#include<bits/stdc++.h>
using namespace std;
#define fi first
#define se second
#define pb push_back
#define ins insert
#define er erase
typedef pair<long long, long long> ii;
typedef pair<ii, int> iii;
typedef pair<ii, ii> iiii;
const int oo = 1e18 + 7, mod = 1e9 + 7;
/*
For educational purposes, I will implement the solution both in divide_and_conquer_DP style - O(N * K * log2(N)) (probably get 71 points) and convex hull trick style - O(N * K)
This code is divide_and_conquer DP
*/
const int N = 2e5 + 5, K = 205;
long long n, k, a[N], suff[N];
long long dp[N], lst_dp[N];
int opt[N];
int lst[N][K];
long long f(int i, int j){
return lst_dp[j] + (suff[j + 1] - suff[i + 1]) * suff[i + 1];
}
/*
Condition of D&Q DP: optimal position of x <= optimal position of (x + 1)
Suppose we are trying to calculate the value of opt[x] with l <= x <= r
We take the middle element mid = (l + r) >> 1 and calulate its opt value = y
=> opt[x] < y with l <= x < mid, and opt[x] > y with mid < x <= r
We can easily see that the complexity is O(n * log2(n))
I will say that this D&Q is nice
*/
void divide(int l, int r, int optl, int optr){
if(l > r) return;
//cout << l << " " << r << " " << optl << " " << optr << "\n";
if(optl == optr){
for(int i = l; i <= r; i++){
opt[i] = optl;
}
return;
}
int mid = (l + r) >> 1;
ii best = {-1, oo};
for(int i = optl; i <= min(optr, mid - 1); i++){
best = max(best, {f(mid, i), i});
//if(mid == 4) cout << mid << " " << f(mid, i) << "\n";
}
opt[mid] = best.se;
divide(l, mid - 1, optl, best.se);
divide(mid + 1, r, best.se, optr);
}
signed main(){
ios_base::sync_with_stdio(0);
cin >> n >> k;
for(int i = 1; i <= n; i++) cin >> a[i];
for(int i = n; i >= 1; i--) suff[i] = (suff[i + 1] + a[i]);
for(int i = 1; i <= k; i++){
for(int j = 1; j <= n; j++){
opt[j] = 0;
lst_dp[j] = dp[j];
}
divide(1, n, 0, n - 1);
for(int j = 1; j <= n; j++) lst[j][i] = opt[j];
for(int j = 1; j <= n; j++) dp[j] = f(j, opt[j]);
//for(int j = 1; j <= n; j++) cout << i << " " << j << " " << dp[j] << " " << opt[j] << "\n";
}
int ind = k;
for(int i = k + 1; i <= n; i++){
if(dp[i] > dp[ind]) ind = i;
}
cout << dp[ind] << "\n";
vector<int> pos;
pos.clear();
int tmp = k;
while(tmp){
pos.pb(ind);
ind = lst[ind][tmp];
tmp--;
}
for(int i = pos.size() - 1; i >= 0; i--) cout << pos[i] << " ";
}
Compilation message
sequence.cpp:14:21: warning: overflow in conversion from 'double' to 'int' changes value from '1.0e+18' to '2147483647' [-Woverflow]
14 | const int oo = 1e18 + 7, mod = 1e9 + 7;
| ~~~~~^~~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
384 KB |
contestant found the optimal answer: 108 == 108 |
| 2 |
Correct |
0 ms |
384 KB |
contestant found the optimal answer: 999 == 999 |
| 3 |
Correct |
1 ms |
384 KB |
contestant found the optimal answer: 0 == 0 |
| 4 |
Correct |
1 ms |
384 KB |
contestant found the optimal answer: 1542524 == 1542524 |
| 5 |
Correct |
1 ms |
384 KB |
contestant found the optimal answer: 4500000000 == 4500000000 |
| 6 |
Correct |
1 ms |
384 KB |
contestant found the optimal answer: 1 == 1 |
| 7 |
Correct |
1 ms |
384 KB |
contestant found the optimal answer: 1 == 1 |
| 8 |
Correct |
1 ms |
384 KB |
contestant found the optimal answer: 1 == 1 |
| 9 |
Correct |
0 ms |
384 KB |
contestant found the optimal answer: 100400096 == 100400096 |
| 10 |
Correct |
0 ms |
384 KB |
contestant found the optimal answer: 900320000 == 900320000 |
| 11 |
Correct |
0 ms |
384 KB |
contestant found the optimal answer: 3698080248 == 3698080248 |
| 12 |
Correct |
1 ms |
384 KB |
contestant found the optimal answer: 3200320000 == 3200320000 |
| 13 |
Correct |
1 ms |
384 KB |
contestant found the optimal answer: 140072 == 140072 |
| 14 |
Correct |
0 ms |
384 KB |
contestant found the optimal answer: 376041456 == 376041456 |
| 15 |
Correct |
0 ms |
384 KB |
contestant found the optimal answer: 805 == 805 |
| 16 |
Correct |
0 ms |
384 KB |
contestant found the optimal answer: 900189994 == 900189994 |
| 17 |
Correct |
0 ms |
384 KB |
contestant found the optimal answer: 999919994 == 999919994 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
384 KB |
contestant found the optimal answer: 1093956 == 1093956 |
| 2 |
Correct |
0 ms |
384 KB |
contestant found the optimal answer: 302460000 == 302460000 |
| 3 |
Correct |
1 ms |
384 KB |
contestant found the optimal answer: 122453454361 == 122453454361 |
| 4 |
Correct |
1 ms |
384 KB |
contestant found the optimal answer: 93663683509 == 93663683509 |
| 5 |
Correct |
1 ms |
384 KB |
contestant found the optimal answer: 1005304678 == 1005304678 |
| 6 |
Correct |
1 ms |
384 KB |
contestant found the optimal answer: 933702 == 933702 |
| 7 |
