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Submission #557405

# Submission time Handle Problem Language Result Execution time Memory
557405 2022-05-05T09:31:08 Z Ai7081 Split the sequence (APIO14_sequence) C++17
100 / 100
 498 ms 83824 KB 
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define pii pair<ll, ll>

const int N = 100005;
const int K = 205;

struct Line{
    ll m, c, idx;
    ll operator() (ll x) {return m*x + c;}
};

ll n, k, a, dp[2][N], sum[N];
int rev[K][N], ptr;
vector<Line> v;

bool check(Line x, Line y, Line z) {
    return (z.c-y.c)*(x.m-y.m) < (y.c-x.c)*(y.m-z.m);
}

void add(Line L) {
    while (v.size()>=2 && check(v[v.size()-2], v.back(), L)) v.pop_back();
    while (!v.empty() && v.back().m == L.m && v.back().c <= L.c) v.pop_back();
    v.push_back(L);
}

pii query(ll x) {
    ptr = min(ptr, (int)v.size()-1);
    while (ptr != v.size()-1 && v[ptr](x) <= v[ptr+1](x)) ptr++;
    return {v[ptr](x), v[ptr].idx};
}

int main() {
    scanf(" %lld %lld", &n, &k);
    k++;
    for (int i=1; i<=n; i++) scanf(" %lld", &a), sum[i] = sum[i-1] + a;
    for (int i=2; i<=k; i++) {
        ptr = 0;
        v.clear();
        for (int j=i; j<=n; j++) {
            add({sum[j-1], dp[(i-1)&1][j-1] - sum[j-1]*sum[j-1], j-1});
            pii res = query(sum[j]);
            dp[i&1][j] = res.first;
            rev[i][j] = res.second;
        }
    }
    printf("%lld\n", dp[k&1][n]);
    vector<ll> out;
    while (rev[k][n]) {
        out.push_back(rev[k][n]);
        n = rev[k][n];
        k--;
    }
    for (int i=out.size()-1; i>=0; i--) printf("%lld ", out[i]);
    return 0;
}

/*
7 3
4 1 3 4 0 2 3
*/

Compilation message

sequence.cpp: In function 'std::pair<long long int, long long int> query(long long int)':
sequence.cpp:30:16: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<Line>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   30 |     while (ptr != v.size()-1 && v[ptr](x) <= v[ptr+1](x)) ptr++;
      |            ~~~~^~~~~~~~~~~~~
sequence.cpp: In function 'int main()':
sequence.cpp:35:10: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
   35 |     scanf(" %lld %lld", &n, &k);
      |     ~~~~~^~~~~~~~~~~~~~~~~~~~~~
sequence.cpp:37:35: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
   37 |     for (int i=1; i<=n; i++) scanf(" %lld", &a), sum[i] = sum[i-1] + a;
      |                              ~~~~~^~~~~~~~~~~~~

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 340 KB contestant found the optimal answer: 108 == 108
2 Correct 0 ms 340 KB contestant found the optimal answer: 999 == 999
3 Correct 0 ms 212 KB contestant found the optimal answer: 0 == 0
4 Correct 1 ms 340 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 0 ms 340 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 1 ms 212 KB contestant found the optimal answer: 1 == 1
7 Correct 0 ms 212 KB contestant found the optimal answer: 1 == 1
8 Correct 0 ms 212 KB contestant found the optimal answer: 1 == 1
9 Correct 0 ms 340 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 0 ms 340 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 0 ms 340 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 1 ms 340 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 0 ms 340 KB contestant found the optimal answer: 140072 == 140072
14 Correct 0 ms 340 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 0 ms 340 KB contestant found the optimal answer: 805 == 805
16 Correct 1 ms 340 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 0 ms 340 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 340 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 0 ms 340 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 1 ms 468 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 1 ms 340 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 0 ms 340 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 0 ms 340 KB contestant found the optimal answer: 933702 == 933702
7 Correct 0 ms 340 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 0 ms 340 KB contestant found the optimal answer: 687136 == 687136
9 Correct 0 ms 340 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 0 ms 340 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 340 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 0 ms 340 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 2 ms 1364 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 0 ms 340 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 1 ms 980 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 1 ms 1236 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 1 ms 1364 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 1 ms 468 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 1 ms 468 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 1 ms 596 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 1 ms 340 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 4 ms 2004 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 1 ms 340 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 6 ms 2028 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 4 ms 1748 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 5 ms 2056 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 4 ms 2004 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 1 ms 724 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 3 ms 980 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 916 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 2 ms 916 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 59 ms 9584 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 2 ms 976 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 36 ms 6080 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 34 ms 6856 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 38 ms 7324 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 25 ms 6232 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 32 ms 7000 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 41 ms 8648 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 17 ms 5820 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 17 ms 5800 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 332 ms 83824 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 18 ms 6780 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 498 ms 83092 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 322 ms 59628 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 371 ms 64296 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 248 ms 53260 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 267 ms 60084 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 348 ms 75620 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845