#include <bits/stdc++.h> #include <ext/pb_ds/assoc_container.hpp> #include <ext/pb_ds/tree_policy.hpp> #define ll long long #define ld long double #define ull unsigned long long #define ff first #define ss second #define pii pair<int,int> #define pll pair<long long, long long> #define vi vector<int> #define vl vector<long long> #define pb push_back #define rep(i, b) for(int i = 0; i < (b); ++i) #define rep2(i,a,b) for(int i = a; i <= (b); ++i) #define rep3(i,a,b,c) for(int i = a; i <= (b); i+=c) #define count_bits(x) __builtin_popcountll((x)) #define all(x) (x).begin(),(x).end() #define siz(x) (int)(x).size() #define forall(it,x) for(auto& it:(x)) using namespace __gnu_pbds; using namespace std; typedef tree<int, null_type, less<int>, rb_tree_tag,tree_order_statistics_node_update> ordered_set; //mt19937 mt;void random_start(){mt.seed(chrono::time_point_cast<chrono::milliseconds>(chrono::high_resolution_clock::now()).time_since_epoch().count());} //ll los(ll a, ll b) {return a + (mt() % (b-a+1));} const int INF = 1e9+50; const ll INF_L = 1e18+40; const ll MOD = 1e9+7; ll dp[200'001]; ll a[200'001]; int n; bool check(ll mid) { rep2(p,1,n) { bool is_ok = 0; for(ll i = 0; i <= a[p]+3 && (i*(i-1)*(i-2))/6 <= a[p]; i++) { if(dp[p-1] + i > mid) return 0; // cout << i << " " << dp[p-1] * i * (mid - dp[p-1] - i) + ((i * (i-1))/2) * (dp[p-1] + (mid - dp[p-1] - i)) + ((i-2)*(i-1)*i)/6 << " val\n"; if(dp[p-1] * i * (mid - dp[p-1] - i) + ((i * (i-1))/2) * (dp[p-1] + (mid - dp[p-1] - i)) + ((i-2)*(i-1)*i)/6 >= a[p]) { dp[p] = dp[p-1] + i; is_ok = 1; break; } } // cout << dp[p] << " " << mid << " " << p << " dp\n"; if(!is_ok) return 0; } return 1; } void solve() { cin >> n; rep2(i,1,n) cin >> a[i]; ll l = 1; ll r = 1e9; ll ans = -1; while(l <= r) { // cout << l << " " << r << " bin\n"; ll mid = (l+r)/2; if(check(mid)) { ans = mid; r = mid-1; } else { l = mid+1; } } cout << ans << "\n"; } int main() { ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0); //random_start(); int t = 1; cin >> t; while(t--) solve(); }
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 | #include <bits/stdc++.h> #include <ext/pb_ds/assoc_container.hpp> #include <ext/pb_ds/tree_policy.hpp> #define ll long long #define ld long double #define ull unsigned long long #define ff first #define ss second #define pii pair<int,int> #define pll pair<long long, long long> #define vi vector<int> #define vl vector<long long> #define pb push_back #define rep(i, b) for(int i = 0; i < (b); ++i) #define rep2(i,a,b) for(int i = a; i <= (b); ++i) #define rep3(i,a,b,c) for(int i = a; i <= (b); i+=c) #define count_bits(x) __builtin_popcountll((x)) #define all(x) (x).begin(),(x).end() #define siz(x) (int)(x).size() #define forall(it,x) for(auto& it:(x)) using namespace __gnu_pbds; using namespace std; typedef tree<int, null_type, less<int>, rb_tree_tag,tree_order_statistics_node_update> ordered_set; //mt19937 mt;void random_start(){mt.seed(chrono::time_point_cast<chrono::milliseconds>(chrono::high_resolution_clock::now()).time_since_epoch().count());} //ll los(ll a, ll b) {return a + (mt() % (b-a+1));} const int INF = 1e9+50; const ll INF_L = 1e18+40; const ll MOD = 1e9+7; ll dp[200'001]; ll a[200'001]; int n; bool check(ll mid) { rep2(p,1,n) { bool is_ok = 0; for(ll i = 0; i <= a[p]+3 && (i*(i-1)*(i-2))/6 <= a[p]; i++) { if(dp[p-1] + i > mid) return 0; // cout << i << " " << dp[p-1] * i * (mid - dp[p-1] - i) + ((i * (i-1))/2) * (dp[p-1] + (mid - dp[p-1] - i)) + ((i-2)*(i-1)*i)/6 << " val\n"; if(dp[p-1] * i * (mid - dp[p-1] - i) + ((i * (i-1))/2) * (dp[p-1] + (mid - dp[p-1] - i)) + ((i-2)*(i-1)*i)/6 >= a[p]) { dp[p] = dp[p-1] + i; is_ok = 1; break; } } // cout << dp[p] << " " << mid << " " << p << " dp\n"; if(!is_ok) return 0; } return 1; } void solve() { cin >> n; rep2(i,1,n) cin >> a[i]; ll l = 1; ll r = 1e9; ll ans = -1; while(l <= r) { // cout << l << " " << r << " bin\n"; ll mid = (l+r)/2; if(check(mid)) { ans = mid; r = mid-1; } else { l = mid+1; } } cout << ans << "\n"; } int main() { ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0); //random_start(); int t = 1; cin >> t; while(t--) solve(); } |