
};
// Adjacency list to store the graph. Max nodes 100.
vector<Edge> adj[105];
int node_cnt = 0;
int H[25]; // H[k] stores the node index that is the root of a full binary DAG of height k
// Function to allocate a new node
int new_node() {
return ++node_cnt;
}
// Function to add a directed edge
void add_edge(int u, int v, int w) {
adj[u].push_back({v, w});
}
// Lazily retrieve (or create) the node H[k]
// H[k] is the root of a DAG that generates all binary strings of length k.
// H[0] is the Sink node.
int get_H(int k) {
if (H[k] != 0) return H[k];
// Create new node for H[k]
int u = new_node();
H[k] = u;
// Recursively ensure H[k-1] exists
int target = get_H(k - 1);
// Connect H[k] to H[k-1] with both 0 and 1
add_edge(u, target, 0);
add_edge(u, target, 1);
return u;
}
// Construct a path/DAG for values >= val (suffix logic)
// 'u' is the current node
// 'bit' is the current bit index we are deciding (from MSB downwards)
// 'val' is the lower bound value
void add_chain_lower(int u, int bit, int val) {
if (bit < 0) return;
int bit_val = (val >> bit) & 1;
if (bit_val == 1) {
// We are constrained to 1. The '0' path would be less than val (invalid).
if (bit == 0) {
add_edge(u, H[0], 1);
} else {
int next_node = new_node();
add_edge(u, next_node, 1);
add_chain_lower(next_node, bit - 1, val);
}
} else {
// bit_val is 0.
// We can go '0', continuing the constraint.
if (bit == 0) {
add_edge(u, H[0], 0);
} else {
int next_tight = new_node();
add_edge(u, next_tight, 0);
add_chain_lower(next_tight, bit - 1, val);
}
// We can also go '1'. Since 1 > 0, all subsequent bits are free.
// The remaining length is 'bit'. Target is H[bit].
add_edge(u, get_H(bit), 1);
}
}
// Construct a path/DAG for values <= val (suffix logic)
void add_chain_upper(int u, int bit, int val) {
if (bit < 0) return;
int bit_val = (val >> bit) & 1;
if (bit_val == 0) {
// Constrained to 0.
if (bit == 0) {
add_edge(u, H[0], 0);
} else {
int next_node = new_node();
add_edge(u, next_node, 0);
add_chain_upper(next_node, bit - 1, val);
}
} else {
// bit_val is 1.
// Can go '1' (constrained).
if (bit == 0) {
add_edge(u, H[0], 1);
} else {
int next_tight = new_node();
add_edge(u, next_tight, 1);
add_chain_upper(next_tight, bit - 1, val);
}
// Can go '0' (loose). Since 0 < 1, subsequent bits free.
add_edge(u, get_H(bit), 0);
}
}
// Construct DAG for range [L, R] with fixed length
void add_chain_between(int u, int bit, int L, int R) {
if (bit < 0) return;
int L_bit = (L >> bit) & 1;
int R_bit = (R >> bit) & 1;
if (L_bit == R_bit) {
// Common prefix
if (bit == 0) {
add_edge(u, H[0], L_bit);
} else {
int next_node = new_node();
add_edge(u, next_node, L_bit);
add_chain_between(next_node, bit - 1, L, R);
}
} else {
// Divergence point. L must be 0, R must be 1.
// Lower branch: choose 0. Constraints come from L (lower bound).
if (bit == 0) {
add_edge(u, H[0], 0);
} else {
int v0 = new_node();
add_edge(u, v0, 0);
add_chain_lower(v0, bit - 1, L);
}
// Upper branch: choose 1. Constraints come from R (upper bound).
if (bit == 0) {
add_edge(u, H[0], 1);
} else {
int v1 = new_node();
add_edge(u, v1, 1);
add_chain_upper(v1, bit - 1, R);
}
}
}
// Calculate number of bits required to represent n
int get_len(int n) {
if (n == 0) return 0;
return 32 - __builtin_clz(n);
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
int L, R;
if (!(cin >> L >> R)) return 0;
int Source = new_node(); // Node 1 is Source
int Sink = new_node(); // Node 2 is Sink
H[0] = Sink;
int lenL = get_len(L);
int lenR = get_len(R);
// Because we cannot have leading zeros, the MSB for any number in [L, R] is 1.
// We handle the MSB explicitly by creating an edge '1' from Source.
// The recursive functions handle bits from len-2 down to 0.
if (lenL == lenR) {
// All numbers have the same bit length
if (lenL == 1) {
// Range [1, 1]
add_edge(Source, Sink, 1);
} else {
int v = new_node();
add_edge(Source, v, 1);
add_chain_between(v, lenL - 2, L, R);
}
} else {
// Numbers have different lengths. We process each length group.
// 1. Numbers of length lenL: Range [L, 2^lenL - 1]
if (lenL == 1) {
add_edge(Source, Sink, 1);
} else {
int vL = new_node();
add_edge(Source, vL, 1);
add_chain_lower(vL, lenL - 2, L);
}
// 2. Numbers of intermediate lengths: Range [2^(k-1), 2^k - 1] for k in (lenL, lenR)
// These are full ranges of length k. Corresponds to '1' followed by any k-1 bits.
for (int k = lenL + 1; k < lenR; ++k) {
// Edge '1' leads to H[k-1] which generates all strings of length k-1
add_edge(Source, get_H(k - 1), 1);
}
// 3. Numbers of length lenR: Range [2^(lenR-1), R]
if (lenR > 1) {
int vR = new_node();
add_edge(Source, vR, 1);
add_chain_upper(vR, lenR - 2, R);
}
}
// Output graph
cout << node_cnt << "\n";
for (int i = 1; i <= node_cnt; ++i) {
cout << adj[i].size();
for (auto& e : adj[i]) {
cout << " " << e.to << " " << e.w;
}
cout << "\n";
}
return 0;
} |