File size: 4,583 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 | #include <bits/stdc++.h>
using namespace std;
struct Edge {
int to;
int w;
};
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
long long L, R;
if (!(cin >> L >> R)) return 0;
auto bitlen = [&](long long x)->int{
int b = 0;
while (x) { b++; x >>= 1; }
return b;
};
int maxLen = bitlen(R); // maximum number of bits needed
// Graph structures
vector<vector<Edge>> g(1); // 1-based; g[0] unused
auto newNode = [&]()->int{
g.push_back({});
return (int)g.size() - 1;
};
auto addEdge = [&](int u, int v, int w){
// avoid duplicate identical edges
for (auto &e : g[u]) {
if (e.to == v && e.w == w) return;
}
g[u].push_back({v, w});
};
int root = newNode(); // id = 1
// Prepare suffix nodes S[k]: represent "k remaining arbitrary bits"
// S[0] is sink; S[k] (k>=1) has edges 0/1 -> S[k-1]
vector<int> S(maxLen + 1, -1);
S[0] = newNode(); // sink
for (int k = 1; k <= maxLen; ++k) {
S[k] = newNode();
}
for (int k = 1; k <= maxLen; ++k) {
addEdge(S[k], S[k-1], 0);
addEdge(S[k], S[k-1], 1);
}
// Map prefix (value,len) -> node id
unordered_map<unsigned long long, int> prefId;
prefId.reserve(4096);
prefId.max_load_factor(0.7f);
auto keyOf = [](unsigned int val, int len)->unsigned long long{
return ( (unsigned long long)val << 6 ) | (unsigned long long)len; // len <= 60 safe here (we use <= 20)
};
// Ensure path for prefix (val, len) from root exists; return node id
function<int(unsigned int,int)> ensurePrefix = [&](unsigned int val, int len)->int{
if (len == 0) return root;
unsigned long long key = keyOf(val, len);
auto it = prefId.find(key);
if (it != prefId.end()) return it->second;
// Build path from root
int cur = root;
for (int i = 1; i <= len; ++i) {
unsigned int pval = val >> (len - i); // prefix value of length i
unsigned long long pkey = keyOf(pval, i);
auto it2 = prefId.find(pkey);
int nxt;
int bit = (pval & 1); // i-th bit of full prefix (most significant first)
if (it2 != prefId.end()) {
nxt = it2->second;
} else {
nxt = newNode();
prefId[pkey] = nxt;
}
// add edge from cur to nxt with label 'bit'
addEdge(cur, nxt, bit);
cur = nxt;
}
return cur;
};
// Decompose [L, R] per bit-length to avoid leading zeros
int lowLen = bitlen(L);
for (int len = lowLen; len <= maxLen; ++len) {
long long lo = max(L, 1LL << (len - 1));
long long hi = min(R, (1LL << len) - 1);
if (lo > hi) continue;
long long x = lo;
while (x <= hi) {
int k = 0;
// Find largest block 2^k such that x is divisible by 2^k and x + 2^k - 1 <= hi
// Equivalent to k = min(ctz(x), floor(log2(hi - x + 1)))
int tz = 0;
if (x != 0) tz = __builtin_ctzll(x);
int lim = 63 - __builtin_clzll(hi - x + 1);
k = min(tz, lim);
// Also ensure k <= len-1 (since within fixed length)
k = min(k, len - 1);
// However, due to restriction within [2^{len-1}, 2^len-1], it's safe.
long long blockSize = 1LL << k;
long long a = x;
// prefix value and length
unsigned int prefVal = (unsigned int)(a >> k);
int prefLen = len - k;
if (k > 0) {
int pnode = ensurePrefix(prefVal, prefLen);
// From this prefix, allow any k bits
addEdge(pnode, S[k-1], 0);
addEdge(pnode, S[k-1], 1);
} else {
// Single number; add edge from parent prefix to sink with last bit
int preLen = prefLen - 1;
unsigned int preVal = (preLen > 0) ? (prefVal >> 1) : 0;
int parentNode = ensurePrefix(preVal, preLen);
int lastBit = prefVal & 1;
addEdge(parentNode, S[0], lastBit);
}
x += blockSize;
}
}
// Output
int n = (int)g.size() - 1;
cout << n << "\n";
for (int i = 1; i <= n; ++i) {
cout << (int)g[i].size();
for (auto &e : g[i]) {
cout << " " << e.to << " " << e.w;
}
cout << "\n";
}
return 0;
} |