#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
typedef double db;
typedef string str;
typedef pair<int,int> pi;
typedef pair<ll,ll> pl;
typedef pair<db,db> pd;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<db> vd;
typedef vector<str> vs;
typedef vector<pi> vpi;
typedef vector<pl> vpl;
typedef vector<pd> vpd;
#define mp make_pair
#define f first
#define s second
#define sz(x) (int)x.size()
#define all(x) begin(x), end(x)
#define rall(x) (x).rbegin(), (x).rend()
#define rsz resize
#define ins insert
#define ft front()
#define bk back()
#define pf push_front
#define pb push_back
#define eb emplace_back
#define lb lower_bound
#define ub upper_bound
#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define F0R(i,a) FOR(i,0,a)
#define ROF(i,a,b) for (int i = (b)-1; i >= (a); --i)
#define R0F(i,a) ROF(i,0,a)
#define trav(a,x) for (auto& a: x)
const int MOD = 1e9+7; // 998244353;
const int MX = 2e5+5;
const ll INF = 1e18;
const ld PI = acos((ld)-1);
const int xd[4] = {1,0,-1,0}, yd[4] = {0,1,0,-1};
template<class T> bool ckmin(T& a, const T& b) {
return b < a ? a = b, 1 : 0; }
template<class T> bool ckmax(T& a, const T& b) {
return a < b ? a = b, 1 : 0; }
int pct(int x) { return __builtin_popcount(x); }
int bit(int x) { return 31-__builtin_clz(x); } // floor(log2(x))
int cdiv(int a, int b) { return a/b+!(a<0||a%b == 0); } // division of a by b rounded up, assumes b > 0
// INPUT
template<class A> void re(complex<A>& c);
template<class A, class B> void re(pair<A,B>& p);
template<class A> void re(vector<A>& v);
template<class A, size_t SZ> void re(array<A,SZ>& a);
template<class T> void re(T& x) { cin >> x; }
void re(db& d) { str t; re(t); d = stod(t); }
void re(ld& d) { str t; re(t); d = stold(t); }
template<class H, class... T> void re(H& h, T&... t) { re(h); re(t...); }
template<class A> void re(complex<A>& c) { A a,b; re(a,b); c = {a,b}; }
template<class A, class B> void re(pair<A,B>& p) { re(p.f,p.s); }
template<class A> void re(vector<A>& x) { trav(a,x) re(a); }
template<class A, size_t SZ> void re(array<A,SZ>& x) { trav(a,x) re(a); }
// TO_STRING
#define ts to_string
template<class A, class B> str ts(pair<A,B> p);
template<class A> str ts(complex<A> c) { return ts(mp(c.real(),c.imag())); }
str ts(bool b) { return b ? "true" : "false"; }
str ts(char c) { str s = ""; s += c; return s; }
str ts(str s) { return s; }
str ts(const char* s) { return (str)s; }
str ts(vector<bool> v) {
bool fst = 1; str res = "{";
F0R(i,sz(v)) {
if (!fst) res += ", ";
fst = 0; res += ts(v[i]);
}
res += "}"; return res;
}
template<size_t SZ> str ts(bitset<SZ> b) {
str res = ""; F0R(i,SZ) res += char('0'+b[i]);
return res; }
template<class T> str ts(T v) {
bool fst = 1; str res = "{";
for (const auto& x: v) {
if (!fst) res += ", ";
fst = 0; res += ts(x);
}
res += "}"; return res;
}
template<class A, class B> str ts(pair<A,B> p) {
return "("+ts(p.f)+", "+ts(p.s)+")"; }
// OUTPUT
template<class A> void pr(A x) { cout << ts(x); }
template<class H, class... T> void pr(const H& h, const T&... t) {
pr(h); pr(t...); }
void ps() { pr("\n"); } // print w/ spaces
template<class H, class... T> void ps(const H& h, const T&... t) {
pr(h); if (sizeof...(t)) pr(" "); ps(t...); }
// DEBUG
void DBG() { cerr << "]" << endl; }
template<class H, class... T> void DBG(H h, T... t) {
cerr << to_string(h); if (sizeof...(t)) cerr << ", ";
DBG(t...); }
#ifdef LOCAL // compile with -DLOCAL
#define dbg(...) cerr << "[" << #__VA_ARGS__ << "]: [", DBG(__VA_ARGS__)
#else
#define dbg(...) 42
#endif
// FILE I/O
void setIn(string s) { freopen(s.c_str(),"r",stdin); }
void setOut(string s) { freopen(s.c_str(),"w",stdout); }
void unsyncIO() { ios_base::sync_with_stdio(0); cin.tie(0); }
void setIO(string s = "") {
unsyncIO();
// cin.exceptions(cin.failbit);
// throws exception when do smth illegal
// ex. try to read letter into int
if (sz(s)) { setIn(s+".in"), setOut(s+".out"); } // for USACO
}
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count());
/**
* Description: LineContainer assuming both slopes and queries monotonic.
