// --------------------------------------------------<TEMPLATE>--------------------------------------------------
// --------------------<optimizations>--------------------
/*
#pragma GCC optimize("Ofast,unroll-loops")
#pragma GCC target("avx,avx2,fma")
*/
// -------------------</optimizations>--------------------
// ---------------<Headers and namespaces>----------------
#include <bits/stdc++.h>
using namespace std;
/*
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
*/
// ---------------</Headers and namespaces>---------------
// -----------------<Defines and typedefs>----------------
// typedef tree<int,null_type,less<int>,rb_tree_tag,
// tree_order_statistics_node_update> indexed_set; // use less_equal for multiset
// order_of_key (val): returns the no. of values less than val
// find_by_order (k): returns the iterator to kth largest element.(0-based)
typedef long double LD;
typedef long long ll;
#define int ll
#define pb push_back
#define mp make_pair
#define REP(i,n) for (int i = 0; i < n; i++)
#define FOR(i,a,b) for (int i = a; i < b; i++)
#define REPD(i,n) for (int i = n-1; i >= 0; i--)
#define FORD(i,a,b) for (int i = a; i >= b; i--)
#define remax(a,b) a = max(a,b)
#define remin(a,b) a = min(a,b)
#define all(v) v.begin(),v.end()
typedef map<int,int> mii;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef pair<int,int> pii;
typedef vector<pii> vpii;
#define F first
#define S second
#define PQ(type) priority_queue<type>
#define PQD(type) priority_queue<type,vector<type>,greater<type> >
#define WL(t) while(t --)
#define SZ(x) ((int)(x).size())
#define runtime() ((double)clock() / CLOCKS_PER_SEC)
#define inrange(i,a,b) ((i>=min(a,b)) && (i<=max(a,b)))
/*
// -----<SCANF>-----
#define sfi(x) scanf("%d",&x);
#define sfi2(x,y) scanf("%d%d",&x,&y);
#define sfi3(x,y,z) scanf("%d%d%d",&x,&y,&z);
#define sfl(x) scanf("%lld",&x);
#define sfl2(x,y) scanf("%lld%lld",&x,&y);
#define sfl3(x,y,z) scanf("%lld%lld%lld",&x,&y,&z);
#define sfl4(x,y,z,x1) scanf("%lld%lld%lld%lld",&x,&y,&z,&x1);
#define sfl5(x,y,z,x1,y1) scanf("%lld%lld%lld%lld%lld",&x,&y,&z,&x1,&y1);
#define sfl6(x,y,z,x1,y1,z1) scanf("%lld%lld%lld%lld%lld%lld",&x,&y,&z,&x1,&y1,&z1);
#define sfs(x) scanf("%s",x);
#define sfs2(x,y) scanf("%s%s",x,y);
#define sfs3(x,y,z) scanf("%s%s%s",x,y,z);
// ----</SCANF>-----
// ----<PRINTF>-----
#define pfi(x) printf("%d\n",x);
#define pfi2(x,y) printf("%d %d\n",x,y);
#define pfi3(x,y,z) printf("%d %d %d\n",x,y,z);
#define pfl(x) printf("%lld\n",x);
#define pfl2(x,y) printf("%lld %lld\n",x,y);
#define pfl3(x,y,z) printf("%lld %lld %lld\n",x,y,z);
#define pfs(x) printf("%s\n",x);
#define pfs2(x,y) printf("%s %s\n",x,y);
#define pfs3(x,y,z) printf("%s %s %s\n",x,y,z);
#define pwe(x) printf("%lld ",x); // print without end
// ----</PRINTF>----
*/
#define FLSH fflush(stdout)
#define fileIO(name) \
freopen(name".in", "r", stdin); \
freopen(name".out", "w", stdout);
#define PRECISION(x) cout << fixed << setprecision(x);
#define FAST_IO ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
// ----------------</Defines and typedefs>----------------
// -------------------<Debugging stuff>-------------------
#ifdef TRACE
#define trace(...) __f(#__VA_ARGS__, __VA_ARGS__)
template <typename Arg1>
void __f(const char* name, Arg1&& arg1){
cout << name << " : " << arg1 << std::endl;
}
template <typename Arg1, typename... Args>
void __f(const char* names, Arg1&& arg1, Args&&... args){
const char* comma = strchr(names + 1, ',');cout.write(names, comma - names) << " : " << arg1<<" | ";__f(comma+1, args...);
}
#else
#define trace(...)
