#include <iostream>
using namespace std;
#define maxn 100000
#define maxk 200
#define ll long long
int best[maxn][maxk];
//arr is prefix sums
int main()
{
ll dp[maxn], prv[maxn], arr[maxn];
//prv is not quite necessary
int n, k;
cin >> n >> k;
k++;
//array endgth n, split into k+1 intervals, each time points = product of sums of two sides
//if decided how intervals will be picked: then how to arrange which to select?
//answer for a set of intervals = sum ab where a, b are distinct in it
//true by induction on set's size
//= ((sum a)^2 - sum a^2)/2 where first sum is known (sum of array) and second is split up
//divide up the array optimally to minimize sum (segment sum)^2? dp with prefix sums
for (int i = 0; i < n; i++)
{
cin >> arr[i];
if (i) arr[i] += arr[i-1];
//1 interval
dp[i] = arr[i]*arr[i];
best[i][0] = -1;
//cut at -1 means this is final interval
}
int stack[maxn];
ll cut[maxn];
cut[0] = 0;
//stack[0] is best from cut[0] to cut[1]-1, ...
int end, start;
for (int t = 1; t < k; t++)
{
//t+1 intervals to make 0..i-1; if t = 0 then just interval sum ^ 2
//else: dp[i] = min_x<i arr[i]^2 - 2*arr[x]*arr[i] + arr[x]^2 + prv[x]
//with x >= t-1 (i >= t to make it well defined)
//do all of dp[?] in O(n)? need to insert another x or query best x for given i
//monotonic stack: record pair<int,ll>: best value of x for arr[i] <= that ll
for (int i = 0; i < n; i++) prv[i] = dp[i];
end = 0;
start = 0;
for (int i = t; i < n; i++)
{
//x = i-1: insert it into the monotonic stack
ll x = 0;
bool special = false;
while (start != end)
{
//see when it beats the last function, then truncate
//definitely should work at some value of arr[i]: prv is increasing not too fast
//just assume it ought to work
//solve for smallest int x:
//arr[stack[end-1]]*arr[stack[end-1]]+prv[stack[end-1]]-2*arr[stack[end-1]]*x >
//arr[i-1]*arr[i-1]+prv[i-1]-2*arr[i-1]*x
//or tmp2x > tmp1 or x = ceil of (tmp1+1)/tmp2
//just take floor and +1 if needed
if (arr[i-1] == arr[stack[end-1]])
{
//impossible to beat previous function, so done
special = true;
break;
}
ll tmp1 = arr[i-1]*arr[i-1]+prv[i-1]-arr[stack[end-1]]*arr[stack[end-1]]-prv[stack[end-1]],
tmp2 = 2*arr[i-1]-2*arr[stack[end-1]];
x = (tmp1+1)/tmp2;
if ((tmp1+1)%tmp2) x++;
//if at some point it is optimal, it will continue to be optimal later
if (x > cut[end-1])
{
//previous one is sometimes optimal so cannot discard
break;
}
end--;
}
if (!special)
{
stack[end] = i-1;
cut[end] = x;
end++;
cut[end] = 1e18;
}
//the last curve is always optimal, but previous one is up to x-1 only
//now find which curve is best for arr[i]: pop from front of the stack
while (start != end)
{
if (cut[start+1] > arr[i]) break;
start++;
}
best[i][t] = stack[start];
dp[i] = (arr[i]-arr[stack[start]])*(arr[i]-arr[stack[start]])+prv[stack[start]];
}
}
//now dp[n-1] is the answer
cout << (arr[n-1]*arr[n-1]-dp[n-1])/2 << '\n';
int cur = n-1;
while (k)
{
cur = best[cur][--k];
if (cur != -1) cout << cur+1 << ' ';
}
}
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
2 ms |
3796 KB |
contestant found the optimal answer: 108 == 108 |
| 2 |
Correct |
2 ms |
3796 KB |
contestant found the optimal answer: 999 == 999 |
| 3 |
Correct |
3 ms |
3796 KB |
contestant found the optimal answer: 0 == 0 |
| 4 |
Correct |
2 ms |
3828 KB |
contestant found the optimal answer: 1542524 == 1542524 |
| 5 |
Correct |
2 ms |
3796 KB |
contestant found the optimal answer: 4500000000 == 4500000000 |
| 6 |
Correct |
2 ms |
3796 KB |
contestant found the optimal answer: 1 == 1 |
| 7 |
Correct |
2 ms |
3796 KB |
contestant found the optimal answer: 1 == 1 |
| 8 |
Correct |
2 ms |
3796 KB |
contestant found the optimal answer: 1 == 1 |
| 9 |
Correct |
2 ms |
3796 KB |
contestant found the optimal answer: 100400096 == 100400096 |
