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Submission #49411

# Submission time Handle Problem Language Result Execution time Memory
49411 2018-05-28T13:28:47 Z Benq Split the sequence (APIO14_sequence) C++14
100 / 100
 923 ms 83196 KB 
#include <bits/stdc++.h>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>
 
using namespace std;
using namespace __gnu_pbds;
 
typedef long long ll;
typedef long double ld;
typedef complex<ld> cd;
 
typedef pair<int, ll> pi;
typedef pair<ll,ll> pl;
typedef pair<ld,ld> pd;
 
typedef vector<int> vi;
typedef vector<ld> vd;
typedef vector<ll> vl;
typedef vector<pi> vpi;
typedef vector<pl> vpl;
typedef vector<cd> vcd;
 
template <class T> using Tree = tree<T, null_type, less<T>, rb_tree_tag,tree_order_statistics_node_update>;
 
#define FOR(i, a, b) for (int i=a; i<(b); i++)
#define F0R(i, a) for (int i=0; i<(a); i++)
#define FORd(i,a,b) for (int i = (b)-1; i >= a; i--)
#define F0Rd(i,a) for (int i = (a)-1; i >= 0; i--)
 
#define sz(x) (int)(x).size()
#define mp make_pair
#define pb push_back
#define f first
#define s second
#define lb lower_bound
#define ub upper_bound
#define all(x) x.begin(), x.end()
 
const int MOD = 1000000007;
const ll INF = 1e18;
const int MX = 100001;
 
ll ans = 0;
int n,k;
ll num[MX], sum[MX];
array<ll,MX> dp, dp2;
int pre[202][MX];
 
ll eval(int y, int x) {
    return (sum[x]-sum[y])*(sum[x]-sum[y])+dp2[y];
}
 
ll bet(int x, int y) { 
    if (sum[y] == sum[x]) return 1e18;
    return (sum[y]*sum[y]+dp2[y]-sum[x]*sum[x]-dp2[x])/(2*sum[y]-2*sum[x]);
}

struct {
	int d[2*MX], opt[2*MX];
	int l = 0, r = -1;
	void clear() { l = 0, r = -1; }
	int front() { return d[l]; }
	int size() { return r-l+1; }
	int back() { return d[r]; }
	void pop_back() { r --; }
	void push_back(int x, int t) { 
		d[++r] = x; 
		if (size() > 1) opt[r-1] = t;
	}
	void pop_front() { l ++; }
	void push_front(int x) { d[--l] = x; }
	bool deleteFront(int x) {
		if (size() <= 1) return 0;
		return eval(d[l],x) >= eval(d[l+1],x);
	}
	bool deleteBack(int x) {
		if (size() <= 1) {
			int t = -1;
			if (size() == 1) t = bet(d[r],x);
			push_back(x,t);
			return 0;
		}
		int t = bet(d[r],x);
		if (opt[r-1] >= t) return 1;
		push_back(x,t);
		return 0;
	}
} bes;
 
void ins(int x) {
	while (bes.deleteBack(x)) bes.pop_back();
	// bes.pb(x);
}
 
void compute(int ind, int x) {
	while (bes.deleteFront(x)) bes.pop_front();
	dp[x] = eval(bes.front(),x);
	pre[ind][x] = bes.front();
}

void solve(int ind) {
    swap(dp,dp2);
    bes.clear();
    FOR(j,ind,n+1) {
        ins(j-1);
        compute(ind,j);
        // cout << "HI " << ind << " " << j << " " << dp2[0] << " " << dp[j] << "\n";
    }
    // cout << "----\n";
}
int main() {
    ios_base::sync_with_stdio(0); cin.tie(0);
    cin >> n >> k; k++;
    FOR(i,1,n+1) {
        // num[i] = rand() % 10000; 
        cin >> num[i];
        sum[i] = num[i]+sum[i-1];
    }
    FOR(i,1,n+1) dp[i] = 1e18;
    FOR(i,1,k+1) solve(i);
    int x = n;
    vi v;
    FORd(i,1,k+1) {
        x = pre[i][x];
        if (i > 1) v.pb(x);
    }
    reverse(all(v));
    cout << (sum[n]*sum[n]-dp[n])/2 << "\n";
    for (int i: v) cout << i << " ";
}
 
// read the question correctly (is y a vowel? what are the exact constraints?)

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 1888 KB contestant found the optimal answer: 108 == 108
2 Correct 4 ms 2020 KB contestant found the optimal answer: 999 == 999
3 Correct 5 ms 2100 KB contestant found the optimal answer: 0 == 0
4 Correct 5 ms 2100 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 5 ms 2152 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 4 ms 2152 KB contestant found the optimal answer: 1 == 1
7 Correct 4 ms 2152 KB contestant found the optimal answer: 1 == 1
8 Correct 4 ms 2152 KB contestant found the optimal answer: 1 == 1
9 Correct 4 ms 2152 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 5 ms 2152 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 5 ms 2152 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 4 ms 2164 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 4 ms 2256 KB contestant found the optimal answer: 140072 == 140072
14 Correct 5 ms 2256 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 5 ms 2256 KB contestant found the optimal answer: 805 == 805
16 Correct 5 ms 2256 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 4 ms 2256 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 2256 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 5 ms 2256 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 12 ms 2408 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 5 ms 2408 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 6 ms 2408 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 5 ms 2408 KB contestant found the optimal answer: 933702 == 933702
7 Correct 9 ms 2408 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 6 ms 2408 KB contestant found the optimal answer: 687136 == 687136
9 Correct 5 ms 2408 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 7 ms 2412 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 2412 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 4 ms 2412 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 31 ms 3196 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 4 ms 3196 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 22 ms 3196 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 26 ms 3196 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 28 ms 3200 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 9 ms 3200 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 7 ms 3200 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 11 ms 3200 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 3200 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 4 ms 3200 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 34 ms 3840 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 6 ms 3840 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 40 ms 3856 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 31 ms 3856 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 37 ms 3856 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 38 ms 3868 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 13 ms 3868 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 19 ms 3868 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 8 ms 3868 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 8 ms 3868 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 96 ms 11132 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 8 ms 11132 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 75 ms 11132 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 87 ms 11132 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 94 ms 11132 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 71 ms 11132 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 78 ms 11132 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 101 ms 11132 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 32 ms 11132 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 29 ms 11132 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 740 ms 83196 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 26 ms 83196 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 923 ms 83196 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 671 ms 83196 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 652 ms 83196 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 508 ms 83196 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 512 ms 83196 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 665 ms 83196 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845