#include <bits/stdc++.h> #include <ext/pb_ds/assoc_container.hpp> #include <ext/pb_ds/tree_policy.hpp> #include <ext/pb_ds/detail/standard_policies.hpp> using namespace __gnu_pbds; using namespace std; typedef tree< pair<long long, int>, null_type, less <pair<long long, int>>, rb_tree_tag, tree_order_statistics_node_update > ordered_set; const int MAXV = 1000 * 1000 * 1000; pair <bool, vector<int>> check(int n, int k, long long x, vector <int> &a, vector <int> &b, bool trackSol) { int l = 0, r = 0; long long dpL = 0, dpR = 0, dpMin = 0; vector <int> ansHints; ordered_set diffNeg, diffPos; int timestamp = 0; for (int i = 0; i < n; i++) { r++; dpL += b[i]; dpR += a[i]; dpMin += min(a[i], b[i]); if (dpMin > x) { return {false, {}}; } long long abDiff = a[i] - b[i]; if (abDiff < 0) { diffNeg.insert({abDiff, timestamp++}); } else if (abDiff > 0) { diffPos.insert({abDiff, timestamp++}); } if (trackSol) { int idx; if (abDiff < 0) { idx = l + diffNeg.order_of_key({abDiff, -1}); } else if (abDiff > 0) { idx = r - (diffPos.size() - diffPos.order_of_key({abDiff, -1})); } else { idx = l + diffNeg.size(); } ansHints.push_back(idx); } if (dpMin < 0) { long long dpCurrLeft = dpMin, dpCurrRight = dpMin; while (!diffNeg.empty() && dpCurrLeft <= 0) { auto it = prev(diffNeg.end()); dpCurrLeft -= it->first; diffNeg.erase(it); } while (!diffPos.empty() && dpCurrRight <= 0) { auto it = diffPos.begin(); dpCurrRight += it->first; diffPos.erase(it); } if (dpCurrLeft > 0) diffNeg.insert({-dpCurrLeft, timestamp++}); if (dpCurrRight > 0) diffPos.insert({dpCurrRight, timestamp++}); dpMin = 0; dpL = max(dpL, 0LL); dpR = max(dpR, 0LL); } while (dpL > x) { dpL += diffNeg.begin()->first; diffNeg.erase(diffNeg.begin()); l++; } while (dpR > x) { auto it = prev(diffPos.end()); dpR -= it->first; diffPos.erase(it); r--; } } return {l <= k && k <= r, ansHints}; } string recover(int n, int k, vector <int> &ansHints) { string ans(n, 'B'); for (int i = n - 1; i >= 0; i--) { if (k > ansHints[i]) { ans[i] = 'A'; k--; } } return ans; } pair <long long, string> solve(int n, int k, vector <int> &a, vector <int> &b) { long long l = -1, r = (long long) n * MAXV; while (r - l > 1) { long long mid = (l + r) / 2; if (check(n, k, mid, a, b, false).first) { r = mid; } else { l = mid; } } auto ansHints = check(n, k, r, a, b, true).second; return {r, recover(n, k, ansHints)}; } int main() { ios_base::sync_with_stdio(false); int n, k; cin >> n >> k; vector <int> a(n), b(n); for (int &ai : a) cin >> ai; for (int &bi : b) cin >> bi; auto [cost, sol] = solve(n, k, a, b); cout << cost << '\n' << sol << endl; 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 | #include <bits/stdc++.h> #include <ext/pb_ds/assoc_container.hpp> #include <ext/pb_ds/tree_policy.hpp> #include <ext/pb_ds/detail/standard_policies.hpp> using namespace __gnu_pbds; using namespace std; typedef tree< pair<long long, int>, null_type, less <pair<long long, int>>, rb_tree_tag, tree_order_statistics_node_update > ordered_set; const int MAXV = 1000 * 1000 * 1000; pair <bool, vector<int>> check(int n, int k, long long x, vector <int> &a, vector <int> &b, bool trackSol) { int l = 0, r = 0; long long dpL = 0, dpR = 0, dpMin = 0; vector <int> ansHints; ordered_set diffNeg, diffPos; int timestamp = 0; for (int i = 0; i < n; i++) { r++; dpL += b[i]; dpR += a[i]; dpMin += min(a[i], b[i]); if (dpMin > x) { return {false, {}}; } long long abDiff = a[i] - b[i]; if (abDiff < 0) { diffNeg.insert({abDiff, timestamp++}); } else if (abDiff > 0) { diffPos.insert({abDiff, timestamp++}); } if (trackSol) { int idx; if (abDiff < 0) { idx = l + diffNeg.order_of_key({abDiff, -1}); } else if (abDiff > 0) { idx = r - (diffPos.size() - diffPos.order_of_key({abDiff, -1})); } else { idx = l + diffNeg.size(); } ansHints.push_back(idx); } if (dpMin < 0) { long long dpCurrLeft = dpMin, dpCurrRight = dpMin; while (!diffNeg.empty() && dpCurrLeft <= 0) { auto it = prev(diffNeg.end()); dpCurrLeft -= it->first; diffNeg.erase(it); } while (!diffPos.empty() && dpCurrRight <= 0) { auto it = diffPos.begin(); dpCurrRight += it->first; diffPos.erase(it); } if (dpCurrLeft > 0) diffNeg.insert({-dpCurrLeft, timestamp++}); if (dpCurrRight > 0) diffPos.insert({dpCurrRight, timestamp++}); dpMin = 0; dpL = max(dpL, 0LL); dpR = max(dpR, 0LL); } while (dpL > x) { dpL += diffNeg.begin()->first; diffNeg.erase(diffNeg.begin()); l++; } while (dpR > x) { auto it = prev(diffPos.end()); dpR -= it->first; diffPos.erase(it); r--; } } return {l <= k && k <= r, ansHints}; } string recover(int n, int k, vector <int> &ansHints) { string ans(n, 'B'); for (int i = n - 1; i >= 0; i--) { if (k > ansHints[i]) { ans[i] = 'A'; k--; } } return ans; } pair <long long, string> solve(int n, int k, vector <int> &a, vector <int> &b) { long long l = -1, r = (long long) n * MAXV; while (r - l > 1) { long long mid = (l + r) / 2; if (check(n, k, mid, a, b, false).first) { r = mid; } else { l = mid; } } auto ansHints = check(n, k, r, a, b, true).second; return {r, recover(n, k, ansHints)}; } int main() { ios_base::sync_with_stdio(false); int n, k; cin >> n >> k; vector <int> a(n), b(n); for (int &ai : a) cin >> ai; for (int &bi : b) cin >> bi; auto [cost, sol] = solve(n, k, a, b); cout << cost << '\n' << sol << endl; return 0; } |