* Time: O(1)
* Source: Own
* Verification: http://acm.hdu.edu.cn/diy/contest_showproblem.php?cid=36005&pid=1009
*/
/**
* Description: LineContainer; add lines of the form $kx+m$,
* compute greatest $y$-coordinate for any $x$.
* Time: O(\log N)
* Source: KACTL
* https://github.com/kth-competitive-programming/kactl/commit/165807e28402c9be906f6e6a09452431787bb70d?diff=unified
* Verification:
* CSA Squared Ends not working :(
* https://codeforces.com/contest/1083/problem/E
* https://atcoder.jp/contests/arc066/tasks/arc066_d
*/
bool Q;
struct Line {
mutable ll k, m, p; // slope, y-intercept, last optimal x
ll eval (ll x) { return k*x+m; }
bool operator<(const Line& o) const { return Q?p<o.p:k<o.k; }
};
// for doubles, use inf = 1/.0, divi(a,b) = a/b
const ll inf = LLONG_MAX;
// floored div
ll divi(ll a, ll b) { return a/b-((a^b) < 0 && a%b); }
// last x such that first line is better
ll bet(const Line& x, const Line& y) {
if (x.k == y.k) return x.m >= y.m ? inf : -inf;
return divi(y.m-x.m,x.k-y.k); }
struct LC : multiset<Line> {
// updates x->p, determines if y is unneeded
bool isect(iterator x, iterator y) {
if (y == end()) { x->p = inf; return 0; }
x->p = bet(*x,*y); return x->p >= y->p; }
void add(ll k, ll m) {
auto z = insert({k,m,0}), y = z++, x = y;
while (isect(y, z)) z = erase(z);
if (x != begin() && isect(--x, y)) isect(x, y = erase(y));
while ((y = x) != begin() && (--x)->p >= y->p)
isect(x, erase(y));
}
ll query(ll x) {
assert(!empty());
Q = 1; auto l = *lb({0,0,x}); Q = 0;
return l.k*x+l.m;
}
};
struct LCdeque : deque<Line> {
void addBack(Line L) { // assume nonempty
while (1) {
auto a = bk; pop_back(); a.p = bet(a,L);
if (size() && bk.p >= a.p) continue;
pb(a); break;
}
L.p = inf; pb(L);
}
void addFront(Line L) {
while (1) {
if (!size()) { L.p = inf; break; }
if ((L.p = bet(L,ft)) >= ft.p) pop_front();
else break;
}
push_front(L);
}
void add(ll k, ll m) { // line goes to one end of deque
k = -k; //neg
m = -m; //neg
if (!size() || k <= ft.k) addFront({k,m,0});
else assert(k >= bk.k), addBack({k,m,0});
}
int ord = 0; // 1 = increasing, -1 = decreasing
pair<ll, int> query(ll x) {
assert(ord);
if(size() == 0) return mp(INF, -1);
if (ord == 1) {
while (ft.p < x) pop_front();
return mp(-ft.eval(x), -ft.k); //neg
} else {
while(size()>1&&prev(prev(end()))->p>=x)pop_back();
return mp(-bk.eval(x), -ft.k); //neg
}
}
};
ll a[100005];
pair<ll, int> dp[100005];
int stor[100005][205];
pair<ll, int> ndp[100005];
map<ll, int> m;
int main() {
setIO();
int n, k;
cin >> n >> k;
for(int i = 1; i <= n; i++){
cin >> a[i];
}
for(int i = 1; i <= n; i++){
a[i]+=a[i-1];
//ps(i, a[i]);
}
for(int i = 1; i <= n; i++){
m[a[i]] = i;
}
for(int i = 0; i <= n; i++){
dp[i].f = ndp[i].f = INF; //overflow with line?
}
dp[0].f = 0;
for(int i = 1; i <= k+1; i++){
LCdeque lc;
lc.ord = 1;
if(dp[0].f != INF) lc.add(-2*a[0], dp[0].f+a[0]*a[0]);
for(int j = 1; j <= n; j++){
if(a[j] != INF){
pair<ll, int> res = lc.query(a[j]);
res.f+=a[j]*a[j];
ckmin(ndp[j], res);
if(dp[j].f != INF) lc.add(-2*a[j], dp[j].f+a[j]*a[j]);
}
}
for(int j = 0; j <= n; j++){
stor[j][i] = (ndp[j].s)/(-2);
}
for(int j = 0; j <= n; j++){
dp[j] = ndp[j];
ndp[j] = mp(INF, 0);
}
}
ll ans = (a[n]*a[n]-dp[n].f)/2;
ps(ans);
vi sol;
sol.pb(n);
for(int i = k+1; i >= 2; i--){
sol.pb((m[stor[sol.bk][i]]));
}
//ps(sol);
for(int i = 0; i < sz(sol); i++){
if(sol[i] <= sol[i+1]){
sol[i+1] = sol[i]-1;
}
}
reverse(all(sol));
for(int i = 0; i < sz(sol)-1; i++){
cout << sol[i] << " ";
}
// you should actually read the stuff at the bottom
}
/* stuff you should look for
* int overflow, array bounds
* special cases (n=1?)
