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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 | #include <iostream>
#include <vector>
#include <string>
#include <algorithm>
#include <cmath>
using namespace std;
// Adjacency list for the graph. Node indices are 1-based.
vector<pair<int, int>> adj[101];
// Keep track of the total number of nodes used.
int num_nodes = 2; // Start with nodes 1 (start) and 2 (end).
// Calculates the number of bits in the binary representation of n.
int len(long long n) {
if (n == 0) return 1;
return floor(log2(n)) + 1;
}
// Converts n to a binary string of a specific length l.
string to_binary(long long n, int l) {
if (l == 0) return "";
string bin;
for (int i = l - 1; i >= 0; i--) {
bin += ((n >> i) & 1) ? '1' : '0';
}
return bin;
}
// Adds a directed edge from u to v with weight w.
void add_edge(int u, int v, int w) {
adj[u].push_back({v, w});
}
// Returns the node that serves as the entry point for generating k arbitrary bits.
// Node 2 is the end node, which is equivalent to generating 0 bits.
// For k > 0, we use node k+2 as the generator for k bits.
int target_for_gen_node(int k) {
if (k == 0) return 2; // end_node
return k + 2;
}
// Generates paths for all numbers >= val with a fixed length l, starting from start_node.
// Assumes the numbers must start with '1' (no leading zeros).
void gen_ge(long long val, int l, int start_node) {
string s = to_binary(val, l);
int curr = start_node;
for (int i = 0; i < l; ++i) {
// If the current bit in val's binary representation is '0', we can place a '1'
// to form a larger number. The rest of the bits can be arbitrary.
// This is not done for the first bit, as it must be '1'.
if (i > 0 && s[i] == '0') {
add_edge(curr, target_for_gen_node(l - 1 - i), 1);
}
// To continue generating numbers >= val, we must follow the path for val itself.
int next_node = (i == l - 1) ? 2 : ++num_nodes;
add_edge(curr, next_node, s[i] - '0');
curr = next_node;
}
}
// Generates paths for all numbers <= val with a fixed length l, starting from start_node.
// Assumes the numbers must start with '1'.
void gen_le(long long val, int l, int start_node) {
string s = to_binary(val, l);
int curr = start_node;
for (int i = 0; i < l; ++i) {
// If the current bit in val's representation is '1', we can place a '0'
// to form a smaller number. The rest of the bits can be arbitrary.
// Not for the first bit to avoid leading zeros.
if (i > 0 && s[i] == '1') {
add_edge(curr, target_for_gen_node(l - 1 - i), 0);
}
// Follow the path for val itself.
int next_node = (i == l - 1) ? 2 : ++num_nodes;
add_edge(curr, next_node, s[i] - '0');
curr = next_node;
}
}
// Generates paths for suffixes >= val with length l.
void gen_ge_suf(long long val, int l, int start_node) {
if (l <= 0) return;
string s = to_binary(val, l);
int curr = start_node;
for (int i = 0; i < l; ++i) {
if (s[i] == '0') {
add_edge(curr, target_for_gen_node(l - 1 - i), 1);
}
int next_node = (i == l - 1) ? 2 : ++num_nodes;
add_edge(curr, next_node, s[i] - '0');
curr = next_node;
}
}
// Generates paths for suffixes <= val with length l.
void gen_le_suf(long long val, int l, int start_node) {
if (l <= 0) return;
string s = to_binary(val, l);
int curr = start_node;
for (int i = 0; i < l; ++i) {
if (s[i] == '1') {
add_edge(curr, target_for_gen_node(l - 1 - i), 0);
}
int next_node = (i == l - 1) ? 2 : ++num_nodes;
add_edge(curr, next_node, s[i] - '0');
curr = next_node;
}
}
// Generates a single path for the number val.
void gen_path(long long val, int l, int start_node) {
string s = to_binary(val, l);
int curr = start_node;
for (int i = 0; i < l; ++i) {
int next_node = (i == l - 1) ? 2 : ++num_nodes;
add_edge(curr, next_node, s[i] - '0');
curr = next_node;
}
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
long long L, R;
cin >> L >> R;
// Pre-build the generator nodes. Node i+2 generates i arbitrary bits.
for (int i = 1; i <= 20; ++i) {
num_nodes = max(num_nodes, i + 2);
add_edge(i + 2, target_for_gen_node(i - 1), 0);
add_edge(i + 2, target_for_gen_node(i - 1), 1);
}
// Reset num_nodes to be the first available index for construction.
num_nodes = 22;
if (L == R) {
gen_path(L, len(L), 1);
} else {
int lenL = len(L);
int lenR = len(R);
if (lenL < lenR) {
// Numbers with lenL bits: [L, 2^lenL - 1]
gen_ge(L, lenL, 1);
// Numbers with bits between lenL and lenR: [2^(k-1), 2^k - 1]
for (int k = lenL + 1; k < lenR; ++k) {
// All numbers of length k start with '1', followed by k-1 arbitrary bits.
add_edge(1, target_for_gen_node(k - 1), 1);
}
// Numbers with lenR bits: [2^(lenR-1), R]
gen_le(R, lenR, 1);
} else { // lenL == lenR
int k = lenL;
string binL = to_binary(L, k);
string binR = to_binary(R, k);
int p = 0; // Find first differing bit
while (p < k && binL[p] == binR[p]) {
p++;
}
// Build path for the common prefix
int curr = 1;
for (int i = 0; i < p; ++i) {
int next_node = ++num_nodes;
add_edge(curr, next_node, binL[i] - '0');
curr = next_node;
}
int common_node = curr;
int len_suf = k - p - 1;
// L-branch: numbers starting with common_prefix + '0'
int l_branch_start = ++num_nodes;
add_edge(common_node, l_branch_start, 0); // binL[p] must be '0'
long long l_suf_val = L & ((1LL << len_suf) - 1);
gen_ge_suf(l_suf_val, len_suf, l_branch_start);
// R-branch: numbers starting with common_prefix + '1'
int r_branch_start = ++num_nodes;
add_edge(common_node, r_branch_start, 1); // binR[p] must be '1'
long long r_suf_val = R & ((1LL << len_suf) - 1);
gen_le_suf(r_suf_val, len_suf, r_branch_start);
}
}
cout << num_nodes << endl;
for (int i = 1; i <= num_nodes; ++i) {
cout << adj[i].size();
// To ensure consistent output for scoring, sort edges.
sort(adj[i].begin(), adj[i].end());
for (auto& edge : adj[i]) {
cout << " " << edge.first << " " << edge.second;
}
cout << endl;
}
return 0;
} |