Correct |
1 ms |
384 KB |
contestant found the optimal answer: 25082842857 == 25082842857 |
| 8 |
Correct |
1 ms |
384 KB |
contestant found the optimal answer: 687136 == 687136 |
| 9 |
Correct |
0 ms |
384 KB |
contestant found the optimal answer: 27295930079 == 27295930079 |
| 10 |
Correct |
0 ms |
384 KB |
contestant found the optimal answer: 29000419931 == 29000419931 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
512 KB |
contestant found the optimal answer: 610590000 == 610590000 |
| 2 |
Correct |
1 ms |
512 KB |
contestant found the optimal answer: 311760000 == 311760000 |
| 3 |
Correct |
1 ms |
512 KB |
contestant found the optimal answer: 1989216017013 == 1989216017013 |
| 4 |
Correct |
1 ms |
512 KB |
contestant found the optimal answer: 1499437552673 == 1499437552673 |
| 5 |
Correct |
2 ms |
512 KB |
contestant found the optimal answer: 1019625819 == 1019625819 |
| 6 |
Correct |
2 ms |
512 KB |
contestant found the optimal answer: 107630884 == 107630884 |
| 7 |
Correct |
2 ms |
512 KB |
contestant found the optimal answer: 475357671774 == 475357671774 |
| 8 |
Correct |
1 ms |
512 KB |
contestant found the optimal answer: 193556962 == 193556962 |
| 9 |
Correct |
1 ms |
512 KB |
contestant found the optimal answer: 482389919803 == 482389919803 |
| 10 |
Correct |
1 ms |
512 KB |
contestant found the optimal answer: 490686959791 == 490686959791 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
1152 KB |
contestant found the optimal answer: 21503404 == 21503404 |
| 2 |
Correct |
1 ms |
1280 KB |
contestant found the optimal answer: 140412195 == 140412195 |
| 3 |
Correct |
7 ms |
1280 KB |
contestant found the optimal answer: 49729674225461 == 49729674225461 |
| 4 |
Correct |
1 ms |
1152 KB |
contestant found the optimal answer: 37485571387523 == 37485571387523 |
| 5 |
Correct |
11 ms |
1280 KB |
contestant found the optimal answer: 679388326 == 679388326 |
| 6 |
Correct |
9 ms |
1280 KB |
contestant found the optimal answer: 4699030287 == 4699030287 |
| 7 |
Correct |
8 ms |
1152 KB |
contestant found the optimal answer: 12418819758185 == 12418819758185 |
| 8 |
Correct |
8 ms |
1280 KB |
contestant found the optimal answer: 31093317350 == 31093317350 |
| 9 |
Correct |
3 ms |
1152 KB |
contestant found the optimal answer: 12194625429236 == 12194625429236 |
| 10 |
Correct |
5 ms |
1152 KB |
contestant found the optimal answer: 12345131038664 == 12345131038664 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
7 ms |
8704 KB |
contestant found the optimal answer: 1818678304 == 1818678304 |
| 2 |
Correct |
7 ms |
8704 KB |
contestant found the optimal answer: 1326260195 == 1326260195 |
| 3 |
Correct |
84 ms |
8824 KB |
contestant found the optimal answer: 4973126687469639 == 4973126687469639 |
| 4 |
Correct |
7 ms |
8704 KB |
contestant found the optimal answer: 3748491676694116 == 3748491676694116 |
| 5 |
Correct |
88 ms |
8704 KB |
contestant found the optimal answer: 1085432199 == 1085432199 |
| 6 |
Correct |
83 ms |
8704 KB |
contestant found the optimal answer: 514790755404 == 514790755404 |
| 7 |
Correct |
77 ms |
8704 KB |
contestant found the optimal answer: 1256105310476641 == 1256105310476641 |
| 8 |
Correct |
57 ms |
8704 KB |
contestant found the optimal answer: 3099592898816 == 3099592898816 |
| 9 |
Correct |
79 ms |
8796 KB |
contestant found the optimal answer: 1241131419367412 == 1241131419367412 |
| 10 |
Correct |
98 ms |
8824 KB |
contestant found the optimal answer: 1243084101967798 == 1243084101967798 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
70 ms |
84088 KB |
contestant found the optimal answer: 19795776960 == 19795776960 |
| 2 |
Correct |
68 ms |
84220 KB |
contestant found the optimal answer: 19874432173 == 19874432173 |
| 3 |
Correct |
1045 ms |
84088 KB |
contestant found the optimal answer: 497313449256899208 == 497313449256899208 |
| 4 |
Correct |
65 ms |
84088 KB |
contestant found the optimal answer: 374850090734572421 == 374850090734572421 |
| 5 |
Correct |
1726 ms |
84216 KB |
contestant found the optimal answer: 36183271951 == 36183271951 |
| 6 |
Correct |
1069 ms |
84344 KB |
contestant found the optimal answer: 51629847150471 == 51629847150471 |
| 7 |
Correct |
961 ms |
84216 KB |
contestant found the optimal answer: 124074747024496432 == 124074747024496432 |
| 8 |
Correct |
718 ms |
84216 KB |
contestant found the optimal answer: 309959349080800 == 309959349080800 |
| 9 |
Correct |
933 ms |
84216 KB |
contestant found the optimal answer: 124113525649823701 == 124113525649823701 |
| 10 |
Correct |
1179 ms |
84216 KB |
contestant found the optimal answer: 124309619349406845 == 124309619349406845 |