#endif
// ------------------</Debugging stuff>-------------------
// ------------------------<Consts>-----------------------
const int MAXN = 100005;
const int SQRTN = 1003;
const int LOGN = 22;
const double PI=acos(-1);
#ifdef int
const int INF=1e18;
#else
const int INF=1e9;
#endif
const int MOD = 1000000007;
const int FMOD = 998244353;
const double eps = 1e-9;
// -----------------------</Consts>-----------------------
/*
// -------------------------<RNG>-------------------------
mt19937 RNG(chrono::steady_clock::now().time_since_epoch().count());
#define SHUF(v) shuffle(all(v), RNG);
// Use mt19937_64 for 64 bit random numbers.
// ------------------------</RNG>-------------------------
// ----------------------<MATH>---------------------------
template<typename T> T gcd(T a, T b){return(b?__gcd(a,b):a);}
template<typename T> T lcm(T a, T b){return(a*(b/gcd(a,b)));}
int add(int a, int b, int c = MOD){int res=a+b;return(res>=c?res-c:res);}
int mod_neg(int a, int b, int c = MOD){int res;if(abs(a-b)<c)res=a-b;else res=(a-b)%c;return(res<0?res+c:res);}
int mul(int a, int b, int c = MOD){ll res=(ll)a*b;return(res>=c?res%c:res);}
int muln(int a, int b, int c = MOD){ll res=(ll)a*b;return ((res%c)+c)%c;}
ll mulmod(ll a,ll b, ll m = MOD){ll q = (ll)(((LD)a*(LD)b)/(LD)m);ll r=a*b-q*m;if(r>m)r%=m;if(r<0)r+=m;return r;}
template<typename T>T expo(T e, T n){T x=1,p=e;while(n){if(n&1)x=x*p;p=p*p;n>>=1;}return x;}
template<typename T>T power(T e, T n, T m = MOD){T x=1,p=e;while(n){if(n&1)x=mul(x,p,m);p=mul(p,p,m);n>>=1;}return x;}
template<typename T>T extended_euclid(T a, T b, T &x, T &y){T xx=0,yy=1;y=0;x=1;while(b){T q=a/b,t=b;b=a%b;a=t;\
t=xx;xx=x-q*xx;x=t;t=yy;yy=y-q*yy;y=t;}return a;}
template<typename T>T mod_inverse(T a, T n = MOD){T x,y,z=0;T d=extended_euclid(a,n,x,y);return(d>1?-1:mod_neg(x,z,n));}
const int FACSZ = 1; // Make sure to change this
int fact[FACSZ],ifact[FACSZ];
void precom(int c = MOD){
fact[0] = 1;
FOR(i,1,FACSZ) fact[i] = mul(fact[i-1],i,c);
ifact[FACSZ-1] = mod_inverse(fact[FACSZ-1],c);
REPD(i,FACSZ-1){
ifact[i] = mul(i+1,ifact[i+1],c);
}
}
int ncr(int n,int r,int c = MOD){
return mul(mul(ifact[r],ifact[n-r],c),fact[n],c);
}
*/
// ----------------------</MATH>--------------------------
// --------------------------------------------------</TEMPLATE>--------------------------------------------------
void solvethetestcase();
signed main(){
// comment when using scanf,printf
FAST_IO
int t = 1;
// (UNCOMMENT FOR MULTIPLE TEST CASES)
// cin >> t;
FOR(testcase,1,t+1){
// (UNCOMMENT FOR CODEJAM)
// printf("Case #%lld: ",testcase);
solvethetestcase();
}
}
const int H = 1e6;
int n;
pii a[MAXN];
