oj.uz

Submission #88046

# Submission time Handle Problem Language Result Execution time Memory
88046 2018-12-03T14:43:25 Z vanbang9710 Split the sequence (APIO14_sequence) C++14
71 / 100
 2000 ms 86984 KB 
/*
dp+convex hull trick
only add lines to the end of the hull bc slopes increase bc pre[i] increases
answer for i is >= answer for i-1
*/
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define For(i, a, b) for(int i=a; i<b; i++)
#define ffi For(i, 0, N)
#define ffj For(j, 0, K+1)
#define ffa ffi ffj
#define s <<" "<<
#define c <<" : "<<
#define w cout
#define e "\n"
#define pb push_back
#define mp make_pair
#define a first
#define b second
//#define int ll
//500,000,000 operations
const int MAXN = 100000;
//Global Variables
int from[MAXN][201], N, K;
ll pre[MAXN], BIG=1000000000, dp[MAXN][2];
//deque<int> hull; ///(ind)
int hull[MAXN], l=1, r;
 
struct Line { ///Ax+B
    ll A, B, l, r, yb, yl;
    Line() {A=0; B=0;}
    Line(int j, int line) {
        A = pre[j];
        B = dp[j][line%2]-pre[j]*pre[j];
        yb = A*BIG+B;
        //w<< j s ":" s A s B<<e;
        //w<< dp[j][line%2]-pre[j]*pre[j] s B<<e;
    }
}val[MAXN];
 
void put(int ind, int line, ll X) {
    val[ind] = Line(ind, line);
    ll A = val[ind].A, B = val[ind].B;
    while (l != r+1) {
        int j = hull[r];
        if (val[j].yl <= A*val[j].l+B) r--;
        else break;
    }
    if (l != r+1) {
        int last = hull[r];
        if (val[last].yb < val[ind].yb) {
            /// split the range
            ll x = (val[last].B - B)/(A - val[last].A);
            r++; hull[r] = ind;
            val[last].r = x;
            val[ind].l = x+1;
            val[ind].yl = A*(x+1) + B;
            val[ind].r = BIG;
        }
    }
    while (l != r+1 && val[hull[l]].r < X) l++;
 
    if (l==r+1) {
        r++; hull[r] = ind;
        ///range: 0-BIG
        val[ind].l = 0;
        val[ind].yl = B;
        val[ind].r = BIG;
    }
}
 
main() {
    //ifstream cin("test.in");
    ios_base::sync_with_stdio(0); cin.tie(0);
	cin >> N >> K;
	cin >> pre[0];
	For (i, 1, N) {int a; cin >> a; pre[i] = a+pre[i-1];}
	For (j, 1, K+1) {
        l = 1; r = 0;
        put(j-1, j-1, pre[j]);
        For (i, j, N) {
            int k = hull[l];
            dp[i][j%2] = val[k].A*pre[i]+val[k].B;
            from[i][j] = k;
            if (i != N-1) put(i, j-1, pre[i+1]);
            //w<< l s r<<e;
            //w<< "dp["<< i+1 <<"]["<<j<<"]:" s dp[i][j%2]<<e;
        }
	}
	//ffj {ffi w<< from[i][j]+1<< " "; w<<e;}w<<e;
	//ffi w<< pre[i]<<e;
	w<< dp[N-1][K%2]<<e; int at = N-1; for (int j=K; j>=1; j--) {w<< from[at][j]+1<< " ";at = from[at][j];}w<<e;
}

Compilation message

sequence.cpp:73:6: warning: ISO C++ forbids declaration of 'main' with no type [-Wreturn-type]
 main() {
      ^

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 7 ms 5112 KB contestant found the optimal answer: 108 == 108
2 Correct 6 ms 5212 KB contestant found the optimal answer: 999 == 999
3 Correct 6 ms 5212 KB contestant found the optimal answer: 0 == 0
4 Correct 4 ms 5364 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 7 ms 5392 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 7 ms 5392 KB contestant found the optimal answer: 1 == 1
7 Correct 7 ms 5392 KB contestant found the optimal answer: 1 == 1
8 Correct 7 ms 5392 KB contestant found the optimal answer: 1 == 1
9 Correct 7 ms 5392 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 7 ms 5392 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 7 ms 5392 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 6 ms 5392 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 6 ms 5392 KB contestant found the optimal answer: 140072 == 140072
14 Correct 6 ms 5392 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 6 ms 5472 KB contestant found the optimal answer: 805 == 805
16 Correct 6 ms 5472 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 6 ms 5472 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 6 ms 5472 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 6 ms 5472 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 7 ms 5472 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 6 ms 5472 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 6 ms 5472 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 6 ms 5472 KB contestant found the optimal answer: 933702 == 933702
7 Correct 7 ms 5472 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 7 ms 5472 KB contestant found the optimal answer: 687136 == 687136
9 Correct 7 ms 5472 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 6 ms 5472 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 6 ms 5500 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 6 ms 5500 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 6 ms 5500 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 6 ms 5500 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 6 ms 5500 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 7 ms 5500 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 6 ms 5500 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 6 ms 5500 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 6 ms 5500 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 6 ms 5500 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 6 ms 6140 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 6 ms 6140 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 12 ms 6140 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 6 ms 6140 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 13 ms 6140 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 12 ms 6176 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 13 ms 6176 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 12 ms 6176 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 8 ms 6176 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 9 ms 6176 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 13 ms 13436 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 16 ms 13436 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 103 ms 13508 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 15 ms 13508 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 73 ms 13564 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 80 ms 13564 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 87 ms 13564 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 70 ms 13564 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 73 ms 13564 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 96 ms 13572 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 116 ms 86672 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 98 ms 86676 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Execution timed out 2100 ms 86984 KB Time limit exceeded
4 Halted 0 ms 0 KB -