File size: 3,853 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 | #include <bits/stdc++.h>
using namespace std;
struct Graph {
vector<vector<pair<int,int>>> adj; // adj[u] = list of (v, w)
vector<array<int,2>> child; // trie child pointers (0/1), 0 means not created
int n;
int start, finish;
vector<int> gen; // generator nodes for i bits remaining (i>=1). 0 if not created.
Graph() {
n = 0;
adj.push_back({}); // 0-index unused
child.push_back({0,0});
start = newNode(); // 1
finish = newNode(); // 2
gen.assign(32, 0);
}
int newNode() {
++n;
adj.push_back({});
child.push_back({0,0});
return n;
}
void addEdge(int u, int v, int w) {
adj[u].push_back({v,w});
}
int getGen(int i) { // i >= 1
if (gen[i]) return gen[i];
int id = newNode();
gen[i] = id;
if (i == 1) {
addEdge(id, finish, 0);
addEdge(id, finish, 1);
} else {
int to = getGen(i-1);
addEdge(id, to, 0);
addEdge(id, to, 1);
}
return id;
}
// Build path for prefix bits; if createLastNode is false, do not create/advance at last bit.
// Returns tuple(prev node before last bit, last bit, last node id if created else -1)
tuple<int,int,int> buildPrefix(const vector<int>& bits, bool createLastNode) {
int cur = start;
int prev = start;
int lastBit = 0;
for (int i = 0; i < (int)bits.size(); ++i) {
int b = bits[i];
bool last = (i == (int)bits.size() - 1);
if (last && !createLastNode) {
prev = cur;
lastBit = b;
return {prev, lastBit, -1};
} else {
if (child[cur][b] == 0) {
int nxt = newNode();
addEdge(cur, nxt, b);
child[cur][b] = nxt;
}
prev = cur;
cur = child[cur][b];
lastBit = b;
}
}
return {prev, lastBit, cur};
}
};
vector<int> toBits(unsigned int x) {
vector<int> bits;
while (x) {
bits.push_back((x & 1) ? 1 : 0);
x >>= 1;
}
reverse(bits.begin(), bits.end());
if (bits.empty()) bits.push_back(0);
return bits;
}
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
unsigned int L, R;
if (!(cin >> L >> R)) return 0;
// Decompose [L, R] into dyadic blocks (start A, size 2^t)
vector<pair<unsigned int,int>> blocks;
unsigned int cur = L;
while (cur <= R) {
int t = 0;
while (true) {
unsigned int sz = 1u << (t + 1);
if ( (cur % sz) == 0 && cur + sz - 1 <= R) t++;
else break;
}
blocks.push_back({cur, t});
cur += (1u << t);
}
Graph G;
for (auto [A, t] : blocks) {
unsigned int prefixVal = A >> t;
vector<int> bits = toBits(prefixVal);
// ensure no leading zeros: prefixVal >= 1 always, so first bit is 1
if (t == 0) {
auto [prev, lastBit, u] = G.buildPrefix(bits, false);
G.addEdge(prev, G.finish, lastBit);
} else if (t == 1) {
auto [prev, lastBit, u] = G.buildPrefix(bits, true);
G.addEdge(u, G.finish, 0);
G.addEdge(u, G.finish, 1);
} else {
auto [prev, lastBit, u] = G.buildPrefix(bits, true);
int genNode = G.getGen(t - 1);
G.addEdge(u, genNode, 0);
G.addEdge(u, genNode, 1);
}
}
cout << G.n << "\n";
for (int i = 1; i <= G.n; ++i) {
cout << (int)G.adj[i].size();
for (auto &e : G.adj[i]) {
cout << " " << e.first << " " << e.second;
}
cout << "\n";
}
return 0;
} |