#include <algorithm> #include <iostream> #include <vector> #include <cassert> constexpr int64_t INF = 1e18+1; constexpr int64_t LOOKUP_LIM = 97; struct CountTree { std::vector<int> tree; int len{1}; CountTree(int size) { while (len < size) { len *= 2; } tree.resize(len*2, 1); for (int i = len-1; i > 0; i--) { tree[i] = tree[i*2] + tree[i*2+1]; } } int find(int index) { int node = 1; while (node < len) { if (tree[node*2] <= index) { index -= tree[node*2]; node = node*2+1; } else { node = node*2; } } return node-len; } void del(int i) { i += len; tree[i] = 0; i /= 2; while (i > 0) { tree[i] = tree[i*2] + tree[i*2+1]; i /= 2; } } }; struct Entry { int64_t size{0}; int64_t elems[LOOKUP_LIM]; }; // --- int64_t length, order; std::vector<Entry> lookup; int64_t get(int64_t len, int64_t inv) { if (inv < 0) { return 0; } int64_t total = len*(len-1) / 2; if (inv > total) { return 0; } int64_t index = std::min(inv, total-inv); return (index < lookup[len].size ? lookup[len].elems[index] : INF); } void initLookup() { lookup.resize(length+1); for (int64_t i : {0, 1}) { lookup[i].elems[lookup[i].size++] = 1; } for (int64_t len = 2; len <= length; len++) { auto& entry = lookup[len]; int64_t pref = 0; for (int64_t inv = 0; pref < INF; inv++) { int64_t offset = get(len-1, inv) - get(len-1, inv-len); if (offset < 0) { break; } pref += offset; entry.elems[entry.size++] = std::min(pref, INF); // assert(entry.size <= LOOKUP_LIM); } } } // --- void solve(int64_t targetInv) { CountTree tree(length); for (int64_t pos = 0; pos < length; pos++) { int64_t subLen = length-pos-1, last = 0, smaller = 0; int64_t inv = std::max(0ll, targetInv - subLen*(subLen-1)/2); for (; inv <= subLen; inv++) { if (smaller > order) { break; } last = smaller; smaller += get(subLen, targetInv-inv); } int elem = tree.find(inv-1); tree.del(elem); std::cout << elem+1 << " "; order -= last; targetInv -= inv-1; } std::cout << std::endl; } int main() { std::ios::sync_with_stdio(false); std::cin.tie(0); std::cin >> length >> order; int64_t targetInv = length*(length-1) / 2; if (targetInv % 2) { std::cout << "NIE\n"; return 0; } targetInv /= 2; order--; initLookup(); if (get(length, targetInv) > order) { std::cout << "TAK\n"; solve(targetInv); } else { std::cout << "NIE\n"; } return 0; }
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 | #include <algorithm> #include <iostream> #include <vector> #include <cassert> constexpr int64_t INF = 1e18+1; constexpr int64_t LOOKUP_LIM = 97; struct CountTree { std::vector<int> tree; int len{1}; CountTree(int size) { while (len < size) { len *= 2; } tree.resize(len*2, 1); for (int i = len-1; i > 0; i--) { tree[i] = tree[i*2] + tree[i*2+1]; } } int find(int index) { int node = 1; while (node < len) { if (tree[node*2] <= index) { index -= tree[node*2]; node = node*2+1; } else { node = node*2; } } return node-len; } void del(int i) { i += len; tree[i] = 0; i /= 2; while (i > 0) { tree[i] = tree[i*2] + tree[i*2+1]; i /= 2; } } }; struct Entry { int64_t size{0}; int64_t elems[LOOKUP_LIM]; }; // --- int64_t length, order; std::vector<Entry> lookup; int64_t get(int64_t len, int64_t inv) { if (inv < 0) { return 0; } int64_t total = len*(len-1) / 2; if (inv > total) { return 0; } int64_t index = std::min(inv, total-inv); return (index < lookup[len].size ? lookup[len].elems[index] : INF); } void initLookup() { lookup.resize(length+1); for (int64_t i : {0, 1}) { lookup[i].elems[lookup[i].size++] = 1; } for (int64_t len = 2; len <= length; len++) { auto& entry = lookup[len]; int64_t pref = 0; for (int64_t inv = 0; pref < INF; inv++) { int64_t offset = get(len-1, inv) - get(len-1, inv-len); if (offset < 0) { break; } pref += offset; entry.elems[entry.size++] = std::min(pref, INF); // assert(entry.size <= LOOKUP_LIM); } } } // --- void solve(int64_t targetInv) { CountTree tree(length); for (int64_t pos = 0; pos < length; pos++) { int64_t subLen = length-pos-1, last = 0, smaller = 0; int64_t inv = std::max(0ll, targetInv - subLen*(subLen-1)/2); for (; inv <= subLen; inv++) { if (smaller > order) { break; } last = smaller; smaller += get(subLen, targetInv-inv); } int elem = tree.find(inv-1); tree.del(elem); std::cout << elem+1 << " "; order -= last; targetInv -= inv-1; } std::cout << std::endl; } int main() { std::ios::sync_with_stdio(false); std::cin.tie(0); std::cin >> length >> order; int64_t targetInv = length*(length-1) / 2; if (targetInv % 2) { std::cout << "NIE\n"; return 0; } targetInv /= 2; order--; initLookup(); if (get(length, targetInv) > order) { std::cout << "TAK\n"; solve(targetInv); } else { std::cout << "NIE\n"; } return 0; } |