#include <bits/stdc++.h>
using namespace std;
#define int long long
#define TF(i, p, q) for(int i = (p); i <= (q); ++i)
#define TR(i, q, p) for(int i = (q); i >= (p); --i)
#define V vector
#define pb push_back
#define eb emplace_back
#define fi first
#define se second
#define th third
#define rz resize
#define all(V) V.begin(), V.end()
#define rall(V) V.rbegin(), V.rend()
#define sz(V) (int)(V.size())
#define cmin(a, b) a = min(a, b)
#define cmax(a, b) a = max(a, b);
typedef pair<int,int> ii;
typedef queue<int> qi;
typedef queue<ii> qii;
typedef long long ll;
typedef vector<int> vi;
typedef vector<vector<int>>vvi;
typedef vector<vector<bool>>vvb;
typedef vector<bool> vb;
typedef vector<ii> vii;
constexpr int inf = 1e9 + 9;
bool check(int n, int k, vi& tab){
vi sweep(n+1);
int cs = 0;
TF(i, 1, n){
cs += sweep[i];
int val = tab[i] - cs;
if(val < 0) return false;
else if(val > 0 and i > n-k+1) return false;
if(i+k <= n) sweep[i+k] -= val;
cs += val;
}
return true;
}
vii dismantle(int x, int n){
int c = 0; vii primes;
while(x%2 == 0){
c++;
x /= 2;
}
if(c) primes.pb({2, c});
int cp = 3;
while(x > 1 and cp <= n and x >= cp){
if(x%cp == 0){
c = 0;
while(x%cp == 0){
x /= cp;
c++;
}
primes.pb({cp, c});
}
cp += 2;
}
if(x < cp and x > 1) primes.pb({x, 1});
return primes;
}
void mkd(vi& ans, vi& ptr, vii& primes, int ci, int dv, int n, int ms){
for(int&pti= ptr[ci]; pti <= primes[ci].se; pti++){
if(dv > n){
ptr[ci] = 0;
return;
}
if(ci == ms-1){
ans.pb(dv);
}
else mkd(ans, ptr, primes, ci+1, dv, n, ms);
dv *= primes[ci].fi;
}
ptr[ci] = 0;
}
void solve(){
int n; cin >> n; vi tab(n+1);
int S = 0;
TF(i, 1, n){
cin >> tab[i];
S += tab[i];
}
vii primes = dismantle(S, n);
if(sz(primes) == 0){
cout << 1;
return;
}
vi ans;
vi ptr(sz(primes));
mkd(ans, ptr, primes, 0, 1, n, sz(primes));
sort(rall(ans));
for(int v: ans){
if(check(n, v, tab)){
cout << v;
return;
}
}
}
int32_t main(){
ios_base::sync_with_stdio(0);
cin.tie(0); 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 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 | #include <bits/stdc++.h> using namespace std; #define int long long #define TF(i, p, q) for(int i = (p); i <= (q); ++i) #define TR(i, q, p) for(int i = (q); i >= (p); --i) #define V vector #define pb push_back #define eb emplace_back #define fi first #define se second #define th third #define rz resize #define all(V) V.begin(), V.end() #define rall(V) V.rbegin(), V.rend() #define sz(V) (int)(V.size()) #define cmin(a, b) a = min(a, b) #define cmax(a, b) a = max(a, b); typedef pair<int,int> ii; typedef queue<int> qi; typedef queue<ii> qii; typedef long long ll; typedef vector<int> vi; typedef vector<vector<int>>vvi; typedef vector<vector<bool>>vvb; typedef vector<bool> vb; typedef vector<ii> vii; constexpr int inf = 1e9 + 9; bool check(int n, int k, vi& tab){ vi sweep(n+1); int cs = 0; TF(i, 1, n){ cs += sweep[i]; int val = tab[i] - cs; if(val < 0) return false; else if(val > 0 and i > n-k+1) return false; if(i+k <= n) sweep[i+k] -= val; cs += val; } return true; } vii dismantle(int x, int n){ int c = 0; vii primes; while(x%2 == 0){ c++; x /= 2; } if(c) primes.pb({2, c}); int cp = 3; while(x > 1 and cp <= n and x >= cp){ if(x%cp == 0){ c = 0; while(x%cp == 0){ x /= cp; c++; } primes.pb({cp, c}); } cp += 2; } if(x < cp and x > 1) primes.pb({x, 1}); return primes; } void mkd(vi& ans, vi& ptr, vii& primes, int ci, int dv, int n, int ms){ for(int&pti= ptr[ci]; pti <= primes[ci].se; pti++){ if(dv > n){ ptr[ci] = 0; return; } if(ci == ms-1){ ans.pb(dv); } else mkd(ans, ptr, primes, ci+1, dv, n, ms); dv *= primes[ci].fi; } ptr[ci] = 0; } void solve(){ int n; cin >> n; vi tab(n+1); int S = 0; TF(i, 1, n){ cin >> tab[i]; S += tab[i]; } vii primes = dismantle(S, n); if(sz(primes) == 0){ cout << 1; return; } vi ans; vi ptr(sz(primes)); mkd(ans, ptr, primes, 0, 1, n, sz(primes)); sort(rall(ans)); for(int v: ans){ if(check(n, v, tab)){ cout << v; return; } } } int32_t main(){ ios_base::sync_with_stdio(0); cin.tie(0); solve(); } |
English