int dp[MAXN],opt[MAXN];
int f(pii line, int x){
return line.F*x+line.S;
}
pii seg[4*H];
void upd(int ind,int l,int r,pii line){
if(l > r) return;
int mid = (l+r)/2;
bool chm = (f(line,mid) < f(seg[ind],mid));
bool chr = (f(line,r) < f(seg[ind],r));
if(chm) swap(seg[ind],line);
// trace(ind,l,r,seg[ind].F,seg[ind].S);
if(l == r) return;
if(chm == chr) upd(2*ind,l,mid,line);
else upd(2*ind+1,mid+1,r,line);
}
int quer(int ind,int l,int r,int x){
if(l > x or r < x) return INF;
// trace(ind,l,r,x,seg[ind].F,seg[ind].S,f(seg[ind],x));
if(l == r) return f(seg[ind],x);
int mid = (l+r)/2;
return min(f(seg[ind],x),min(quer(2*ind,l,mid,x),quer(2*ind+1,mid+1,r,x)));
}
void solvethetestcase(){
cin >> n;
FOR(i,1,n+1) cin >> a[i].F;
FOR(i,1,n+1) cin >> a[i].S;
FOR(i,2,n+1) dp[1] += a[i].S;
REP(i,4*H) seg[i] = {-2*a[1].F,dp[1]+a[1].F*a[1].F};
FOR(i,2,n+1){
dp[i] = INF;
int cur = a[i].F*a[i].F-a[i].S+quer(1,0,H,a[i].F);
remin(dp[i],cur);
upd(1,0,H,{-2*a[i].F,dp[i]+a[i].F*a[i].F});
// trace(a[i].F,a[i].S,dp[i]);
}
cout << dp[n] << endl;
}
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
36 ms |
62976 KB |
Output is correct |
| 2 |
Correct |
36 ms |
62968 KB |
Output is correct |
| 3 |
Correct |
43 ms |
62968 KB |
Output is correct |
| 4 |
Correct |
37 ms |
63004 KB |
Output is correct |
| 5 |
Correct |
38 ms |
62968 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
97 ms |
66168 KB |
Output is correct |
| 2 |
Correct |
99 ms |
66320 KB |
Output is correct |
| 3 |
Correct |
104 ms |
66292 KB |
Output is correct |
| 4 |
Correct |
95 ms |
66188 KB |
Output is correct |
| 5 |
Correct |
97 ms |
66168 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
36 ms |
62976 KB |
Output is correct |
| 2 |
Correct |
36 ms |
62968 KB |
Output is correct |
| 3 |
Correct |
43 ms |
62968 KB |
Output is correct |
| 4 |
Correct |
37 ms |
63004 KB |
Output is correct |
| 5 |
Correct |
38 ms |
62968 KB |
Output is correct |
| 6 |
Correct |
97 ms |
66168 KB |
Output is correct |
| 7 |
Correct |
99 ms |
66320 KB |
Output is correct |
| 8 |
Correct |
104 ms |
66292 KB |
Output is correct |
| 9 |
Correct |
95 ms |
66188 KB |
Output is correct |
| 10 |
Correct |
97 ms |
66168 KB |
Output is correct |
| 11 |
Correct |
106 ms |
66552 KB |
Output is correct |
| 12 |
Correct |
111 ms |
66296 KB |
Output is correct |
| 13 |
Correct |
94 ms |
66372 KB |
Output is correct |
| 14 |
Correct |
113 ms |
66428 KB |
Output is correct |
| 15 |
Correct |
90 ms |
66168 KB |
Output is correct |
| 16 |
Correct |
91 ms |
66168 KB |
Output is correct |
| 17 |
Correct |
86 ms |
66424 KB |
Output is correct |
| 18 |
Correct |
89 ms |
66424 KB |
Output is correct |
