#include <bits/stdc++.h> using namespace std; #define debug(x) cerr << #x << " " << x << endl; const int N = 50, root = 0, LOG = 21; vector<int> higher, lower, lower_id; int s1, s2, n, base = root; pair<int, long long> answer[N]; int pref[N], t[N]; struct node { pair<int, int> wyn[LOG]; // pokłucenie, ile int dodawacz; int lazy; // ile dodac do wyniku int sons[LOG]; int sons_size; int l, r; node() { for(int i = 0; i < LOG; i++) wyn[i] = {1e9, 1}; for(int i = 0; i < LOG; i++) sons[i] = -1; dodawacz = 0; lazy = 0; sons_size = 0; l = LOG; r = 0; } }; node tree[(1 << LOG) + 7]; // ? rozmiar pair<int, int> lamus(const pair<int, int>& a, const pair<int, int>& b) { if(a.first > b.first) { return b; } else if(a.first == b.first) { return {a.first, a.second + b.second}; } return a; } int licz_inwersje(vector<int> vek, int mask) { long long tablica = 0; int ret = 0; for(int i = (int)vek.size() - 1; i >= 0; i--) { if(!(mask & (1 << i))) continue; long long tmp = tablica; tmp >>= vek[i]; ret += __builtin_popcount(tmp); tablica += (1ll << vek[i]); } return ret; } void fix(int v) { if(tree[v].sons_size == 0) return; for(int i = tree[v].l; i <= tree[v].r; i++) { tree[v].wyn[i] = {1e9, 1}; } for(int i = 0; i < tree[v].sons_size; i++) { int x = tree[v].sons[i]; for(int i = tree[x].l; i <= tree[x].r; i++) { int b = tree[x].wyn[i].first + tree[x].lazy; if(tree[v].wyn[i].first > b) { tree[v].wyn[i].first = b; tree[v].wyn[i].second = tree[x].wyn[i].second; } else if(tree[v].wyn[i].first == b) { tree[v].wyn[i].second += tree[x].wyn[i].second; } } } } void create(int v, int mask, int w, int gl, int pop_count) { gl --; if(gl == -1) { tree[v].wyn[pop_count] = lamus(tree[v].wyn[pop_count], {w, 1}); tree[v].l = min(tree[v].l, pop_count); tree[v].r = max(tree[v].r, pop_count); return; } int ile_ja_mam = 0; if(tree[v].sons_size == 0) { for(int i = 0; i <= lower_id[gl]; i++) { tree[v].sons[tree[v].sons_size] = ++base; tree[v].sons_size ++; tree[base].dodawacz = i; } } for(int i = 0; i < lower_id[gl]; i++) { if(mask & 1) ile_ja_mam ++; mask /= 2; } create(tree[v].sons[ile_ja_mam], mask, w, gl, pop_count); } void dfs(int v, int gl) { gl --; if(gl == -1) { return; } for(int i = 0; i < tree[v].sons_size; i++) { dfs(tree[v].sons[i], gl); tree[v].l = min(tree[v].l, tree[tree[v].sons[i]].l); tree[v].r = max(tree[v].r, tree[tree[v].sons[i]].r); } fix(v); } void insert(int v, int suma, int w, int gl, int acc) { acc += tree[v].dodawacz; gl --; if(suma == 0) { tree[v].lazy += w * acc; return; } suma -= lower_id[gl]; for(int i = 0; i < tree[v].sons_size; i++) { insert(tree[v].sons[i], suma, w, gl, acc); } fix(v); } void solve() { cin >> n; if(n < 10) s1 = n / 2; // higher 22 else s1 = (n + 2) / 2; // higher 21 s2 = n - s1; // lower for(int i = 0; i < n; i++) { cin >> t[i]; if(t[i] > s2) higher.push_back(t[i]); else lower.push_back(t[i]); } for(int i = 0; i <= n; i++) answer[i] = {1e9, 1}; int cnt_tmp = 0; for(int i = n - 1; i >= 0; i--) { if(t[i] > s2 and (lower_id.size() == 0 or cnt_tmp != 0)) { lower_id.push_back(cnt_tmp); cnt_tmp = 0; } if(t[i] <= s2) { cnt_tmp ++; } } reverse(lower_id.begin(), lower_id.end()); reverse(lower.begin(), lower.end()); for(int i = 0; i < (1 << s2); i++) { create(root, i, licz_inwersje(lower, i), lower_id.size(), __builtin_popcount(i)); } dfs(root, lower_id.size()); int ktury_odwiedzony = 0; int ile_na_pref = 0; for(int i = n - 1; i >= 0; i--) { if(t[i] > s2) { pref[ktury_odwiedzony] = ile_na_pref; ktury_odwiedzony ++; } else { ile_na_pref ++; } } reverse(higher.begin(), higher.end()); for(int i = 0; i < (1 << s1); i++) { if(i != 0) { for(int j = 0; j < s1; j++) { if((i & (1 << j)) > 0 and ((i - 1) & (1 << j)) == 0) { insert(root, pref[j], 1, lower_id.size(), 0); } if((i & (1 << j)) == 0 and ((i - 1) & (1 << j)) > 0) { insert(root, pref[j], -1, lower_id.size(), 0); } } } node ret = tree[root]; int cnt = __builtin_popcount(i); int ile = licz_inwersje(higher, i); for(int j = 0; j <= s2; j++) { pair<int, int> b = {ret.wyn[j].first + ile, ret.wyn[j].second}; if(answer[cnt + j].first > b.first) { answer[cnt + j] = b; } else if(answer[cnt + j].first == b.first) { answer[cnt + j].second += b.second; } } } for(int i = 1; i <= n; i++) { cout << answer[i].first << " " << answer[i].second << endl; } } int32_t main(){ ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); int test = 1; while(test--){ solve(); } 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 | #include <bits/stdc++.h> using namespace std; #define debug(x) cerr << #x << " " << x << endl; const int N = 50, root = 0, LOG = 21; vector<int> higher, lower, lower_id; int s1, s2, n, base = root; pair<int, long long> answer[N]; int pref[N], t[N]; struct node { pair<int, int> wyn[LOG]; // pokłucenie, ile int dodawacz; int lazy; // ile dodac do wyniku int sons[LOG]; int sons_size; int l, r; node() { for(int i = 0; i < LOG; i++) wyn[i] = {1e9, 1}; for(int i = 0; i < LOG; i++) sons[i] = -1; dodawacz = 0; lazy = 0; sons_size = 0; l = LOG; r = 0; } }; node tree[(1 << LOG) + 7]; // ? rozmiar pair<int, int> lamus(const pair<int, int>& a, const pair<int, int>& b) { if(a.first > b.first) { return b; } else if(a.first == b.first) { return {a.first, a.second + b.second}; } return a; } int licz_inwersje(vector<int> vek, int mask) { long long tablica = 0; int ret = 0; for(int i = (int)vek.size() - 1; i >= 0; i--) { if(!(mask & (1 << i))) continue; long long tmp = tablica; tmp >>= vek[i]; ret += __builtin_popcount(tmp); tablica += (1ll << vek[i]); } return ret; } void fix(int v) { if(tree[v].sons_size == 0) return; for(int i = tree[v].l; i <= tree[v].r; i++) { tree[v].wyn[i] = {1e9, 1}; } for(int i = 0; i < tree[v].sons_size; i++) { int x = tree[v].sons[i]; for(int i = tree[x].l; i <= tree[x].r; i++) { int b = tree[x].wyn[i].first + tree[x].lazy; if(tree[v].wyn[i].first > b) { tree[v].wyn[i].first = b; tree[v].wyn[i].second = tree[x].wyn[i].second; } else if(tree[v].wyn[i].first == b) { tree[v].wyn[i].second += tree[x].wyn[i].second; } } } } void create(int v, int mask, int w, int gl, int pop_count) { gl --; if(gl == -1) { tree[v].wyn[pop_count] = lamus(tree[v].wyn[pop_count], {w, 1}); tree[v].l = min(tree[v].l, pop_count); tree[v].r = max(tree[v].r, pop_count); return; } int ile_ja_mam = 0; if(tree[v].sons_size == 0) { for(int i = 0; i <= lower_id[gl]; i++) { tree[v].sons[tree[v].sons_size] = ++base; tree[v].sons_size ++; tree[base].dodawacz = i; } } for(int i = 0; i < lower_id[gl]; i++) { if(mask & 1) ile_ja_mam ++; mask /= 2; } create(tree[v].sons[ile_ja_mam], mask, w, gl, pop_count); } void dfs(int v, int gl) { gl --; if(gl == -1) { return; } for(int i = 0; i < tree[v].sons_size; i++) { dfs(tree[v].sons[i], gl); tree[v].l = min(tree[v].l, tree[tree[v].sons[i]].l); tree[v].r = max(tree[v].r, tree[tree[v].sons[i]].r); } fix(v); } void insert(int v, int suma, int w, int gl, int acc) { acc += tree[v].dodawacz; gl --; if(suma == 0) { tree[v].lazy += w * acc; return; } suma -= lower_id[gl]; for(int i = 0; i < tree[v].sons_size; i++) { insert(tree[v].sons[i], suma, w, gl, acc); } fix(v); } void solve() { cin >> n; if(n < 10) s1 = n / 2; // higher 22 else s1 = (n + 2) / 2; // higher 21 s2 = n - s1; // lower for(int i = 0; i < n; i++) { cin >> t[i]; if(t[i] > s2) higher.push_back(t[i]); else lower.push_back(t[i]); } for(int i = 0; i <= n; i++) answer[i] = {1e9, 1}; int cnt_tmp = 0; for(int i = n - 1; i >= 0; i--) { if(t[i] > s2 and (lower_id.size() == 0 or cnt_tmp != 0)) { lower_id.push_back(cnt_tmp); cnt_tmp = 0; } if(t[i] <= s2) { cnt_tmp ++; } } reverse(lower_id.begin(), lower_id.end()); reverse(lower.begin(), lower.end()); for(int i = 0; i < (1 << s2); i++) { create(root, i, licz_inwersje(lower, i), lower_id.size(), __builtin_popcount(i)); } dfs(root, lower_id.size()); int ktury_odwiedzony = 0; int ile_na_pref = 0; for(int i = n - 1; i >= 0; i--) { if(t[i] > s2) { pref[ktury_odwiedzony] = ile_na_pref; ktury_odwiedzony ++; } else { ile_na_pref ++; } } reverse(higher.begin(), higher.end()); for(int i = 0; i < (1 << s1); i++) { if(i != 0) { for(int j = 0; j < s1; j++) { if((i & (1 << j)) > 0 and ((i - 1) & (1 << j)) == 0) { insert(root, pref[j], 1, lower_id.size(), 0); } if((i & (1 << j)) == 0 and ((i - 1) & (1 << j)) > 0) { insert(root, pref[j], -1, lower_id.size(), 0); } } } node ret = tree[root]; int cnt = __builtin_popcount(i); int ile = licz_inwersje(higher, i); for(int j = 0; j <= s2; j++) { pair<int, int> b = {ret.wyn[j].first + ile, ret.wyn[j].second}; if(answer[cnt + j].first > b.first) { answer[cnt + j] = b; } else if(answer[cnt + j].first == b.first) { answer[cnt + j].second += b.second; } } } for(int i = 1; i <= n; i++) { cout << answer[i].first << " " << answer[i].second << endl; } } int32_t main(){ ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); int test = 1; while(test--){ solve(); } return 0; } |