#include <bits/stdc++.h>
#define ll long long
#define fors(u, n, s) for(ll u = (s); u < (n); u++)
#define foru(u, n) fors(u, n, 0)
#define f first
#define s second
#define vec vector
#define pb push_back
using namespace std;
const int A = 1e6;
int n;
vec<ll> arr;
ll skip_size;
void get_skip(){
int a = -1;
int b = -1;
foru(i, n) {
ll left = i;
ll right = n-1-i;
if(left*right >= A) {
a = i;
break;
}
}
for(int i = n-1; i>=0; i--) {
ll left = i;
ll right = n-1-i;
if(left*right >= A) {
b = i;
break;
}
}
if(a == -1) return;
vec<ll> arr_ = {};
swap(arr, arr_);
for(int i = 0; i < n; i++){
if(i == a){
arr.pb(-1);
i = b;
}else{
arr.pb(arr_[i]);
}
}
skip_size = b-a+1;
}
ll triples(ll left, ll middle, ll right){
ll out = 0;
out += left*middle*right;
out += left*middle*(middle-1)/2;
out += right*middle*(middle-1)/2;
out += middle*(middle-1)*(middle-2)/6;
return out;
}
bool verify(int m){
ll left = 0;
ll right = n+m;
foru(i, arr.size()){
if(arr[i] == -1){
right -= skip_size;
left += skip_size;
if(right < 0) return false;
} else {
right --;
if(right < 0) return false;
ll current = 1;
while(triples(left, current, right) < arr[i]) {
current++;
right--;
if(right < 0) return false;
}
left += current;
}
}
return true;
}
void solve(){
cin >> n;
arr.resize(0);
foru(_i, n) {
int a; cin >> a;
if(a == 0) continue;
arr.pb(a);
}
n = arr.size();
get_skip();
int a = -1; //we know this one doesn't solve
int b = 2e3; //we know this one does solve
while(a+1 != b) {
int m = (a+b)/2;
if(verify(m)) b=m;
else a=m;
}
cout << b+n << endl;
}
int main() {
cin.tie(0); cout.tie(0); ios_base::sync_with_stdio(0);
int t; cin >> t;
foru(_i, t) 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 | #include <bits/stdc++.h> #define ll long long #define fors(u, n, s) for(ll u = (s); u < (n); u++) #define foru(u, n) fors(u, n, 0) #define f first #define s second #define vec vector #define pb push_back using namespace std; const int A = 1e6; int n; vec<ll> arr; ll skip_size; void get_skip(){ int a = -1; int b = -1; foru(i, n) { ll left = i; ll right = n-1-i; if(left*right >= A) { a = i; break; } } for(int i = n-1; i>=0; i--) { ll left = i; ll right = n-1-i; if(left*right >= A) { b = i; break; } } if(a == -1) return; vec<ll> arr_ = {}; swap(arr, arr_); for(int i = 0; i < n; i++){ if(i == a){ arr.pb(-1); i = b; }else{ arr.pb(arr_[i]); } } skip_size = b-a+1; } ll triples(ll left, ll middle, ll right){ ll out = 0; out += left*middle*right; out += left*middle*(middle-1)/2; out += right*middle*(middle-1)/2; out += middle*(middle-1)*(middle-2)/6; return out; } bool verify(int m){ ll left = 0; ll right = n+m; foru(i, arr.size()){ if(arr[i] == -1){ right -= skip_size; left += skip_size; if(right < 0) return false; } else { right --; if(right < 0) return false; ll current = 1; while(triples(left, current, right) < arr[i]) { current++; right--; if(right < 0) return false; } left += current; } } return true; } void solve(){ cin >> n; arr.resize(0); foru(_i, n) { int a; cin >> a; if(a == 0) continue; arr.pb(a); } n = arr.size(); get_skip(); int a = -1; //we know this one doesn't solve int b = 2e3; //we know this one does solve while(a+1 != b) { int m = (a+b)/2; if(verify(m)) b=m; else a=m; } cout << b+n << endl; } int main() { cin.tie(0); cout.tie(0); ios_base::sync_with_stdio(0); int t; cin >> t; foru(_i, t) solve(); return 0; } |
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