File size: 5,453 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 | #include <bits/stdc++.h>
using namespace std;
struct Edge {
int to, w;
};
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int L, R;
if (!(cin >> L >> R)) return 0;
// Graph: 1-indexed nodes
vector<vector<Edge>> g(1); // g[0] unused
auto addNode = [&]() -> int {
g.push_back({});
return (int)g.size() - 1;
};
auto addEdge = [&](int u, int v, int w) {
g[u].push_back({v, w});
};
auto getBits = [&](int x) -> vector<int> {
vector<int> b;
while (x > 0) {
b.push_back(x & 1);
x >>= 1;
}
reverse(b.begin(), b.end());
if (b.empty()) b.push_back(0);
return b;
};
vector<int> Lbits = getBits(L);
vector<int> Rbits = getBits(R);
int kL = (int)Lbits.size();
int kR = (int)Rbits.size();
int start = addNode(); // node 1
// A[k]: node representing "k free bits remaining" (exactly k edges to sink), A[0] is sink placeholder 0
vector<int> A(1, -1); // we'll resize dynamically; A[0] will be 0 (placeholder for sink)
function<int(int)> getA = [&](int k) -> int {
if (k == 0) return 0; // placeholder for sink
if ((int)A.size() <= k) A.resize(k + 1, -1);
if (A[k] != -1) return A[k];
int child = getA(k - 1);
int u = addNode();
A[k] = u;
addEdge(u, child, 0);
addEdge(u, child, 1);
return u;
};
// Lower-bound DP (length = kL), states indexed by idx (next bit position), tight to L
int lowK = 0;
vector<int> lowerMemo;
vector<int>* pLbits = nullptr;
function<int(int)> lowerNode;
lowerNode = [&](int idx) -> int {
if (idx == lowK) return getA(0);
if (lowerMemo[idx] != -1) return lowerMemo[idx];
int u = addNode();
lowerMemo[idx] = u;
int lb = (*pLbits)[idx];
if (lb == 0) {
addEdge(u, lowerNode(idx + 1), 0);
addEdge(u, getA(lowK - idx - 1), 1);
} else {
addEdge(u, lowerNode(idx + 1), 1);
}
return u;
};
// Upper-bound DP (length = kR), states indexed by idx (next bit position), tight to R
int upK = 0;
vector<int> upperMemo;
vector<int>* pRbits = nullptr;
function<int(int)> upperNode;
upperNode = [&](int idx) -> int {
if (idx == upK) return getA(0);
if (upperMemo[idx] != -1) return upperMemo[idx];
int u = addNode();
upperMemo[idx] = u;
int rb = (*pRbits)[idx];
if (rb == 0) {
addEdge(u, upperNode(idx + 1), 0);
} else {
addEdge(u, upperNode(idx + 1), 1);
addEdge(u, getA(upK - idx - 1), 0);
}
return u;
};
// Both-bounds DP (length = kR == kL), states (idx, tL, tU)
int bothK = 0;
vector<vector<vector<int>>> bothMemo;
vector<int>* pLL = nullptr;
vector<int>* pRR = nullptr;
function<int(int,int,int)> bothNode;
bothNode = [&](int idx, int tL, int tU) -> int {
if (idx == bothK) return getA(0);
if (bothMemo[idx][tL][tU] != -1) return bothMemo[idx][tL][tU];
int u = addNode();
bothMemo[idx][tL][tU] = u;
int lb = (*pLL)[idx];
int rb = (*pRR)[idx];
for (int b = 0; b <= 1; ++b) {
if (tL == 1 && b < lb) continue;
if (tU == 1 && b > rb) continue;
int ntL = tL ? (b == lb) : 0;
int ntU = tU ? (b == rb) : 0;
if (idx + 1 == bothK) {
addEdge(u, getA(0), b);
} else if (ntL == 0 && ntU == 0) {
addEdge(u, getA(bothK - idx - 1), b);
} else {
addEdge(u, bothNode(idx + 1, ntL, ntU), b);
}
}
return u;
};
// Build from start
if (kL == kR) {
bothK = kR;
bothMemo.assign(bothK + 1, vector<vector<int>>(2, vector<int>(2, -1)));
pLL = &Lbits;
pRR = &Rbits;
if (bothK == 1) {
addEdge(start, getA(0), 1);
} else {
int node = bothNode(1, 1, 1); // after first '1'
addEdge(start, node, 1);
}
} else {
// Intermediate lengths: allow all with first bit 1
for (int len = kL + 1; len <= kR - 1; ++len) {
addEdge(start, getA(len - 1), 1);
}
// Lower-bound for length kL
lowK = kL;
lowerMemo.assign(lowK + 1, -1);
pLbits = &Lbits;
if (lowK == 1) {
addEdge(start, getA(0), 1);
} else {
int node = lowerNode(1); // after first '1'
addEdge(start, node, 1);
}
// Upper-bound for length kR
upK = kR;
upperMemo.assign(upK + 1, -1);
pRbits = &Rbits;
if (upK == 1) {
addEdge(start, getA(0), 1);
} else {
int node = upperNode(1); // after first '1'
addEdge(start, node, 1);
}
}
// Create sink as the last node
int sink = addNode();
// Replace placeholder 0 with sink id
for (int u = 1; u < (int)g.size(); ++u) {
for (auto &e : g[u]) if (e.to == 0) e.to = sink;
}
// Output
int n = (int)g.size() - 1;
cout << n << "\n";
for (int i = 1; i <= n; ++i) {
cout << g[i].size();
for (auto &e : g[i]) {
cout << " " << e.to << " " << e.w;
}
cout << "\n";
}
return 0;
} |