* do smth instead of nothing and stay organized
* WRITE STUFF DOWN
*/
Compilation message
sequence.cpp: In function 'void setIn(std::__cxx11::string)':
sequence.cpp:123:31: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
void setIn(string s) { freopen(s.c_str(),"r",stdin); }
~~~~~~~^~~~~~~~~~~~~~~~~~~~~
sequence.cpp: In function 'void setOut(std::__cxx11::string)':
sequence.cpp:124:32: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
void setOut(string s) { freopen(s.c_str(),"w",stdout); }
~~~~~~~^~~~~~~~~~~~~~~~~~~~~~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
5 ms |
384 KB |
contestant found the optimal answer: 108 == 108 |
| 2 |
Correct |
4 ms |
384 KB |
contestant found the optimal answer: 999 == 999 |
| 3 |
Correct |
4 ms |
384 KB |
contestant found the optimal answer: 0 == 0 |
| 4 |
Correct |
4 ms |
384 KB |
contestant found the optimal answer: 1542524 == 1542524 |
| 5 |
Correct |
6 ms |
384 KB |
contestant found the optimal answer: 4500000000 == 4500000000 |
| 6 |
Correct |
5 ms |
384 KB |
contestant found the optimal answer: 1 == 1 |
| 7 |
Correct |
4 ms |
384 KB |
contestant found the optimal answer: 1 == 1 |
| 8 |
Correct |
4 ms |
384 KB |
contestant found the optimal answer: 1 == 1 |
| 9 |
Correct |
4 ms |
384 KB |
contestant found the optimal answer: 100400096 == 100400096 |
| 10 |
Correct |
4 ms |
384 KB |
contestant found the optimal answer: 900320000 == 900320000 |
| 11 |
Correct |
5 ms |
384 KB |
contestant found the optimal answer: 3698080248 == 3698080248 |
| 12 |
Correct |
5 ms |
384 KB |
contestant found the optimal answer: 3200320000 == 3200320000 |
| 13 |
Correct |
5 ms |
384 KB |
contestant found the optimal answer: 140072 == 140072 |
| 14 |
Correct |
4 ms |
384 KB |
contestant found the optimal answer: 376041456 == 376041456 |
| 15 |
Correct |
5 ms |
384 KB |
contestant found the optimal answer: 805 == 805 |
| 16 |
Correct |
4 ms |
384 KB |
contestant found the optimal answer: 900189994 == 900189994 |
| 17 |
Correct |
5 ms |
384 KB |
contestant found the optimal answer: 999919994 == 999919994 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
4 ms |
384 KB |
contestant found the optimal answer: 1093956 == 1093956 |
| 2 |
Correct |
5 ms |
384 KB |
contestant found the optimal answer: 302460000 == 302460000 |
| 3 |
Correct |
5 ms |
384 KB |
contestant found the optimal answer: 122453454361 == 122453454361 |
| 4 |
Correct |
5 ms |
384 KB |
contestant found the optimal answer: 93663683509 == 93663683509 |
| 5 |
Correct |
5 ms |
384 KB |
contestant found the optimal answer: 1005304678 == 1005304678 |
| 6 |
Correct |
5 ms |
384 KB |
contestant found the optimal answer: 933702 == 933702 |
| 7 |
Correct |
5 ms |
384 KB |
contestant found the optimal answer: 25082842857 == 25082842857 |
| 8 |
Correct |
5 ms |
384 KB |
contestant found the optimal answer: 687136 == 687136 |
| 9 |
Correct |
5 ms |
384 KB |
contestant found the optimal answer: 27295930079 == 27295930079 |
| 10 |
Correct |
5 ms |
384 KB |
contestant found the optimal answer: 29000419931 == 29000419931 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
5 ms |
512 KB |
contestant found the optimal answer: 610590000 == 610590000 |
| 2 |
Correct |
5 ms |
512 KB |
contestant found the optimal answer: 311760000 == 311760000 |
| 3 |
Correct |
5 ms |
512 KB |
contestant found the optimal answer: 1989216017013 == 1989216017013 |
| 4 |
Correct |
5 ms |
640 KB |
contestant found the optimal answer: 1499437552673 == 1499437552673 |
| 5 |
Correct |
6 ms |
512 KB |
contestant found the optimal answer: 1019625819 == 1019625819 |
| 6 |
Correct |
6 ms |
512 KB |
contestant found the optimal answer: 107630884 == 107630884 |
