#include <bits/stdc++.h>
#define ld long double
using namespace std;
struct Line{
long long m, c;
int idx;
long long getY(long long x){
return m * x + c;
}
ld getX(Line o){
return (ld) (o.c - c) / (ld) (m - o.m);
}
};
Line ch[100010];
int sz = 0, opt = 0;
int n, k;
int a[100010];
long long pref[100010];
pair<long long, int> dp[100010];
int bt[210][100010];
bool cmp(Line a, Line b, Line c){
return a.getX(b) > a.getX(c);
}
void add(Line l){
if(sz > 0){
if(ch[sz - 1].m == l.m && ch[sz - 1].c > l.c) return;
if(ch[sz - 1].m == l.m) sz--;
}
while(sz >= 2 && !cmp(l, ch[sz - 1], ch[sz - 2])) sz--;
ch[sz++] = l;
}
pair<long long, int> findOpt(long long x){
if(opt >= sz) opt = sz - 1;
while(opt + 1 < sz && ch[opt].getY(x) <= ch[opt + 1].getY(x)) opt++;
return {ch[opt].getY(x), ch[opt].idx};
}
void btrack(int i, int j){
if(i == 0 || j == 0) return;
btrack(bt[j][i], j - 1);
printf("%d ", i);
}
int main(){
scanf("%d%d", &n, &k);
for(int i = 1; i <= n; i++){
scanf("%d", &a[i]);
pref[i] = pref[i - 1] + a[i];
}
//Base Case, k = 1
for(int i = 1; i < n; i++){
dp[i].first = pref[i] * (pref[n] - pref[i]);
dp[i].second = 0;
//cout << i << " " << 1 << " " << dp[i][1].first << endl;
}
// DP formula:
// dp[i][j] = max(dp[t][j - 1] + cost(t + 1, i) * cost(i + 1, n))
// for t < i, where cost(i, j) = pref[j] - pref[i - 1]
// Hence, simplifying the formula gives:
// dp[i][j] = max(dp[t][j - 1] - pref[t] * pref[n] + pref[t] * pref[i]) + pref[i] * (pref[n] - pref[i])
// Line equation:
// m = pref[t]
// x = pref[i]
// c = dp[t][j - 1] - pref[t] * pref[n]
// Note that dp[i][j] is defined for j <= i
for(int j = 2; j <= k; j++){
sz = opt = 0;
add(Line({pref[j - 1], dp[j - 1].first - pref[j - 1] * pref[n], j - 1}));
for(int i = j; i < n; i++){
long long temp = dp[i].first;
dp[i] = findOpt(pref[i]);
dp[i].first += pref[i] * (pref[n] - pref[i]);
bt[j][i] = dp[i].second;
add(Line({pref[i], temp - pref[i] * pref[n], i}));
//cout << i << " " << j << " " << dp[i][j].first << " bt: " << dp[i][j].second <<endl;
}
}
long long mx = -1, id = -1;
for(int i = k; i < n; i++){
if(mx < dp[i].first){
mx = dp[i].first;
id = i;
}
}
printf("%lld\n", mx);
btrack(id, k);
printf("\n");
return 0;
}
Compilation message
sequence.cpp: In function 'int main()':
sequence.cpp:57:7: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
scanf("%d%d", &n, &k);
~~~~~^~~~~~~~~~~~~~~~
sequence.cpp:60:8: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
scanf("%d", &a[i]);
~~~~~^~~~~~~~~~~~~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
2 ms |
384 KB |
contestant found the optimal answer: 108 == 108 |
| 2 |
Correct |
2 ms |
384 KB |
contestant found the optimal answer: 999 == 999 |
| 3 |
Correct |
2 ms |
384 KB |
contestant found the optimal answer: 0 == 0 |
| 4 |
Correct |
2 ms |
384 KB |
contestant found the optimal answer: 1542524 == 1542524 |
| 5 |
Correct |
2 ms |
384 KB |
contestant found the optimal answer: 4500000000 == 4500000000 |
| 6 |
Correct |
3 ms |
384 KB |
contestant found the optimal answer: 1 == 1 |
| 7 |
Correct |
2 ms |
384 KB |
contestant found the optimal answer: 1 == 1 |
| 8 |
Correct |
3 ms |
384 KB |
contestant found the optimal answer: 1 == 1 |
| 9 |
Correct |
3 ms |
384 KB |
contestant found the optimal answer: 100400096 == 100400096 |
| 10 |
Correct |
2 ms |
384 KB |
contestant found the optimal answer: 900320000 == 900320000 |
| 11 |
Correct |
2 ms |
384 KB |
contestant found the optimal answer: 3698080248 == 3698080248 |
| 12 |
Correct |
3 ms |
512 KB |
contestant found the optimal answer: 3200320000 == 3200320000 |
| 13 |
Correct |
2 ms |
384 KB |
contestant found the optimal answer: 140072 == 140072 |
| 14 |
Correct |
2 ms |
384 KB |
contestant found the optimal answer: 376041456 == 376041456 |
| 15 |
Correct |
3 ms |
384 KB |
contestant found the optimal answer: 805 == 805 |
| 16 |
Correct |
2 ms |
384 KB |
contestant found the optimal answer: 900189994 == 900189994 |
| 17 |
Correct |
2 ms |
384 KB |
contestant found the optimal answer: 999919994 == 999919994 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
2 ms |
384 KB |
contestant found the optimal answer: 1093956 == 1093956 |
| 2 |
Correct |
3 ms |
384 KB |
contestant found the optimal answer: 302460000 == 302460000 |
| 3 |
Correct |
2 ms |
640 KB |
contestant found the optimal answer: 122453454361 == 122453454361 |
| 4 |
Correct |
2 ms |
384 KB |
contestant found the optimal answer: 93663683509 == 93663683509 |
| 5 |
Correct |
3 ms |
384 KB |
contestant found the optimal answer: 1005304678 == 1005304678 |
| 6 |
Correct |
2 ms |
384 KB |
contestant found the optimal answer: 933702 == 933702 |
| 7 |
Correct |
2 ms |
