File size: 5,682 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 | #include <bits/stdc++.h>
using namespace std;
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int L, R;
cin >> L >> R;
struct Edge { int to, w; };
vector<vector<Edge>> adj;
int n = 0;
auto addNode = [&]() { adj.emplace_back(); return n++; };
int END_NODE = addNode(); // 0
int START = addNode(); // 1
// Free chain
vector<int> freeChain(21, -1);
freeChain[0] = END_NODE;
for (int k = 1; k <= 20; k++) {
int u = addNode();
adj[u].push_back({freeChain[k-1], 0});
adj[u].push_back({freeChain[k-1], 1});
freeChain[k] = u;
}
// Decompose range [lo, hi] at bit length k into aligned blocks
// Each aligned block is a prefix + free chain
// Return list of (prefix_bits, free_length) pairs
// A prefix of length p followed by free_length = k-p means the block starts at prefix * 2^(k-p)
// and has 2^(k-p) elements
// Standard canonical decomposition of [lo, hi] into aligned blocks
// Returns list of (start, power) pairs where each block is [start, start + 2^power - 1]
auto decompose = [](int lo, int hi, int k) -> vector<pair<int,int>> {
vector<pair<int,int>> blocks;
int x = lo;
while (x <= hi) {
// Find largest power p such that:
// 1. x is a multiple of 2^p
// 2. x + 2^p - 1 <= hi
int p = 0;
while (p < k && (x % (1 << (p+1)) == 0) && (x + (1 << (p+1)) - 1 <= hi)) {
p++;
}
blocks.push_back({x, p});
x += (1 << p);
}
return blocks;
};
int lenL = 32 - __builtin_clz(L);
int lenR = 32 - __builtin_clz(R);
for (int len = lenL; len <= lenR; len++) {
int rs = 1 << (len-1);
int re = (1 << len) - 1;
int cL = max(L, rs);
int cR = min(R, re);
if (cL > cR) continue;
int suffLen = len - 1;
int loSuf = cL - rs;
int hiSuf = cR - rs;
if (suffLen == 0) {
adj[START].push_back({END_NODE, 1});
continue;
}
// Decompose [loSuf, hiSuf] into aligned blocks
auto blocks = decompose(loSuf, hiSuf, suffLen);
// For each block (start, power): the block is [start, start + 2^power - 1]
// prefix = start >> power (the upper bits of start)
// prefix has (suffLen - power) bits
// The path: START -1-> prefix bits -> freeChain[power] -> ... -> END
// Build a trie of the prefixes, with leaves connecting to freeChain
// The trie is a DAG where shared prefixes share nodes
// Build prefix paths
// For each block, we have a prefix (suffLen - power bits) followed by free[power]
struct TrieNode {
int nodeId;
int children[2]; // -1 if not set
TrieNode() : nodeId(-1) { children[0] = children[1] = -1; }
};
vector<TrieNode> trie(1); // root
for (auto& [start, power] : blocks) {
int prefLen = suffLen - power;
int prefix = (prefLen > 0) ? (start >> power) : 0;
int cur = 0; // trie root
for (int i = prefLen - 1; i >= 0; i--) {
int bit = (prefix >> i) & 1;
if (trie[cur].children[bit] == -1) {
trie[cur].children[bit] = trie.size();
trie.emplace_back();
}
cur = trie[cur].children[bit];
}
// At leaf: connect to freeChain[power]
trie[cur].nodeId = freeChain[power];
}
// Assign DAG node IDs to trie nodes (except leaves that directly use freeChain)
// Process trie BFS and create nodes
// Root trie node connects to START with weight 1
function<int(int)> buildTrie = [&](int t) -> int {
if (trie[t].nodeId != -1) return trie[t].nodeId;
if (trie[t].children[0] == -1 && trie[t].children[1] == -1) return -1;
int u = addNode();
trie[t].nodeId = u;
for (int b = 0; b < 2; b++) {
if (trie[t].children[b] != -1) {
int child = buildTrie(trie[t].children[b]);
if (child != -1) {
adj[u].push_back({child, b});
}
}
}
return u;
};
int root = buildTrie(0);
if (root >= 0) {
adj[START].push_back({root, 1});
}
}
// Remove unreachable
vector<bool> reach(n, false);
queue<int> q;
q.push(START);
reach[START] = true;
while (!q.empty()) {
int u = q.front(); q.pop();
for (auto& e : adj[u]) {
if (!reach[e.to]) { reach[e.to] = true; q.push(e.to); }
}
}
// Renumber
map<int,int> newId;
int cnt = 0;
newId[START] = ++cnt;
for (int i = 0; i < n; i++) {
if (i != START && reach[i]) newId[i] = ++cnt;
}
cout << cnt << "\n";
vector<int> inv(cnt + 1);
for (auto& [old, nw] : newId) inv[nw] = old;
for (int i = 1; i <= cnt; i++) {
int u = inv[i];
vector<pair<int,int>> edges;
for (auto& e : adj[u]) {
if (newId.count(e.to)) {
edges.push_back({newId[e.to], e.w});
}
}
cout << edges.size();
for (auto& [to, w] : edges) cout << " " << to << " " << w;
cout << "\n";
}
return 0;
}
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