| 7 |
Correct |
6 ms |
512 KB |
contestant found the optimal answer: 475357671774 == 475357671774 |
| 8 |
Correct |
5 ms |
512 KB |
contestant found the optimal answer: 193556962 == 193556962 |
| 9 |
Correct |
5 ms |
512 KB |
contestant found the optimal answer: 482389919803 == 482389919803 |
| 10 |
Correct |
5 ms |
512 KB |
contestant found the optimal answer: 490686959791 == 490686959791 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
5 ms |
1280 KB |
contestant found the optimal answer: 21503404 == 21503404 |
| 2 |
Correct |
5 ms |
1280 KB |
contestant found the optimal answer: 140412195 == 140412195 |
| 3 |
Correct |
11 ms |
1280 KB |
contestant found the optimal answer: 49729674225461 == 49729674225461 |
| 4 |
Correct |
5 ms |
1280 KB |
contestant found the optimal answer: 37485571387523 == 37485571387523 |
| 5 |
Correct |
14 ms |
1280 KB |
contestant found the optimal answer: 679388326 == 679388326 |
| 6 |
Correct |
12 ms |
1280 KB |
contestant found the optimal answer: 4699030287 == 4699030287 |
| 7 |
Correct |
12 ms |
1280 KB |
contestant found the optimal answer: 12418819758185 == 12418819758185 |
| 8 |
Correct |
12 ms |
1280 KB |
contestant found the optimal answer: 31093317350 == 31093317350 |
| 9 |
Correct |
7 ms |
1280 KB |
contestant found the optimal answer: 12194625429236 == 12194625429236 |
| 10 |
Correct |
8 ms |
1280 KB |
contestant found the optimal answer: 12345131038664 == 12345131038664 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
13 ms |
9344 KB |
contestant found the optimal answer: 1818678304 == 1818678304 |
| 2 |
Correct |
11 ms |
9472 KB |
contestant found the optimal answer: 1326260195 == 1326260195 |
| 3 |
Correct |
82 ms |
9600 KB |
contestant found the optimal answer: 4973126687469639 == 4973126687469639 |
| 4 |
Correct |
13 ms |
9472 KB |
contestant found the optimal answer: 3748491676694116 == 3748491676694116 |
| 5 |
Correct |
58 ms |
9472 KB |
contestant found the optimal answer: 1085432199 == 1085432199 |
| 6 |
Correct |
72 ms |
9344 KB |
contestant found the optimal answer: 514790755404 == 514790755404 |
| 7 |
Correct |
68 ms |
9472 KB |
contestant found the optimal answer: 1256105310476641 == 1256105310476641 |
| 8 |
Correct |
56 ms |
9472 KB |
contestant found the optimal answer: 3099592898816 == 3099592898816 |
| 9 |
Correct |
59 ms |
9472 KB |
contestant found the optimal answer: 1241131419367412 == 1241131419367412 |
| 10 |
Correct |
73 ms |
9472 KB |
contestant found the optimal answer: 1243084101967798 == 1243084101967798 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
84 ms |
90488 KB |
contestant found the optimal answer: 19795776960 == 19795776960 |
| 2 |
Correct |
82 ms |
90668 KB |
contestant found the optimal answer: 19874432173 == 19874432173 |
| 3 |
Correct |
832 ms |
92024 KB |
contestant found the optimal answer: 497313449256899208 == 497313449256899208 |
| 4 |
Correct |
86 ms |
92536 KB |
contestant found the optimal answer: 374850090734572421 == 374850090734572421 |
| 5 |
Correct |
973 ms |
91000 KB |
contestant found the optimal answer: 36183271951 == 36183271951 |
| 6 |
Correct |
720 ms |
90720 KB |
contestant found the optimal answer: 51629847150471 == 51629847150471 |
| 7 |
Correct |
689 ms |
92408 KB |
contestant found the optimal answer: 124074747024496432 == 124074747024496432 |
| 8 |
Correct |
621 ms |
92284 KB |
contestant found the optimal answer: 309959349080800 == 309959349080800 |
| 9 |
Correct |
643 ms |
91512 KB |
contestant found the optimal answer: 124113525649823701 == 124113525649823701 |
| 10 |
Correct |
795 ms |
91640 KB |
contestant found the optimal answer: 124309619349406845 == 124309619349406845 |
