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답안 #231454

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
231454 2020-05-13T16:24:54 Z AlexLuchianov 수열 (APIO14_sequence) C++14
100 / 100
 701 ms 86208 KB 
#include <iostream>
#include <fstream>
#include <vector>
#include <algorithm>
#include <cmath>
#include <cassert>

using namespace std;

using ll = long long;
using ld = long double;

#define MIN(a, b) (((a) < (b)) ? (a) : (b))
#define MAX(a, b) (((a) < (b)) ? (b) : (a))

int const nmax = 100000;
ll v[1 + nmax];
ll sum[1 + nmax], dp[1 + nmax], dp2[1 + nmax];

struct Line{
  ll a;
  ll b;
  int id;
  ll eval(ll x){
    return 1LL * x * a + b;
  }
};
vector<Line> st;
vector<ld> points;

ld intersect(Line x, Line y){
  return ((long double)(y.b - x.b)) / (x.a - y.a);
}

void addset(Line lin){
  while(0 < st.size()){
    if(st.back().a == lin.a) {
      if(st.back().b < lin.b) {
        st.pop_back();
        points.pop_back();
      } else
        return ;
    } else {
      if(intersect(st.back(), lin) <= points.back()){
        st.pop_back();
        points.pop_back();
      } else
        break;
    }
  }
  if(0 < st.size()){
    points.push_back(intersect(st.back(), lin));
    st.push_back(lin);
  } else {
    points.push_back(0);
    st.push_back(lin);
  }
}

void optimum(int x, int &ptr){
  while(ptr + 1 < points.size() && points[ptr + 1] <= x)
    ptr++;
}

int last[5 + 200][1 + nmax];

void process(int n, int era){
  st.clear();
  points.clear();
  int ptr = 0;
  for(int i = era;i <= n; i++){
    addset({sum[i - 1], dp[i - 1] - sum[i - 1] * sum[i - 1] , i - 1});
    optimum(sum[i], ptr);
    dp2[i] = st[ptr].eval(sum[i]);
    last[era][i] = st[ptr].id;
  }
  for(int i = 1;i <= n; i++)
    dp[i] = dp2[i];
}

void print(int era, int x){
  if(1 < era)
    print(era - 1, last[era][x]);
  cout << x << " ";
}

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

int main()
{
  ios::sync_with_stdio(0);
  cin.tie(0);

  int n, k;
  cin >> n >> k;
  for(int i = 1;i <= n; i++) {
    cin >> v[i];
    sum[i] = sum[i - 1] + v[i];
  }
  for(int i = 1;i <= n; i++)
    dp[i] = 0;
  for(int i = 2; i <= k + 1; i++)
    process(n, i);
  cout << dp[n] << '\n';
  print(k, last[k + 1][n]);
  return 0;
}

Compilation message

sequence.cpp: In function 'void optimum(int, int&)':
sequence.cpp:61:17: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   while(ptr + 1 < points.size() && points[ptr + 1] <= x)
         ~~~~~~~~^~~~~~~~~~~~~~~

Subtask #1
11.0 / 11.0

# 결과 실행 시간 메모리 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 5 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 5 ms 384 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 4 ms 384 KB contestant found the optimal answer: 1 == 1
7 Correct 5 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 5 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 4 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 5 ms 512 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 4 ms 384 KB contestant found the optimal answer: 805 == 805
16 Correct 5 ms 384 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 5 ms 384 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# 결과 실행 시간 메모리 Grader output
1 Correct 5 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 640 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 5 ms 384 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 4 ms 384 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 4 ms 384 KB contestant found the optimal answer: 933702 == 933702
7 Correct 5 ms 512 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 4 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 512 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# 결과 실행 시간 메모리 Grader output
1 Correct 5 ms 384 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 4 ms 384 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 6 ms 1408 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 5 ms 384 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 5 ms 1152 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 5 ms 1280 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 6 ms 1408 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 5 ms 640 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 640 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# 결과 실행 시간 메모리 Grader output
1 Correct 5 ms 512 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 5 ms 512 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 11 ms 2176 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 5 ms 512 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 12 ms 2176 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 11 ms 1920 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 12 ms 2176 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 11 ms 2176 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 7 ms 768 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 7 ms 1152 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# 결과 실행 시간 메모리 Grader output
1 Correct 7 ms 1408 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 6 ms 1408 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 65 ms 10012 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 7 ms 1508 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 48 ms 6520 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 51 ms 7416 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 59 ms 7832 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 44 ms 6680 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 48 ms 7320 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 59 ms 9116 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# 결과 실행 시간 메모리 Grader output
1 Correct 24 ms 8208 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 25 ms 8208 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 573 ms 86208 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 26 ms 8972 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 701 ms 85368 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 459 ms 61780 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 552 ms 66640 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 424 ms 55548 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 414 ms 62200 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 541 ms 78332 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845