512 KB |
contestant found the optimal answer: 25082842857 == 25082842857 |
| 8 |
Correct |
2 ms |
384 KB |
contestant found the optimal answer: 687136 == 687136 |
| 9 |
Correct |
2 ms |
356 KB |
contestant found the optimal answer: 27295930079 == 27295930079 |
| 10 |
Correct |
3 ms |
384 KB |
contestant found the optimal answer: 29000419931 == 29000419931 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
3 ms |
384 KB |
contestant found the optimal answer: 610590000 == 610590000 |
| 2 |
Correct |
3 ms |
384 KB |
contestant found the optimal answer: 311760000 == 311760000 |
| 3 |
Correct |
3 ms |
1280 KB |
contestant found the optimal answer: 1989216017013 == 1989216017013 |
| 4 |
Correct |
3 ms |
384 KB |
contestant found the optimal answer: 1499437552673 == 1499437552673 |
| 5 |
Correct |
3 ms |
1024 KB |
contestant found the optimal answer: 1019625819 == 1019625819 |
| 6 |
Correct |
3 ms |
1280 KB |
contestant found the optimal answer: 107630884 == 107630884 |
| 7 |
Correct |
3 ms |
1280 KB |
contestant found the optimal answer: 475357671774 == 475357671774 |
| 8 |
Correct |
2 ms |
640 KB |
contestant found the optimal answer: 193556962 == 193556962 |
| 9 |
Correct |
2 ms |
512 KB |
contestant found the optimal answer: 482389919803 == 482389919803 |
| 10 |
Correct |
2 ms |
640 KB |
contestant found the optimal answer: 490686959791 == 490686959791 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
3 ms |
384 KB |
contestant found the optimal answer: 21503404 == 21503404 |
| 2 |
Correct |
3 ms |
384 KB |
contestant found the optimal answer: 140412195 == 140412195 |
| 3 |
Correct |
10 ms |
2176 KB |
contestant found the optimal answer: 49729674225461 == 49729674225461 |
| 4 |
Correct |
2 ms |
384 KB |
contestant found the optimal answer: 37485571387523 == 37485571387523 |
| 5 |
Correct |
7 ms |
2176 KB |
contestant found the optimal answer: 679388326 == 679388326 |
| 6 |
Correct |
7 ms |
1920 KB |
contestant found the optimal answer: 4699030287 == 4699030287 |
| 7 |
Correct |
9 ms |
2176 KB |
contestant found the optimal answer: 12418819758185 == 12418819758185 |
| 8 |
Correct |
9 ms |
2176 KB |
contestant found the optimal answer: 31093317350 == 31093317350 |
| 9 |
Correct |
4 ms |
768 KB |
contestant found the optimal answer: 12194625429236 == 12194625429236 |
| 10 |
Correct |
5 ms |
1024 KB |
contestant found the optimal answer: 12345131038664 == 12345131038664 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
3 ms |
896 KB |
contestant found the optimal answer: 1818678304 == 1818678304 |
| 2 |
Correct |
4 ms |
896 KB |
contestant found the optimal answer: 1326260195 == 1326260195 |
| 3 |
Correct |
61 ms |
9464 KB |
contestant found the optimal answer: 4973126687469639 == 4973126687469639 |
| 4 |
Correct |
4 ms |
896 KB |
contestant found the optimal answer: 3748491676694116 == 3748491676694116 |
| 5 |
Correct |
41 ms |
6008 KB |
contestant found the optimal answer: 1085432199 == 1085432199 |
| 6 |
Correct |
48 ms |
6904 KB |
contestant found the optimal answer: 514790755404 == 514790755404 |
| 7 |
Correct |
56 ms |
7288 KB |
contestant found the optimal answer: 1256105310476641 == 1256105310476641 |
| 8 |
Correct |
36 ms |
6052 KB |
contestant found the optimal answer: 3099592898816 == 3099592898816 |
| 9 |
Correct |
40 ms |
6816 KB |
contestant found the optimal answer: 1241131419367412 == 1241131419367412 |
| 10 |
Correct |
48 ms |
8568 KB |
contestant found the optimal answer: 1243084101967798 == 1243084101967798 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
16 ms |
5760 KB |
contestant found the optimal answer: 19795776960 == 19795776960 |
| 2 |
Correct |
21 ms |
5752 KB |
contestant found the optimal answer: 19874432173 == 19874432173 |
| 3 |
Correct |
497 ms |
83444 KB |
contestant found the optimal answer: 497313449256899208 == 497313449256899208 |
| 4 |
Correct |
25 ms |
6136 KB |
contestant found the optimal answer: 374850090734572421 == 374850090734572421 |
| 5 |
Correct |
642 ms |
82868 KB |
contestant found the optimal answer: 36183271951 == 36183271951 |
| 6 |
Correct |
486 ms |
59396 KB |
contestant found the optimal answer: 51629847150471 == 51629847150471 |
| 7 |
Correct |
516 ms |
63828 KB |
contestant found the optimal answer: 124074747024496432 == 124074747024496432 |
| 8 |
Correct |
375 ms |
52856 KB |
contestant found the optimal answer: 309959349080800 == 309959349080800 |
| 9 |
Correct |
382 ms |
59632 KB |
contestant found the optimal answer: 124113525649823701 == 124113525649823701 |
| 10 |
Correct |
530 ms |
75228 KB |
contestant found the optimal answer: 124309619349406845 == 124309619349406845 |
