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Submission #23336

# Submission time Handle Problem Language Result Execution time Memory
23336 2017-05-06T10:48:04 Z Nurlykhan Split the sequence (APIO14_sequence) C++14
100 / 100
 1316 ms 83984 KB 
#include <bits/stdc++.h>
 
#define pii pair<int, int>
#define f first
#define s second
#define pb push_back
#define mp make_pair
#define ll long long 
#define ld long double
#define sz(v) int(v.size())
#define all(v) v.begin(), v.end()
 
using namespace std;
 
const int N = (int) 1e5 + 7;
const int M = (int) 2e6 + 7;
const int K = 202;
const ll LINF = (ll) 1e16;
const int INF = (int) 1e9 + 7;
const double EPS = (double) 1e-9;
ll dp[N][2], a[N];
int p[N][K];
int n, k;
 
ll sum(int l, int r) {
    if (l == 0) {
        return a[r];
    }
    return a[r] - a[l - 1];
}
 
ld inter(int i, int x, int y) {
    if (a[y] == a[x]) return INF;
    return (dp[y][i % 2] - dp[x][i % 2]) * 1.0 / (a[y] - a[x]);
}
 
int st[N];
int l, r;
 
ll f(int i, int j, ll x) {
    return x *  1ll * a[i] + dp[i][j % 2];
}
 
int get(int j, int x) {
    int id = l;
    while (id + 1 <= r && f(st[id + 1], j, x) >= f(st[id], j, x)) id++;
    return st[id];
}

ll dp1[202][202];

void solve() {
    for (int i = 1; i <= n; i++) {
        dp1[i][1] = sum(1, i) * sum(i + 1, n);
    }
    for (int i = 2; i <= k; i++) {
        for (int j = i; j <= n; j++) {
            for (int t = 1; t < j; t++) {
                if (dp1[j][i] < dp1[t][i-1] + sum(j + 1, n) * sum(t + 1, j)) {
                    dp1[j][i] = dp1[t][i-1] + sum(j + 1, n) * sum(t + 1, j);
                    p[j][i] = t;
                }
            }
        }
    }
    int j = 1;
    for (int i = 1; i <= n; i++) {
        if (dp1[j][k] < dp1[i][k]) j = i;
    }
    cout << dp1[j][k] << endl;
    vector<int> ans;
    while (j > 0 && k > 0) {
        ans.pb(j);
        j = p[j][k];
        k--;
    }
    reverse(all(ans));
    for (auto it : ans) cout << it << " ";
    exit(0);
}
 
int main() {
    #define fn "balls"
    #ifdef witch
        freopen("input.txt", "r", stdin);
        freopen("output.txt", "w", stdout);
    #else
//        freopen(fn".in", "r", stdin);
//        freopen(fn".out", "w", stdout);
    #endif
    cin >> n >> k;
    for (int i = 1; i <= n; i++) {
        cin >> a[i];
        a[i] += a[i - 1];
    }
    if (n <= 200) {
        //assert(0);
        solve();
    }
    for (int i = 1; i <= n; i++) {
        dp[i][1] = sum(1, i) * sum(i + 1, n);
    }
    for (int i = 2; i <= k; i++) {
        l = 1, r = 0;
        for (int j = 1; j <= n; j++) {
            while (l + 1 <= r && inter(i - 1, st[r], j) - inter(i - 1, st[r - 1], st[r]) > -EPS) {
                --r;
            }
            while (l + 1 <= r && f(st[l], i - 1, -sum(j + 1, n)) <= f(st[l + 1], i - 1, -sum(j + 1, n))) {
                ++l;
            }
            /*
            y[t] = (a[j] - a[t]) * (a[n] - a[j]) + dp[t][i - 1]
            a[j]*a[n]-a[j]*a[j]-a[t]*a[n]+a[t]*a[j]
            
            a[t]*(-a[n]+a[j])+dp[t][i-1]+a[j]*(a[n]-a[j])
 
            k=a[j]-a[t]
            */
            dp[j][i % 2] = 0;
            //if (l <= r) {
                for (int it = max(1, l - 2); it <= min(l + 2, r); it++) {
                    int t = st[it];
                    if (dp[j][i % 2] < dp[t][1 - i % 2] + sum(j + 1, n) * sum(t + 1, j)) {
                        dp[j][i % 2] = dp[t][1 - i % 2] + sum(j + 1, n) * sum(t + 1, j);
                        p[j][i] = t;
                    }
                }
            //}
            st[++r] = j;
        }
    }
    int j = 1;
    for (int i = 1; i <= n; i++) {
        if (dp[j][k % 2] < dp[i][k % 2]) j = i;
    }
    cout << dp[j][k % 2] << endl;
    vector<int> ans;
    while (j > 0 && k > 0) {
        ans.pb(j);
        j = p[j][k];
        k--;
    }
    reverse(all(ans));
    for (auto it : ans) cout << it << " ";
    return 0;
}

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 83984 KB contestant found the optimal answer: 108 == 108
2 Correct 0 ms 83984 KB contestant found the optimal answer: 999 == 999
3 Correct 0 ms 83984 KB contestant found the optimal answer: 0 == 0
4 Correct 0 ms 83984 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 0 ms 83984 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 0 ms 83984 KB contestant found the optimal answer: 1 == 1
7 Correct 0 ms 83984 KB contestant found the optimal answer: 1 == 1
8 Correct 0 ms 83984 KB contestant found the optimal answer: 1 == 1
9 Correct 0 ms 83984 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 0 ms 83984 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 0 ms 83984 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 0 ms 83984 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 0 ms 83984 KB contestant found the optimal answer: 140072 == 140072
14 Correct 0 ms 83984 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 0 ms 83984 KB contestant found the optimal answer: 805 == 805
16 Correct 0 ms 83984 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 0 ms 83984 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 83984 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 0 ms 83984 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 0 ms 83984 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 0 ms 83984 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 0 ms 83984 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 0 ms 83984 KB contestant found the optimal answer: 933702 == 933702
7 Correct 0 ms 83984 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 0 ms 83984 KB contestant found the optimal answer: 687136 == 687136
9 Correct 0 ms 83984 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 0 ms 83984 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 83984 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 0 ms 83984 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 3 ms 83984 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 0 ms 83984 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 3 ms 83984 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 3 ms 83984 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 3 ms 83984 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 0 ms 83984 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 0 ms 83984 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 0 ms 83984 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 83984 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 0 ms 83984 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 6 ms 83984 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 0 ms 83984 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 6 ms 83984 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 6 ms 83984 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 6 ms 83984 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 3 ms 83984 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 0 ms 83984 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 3 ms 83984 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 83984 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 3 ms 83984 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 76 ms 83984 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 3 ms 83984 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 56 ms 83984 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 63 ms 83984 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 66 ms 83984 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 49 ms 83984 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 56 ms 83984 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 73 ms 83984 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 36 ms 83984 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 36 ms 83984 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 1316 ms 83984 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 46 ms 83984 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 1303 ms 83984 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 1056 ms 83984 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 1176 ms 83984 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 823 ms 83984 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 983 ms 83984 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 1316 ms 83984 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845