| 10 |
Correct |
2 ms |
3796 KB |
contestant found the optimal answer: 900320000 == 900320000 |
| 11 |
Correct |
2 ms |
3796 KB |
contestant found the optimal answer: 3698080248 == 3698080248 |
| 12 |
Correct |
2 ms |
3796 KB |
contestant found the optimal answer: 3200320000 == 3200320000 |
| 13 |
Correct |
2 ms |
3796 KB |
contestant found the optimal answer: 140072 == 140072 |
| 14 |
Correct |
2 ms |
3820 KB |
contestant found the optimal answer: 376041456 == 376041456 |
| 15 |
Correct |
2 ms |
3796 KB |
contestant found the optimal answer: 805 == 805 |
| 16 |
Correct |
2 ms |
3796 KB |
contestant found the optimal answer: 900189994 == 900189994 |
| 17 |
Correct |
2 ms |
3796 KB |
contestant found the optimal answer: 999919994 == 999919994 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
2 ms |
3796 KB |
contestant found the optimal answer: 1093956 == 1093956 |
| 2 |
Correct |
2 ms |
3796 KB |
contestant found the optimal answer: 302460000 == 302460000 |
| 3 |
Correct |
2 ms |
3796 KB |
contestant found the optimal answer: 122453454361 == 122453454361 |
| 4 |
Correct |
2 ms |
3824 KB |
contestant found the optimal answer: 93663683509 == 93663683509 |
| 5 |
Correct |
2 ms |
3796 KB |
contestant found the optimal answer: 1005304678 == 1005304678 |
| 6 |
Correct |
2 ms |
3796 KB |
contestant found the optimal answer: 933702 == 933702 |
| 7 |
Correct |
2 ms |
3796 KB |
contestant found the optimal answer: 25082842857 == 25082842857 |
| 8 |
Correct |
2 ms |
3796 KB |
contestant found the optimal answer: 687136 == 687136 |
| 9 |
Correct |
2 ms |
3828 KB |
contestant found the optimal answer: 27295930079 == 27295930079 |
| 10 |
Correct |
2 ms |
3824 KB |
contestant found the optimal answer: 29000419931 == 29000419931 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
3 ms |
3924 KB |
contestant found the optimal answer: 610590000 == 610590000 |
| 2 |
Correct |
2 ms |
3924 KB |
contestant found the optimal answer: 311760000 == 311760000 |
| 3 |
Correct |
2 ms |
3948 KB |
contestant found the optimal answer: 1989216017013 == 1989216017013 |
| 4 |
Correct |
2 ms |
3924 KB |
contestant found the optimal answer: 1499437552673 == 1499437552673 |
| 5 |
Correct |
3 ms |
3924 KB |
contestant found the optimal answer: 1019625819 == 1019625819 |
| 6 |
Correct |
3 ms |
3924 KB |
contestant found the optimal answer: 107630884 == 107630884 |
| 7 |
Correct |
2 ms |
3924 KB |
contestant found the optimal answer: 475357671774 == 475357671774 |
| 8 |
Correct |
2 ms |
3956 KB |
contestant found the optimal answer: 193556962 == 193556962 |
| 9 |
Correct |
2 ms |
3924 KB |
contestant found the optimal answer: 482389919803 == 482389919803 |
| 10 |
Correct |
2 ms |
3924 KB |
contestant found the optimal answer: 490686959791 == 490686959791 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
2 ms |
4564 KB |
contestant found the optimal answer: 21503404 == 21503404 |
| 2 |
Correct |
2 ms |
4596 KB |
contestant found the optimal answer: 140412195 == 140412195 |
| 3 |
Correct |
4 ms |
4596 KB |
contestant found the optimal answer: 49729674225461 == 49729674225461 |
| 4 |
Correct |
3 ms |
4564 KB |
contestant found the optimal answer: 37485571387523 == 37485571387523 |
| 5 |
Correct |
5 ms |
4564 KB |
contestant found the optimal answer: 679388326 == 679388326 |
| 6 |
Correct |
5 ms |
4564 KB |
contestant found the optimal answer: 4699030287 == 4699030287 |
| 7 |
Correct |
6 ms |
4600 KB |
contestant found the optimal answer: 12418819758185 == 12418819758185 |
| 8 |
Correct |
5 ms |
4564 KB |
contestant found the optimal answer: 31093317350 == 31093317350 |
| 9 |
Correct |
3 ms |
4596 KB |
contestant found the optimal answer: 12194625429236 == 12194625429236 |
| 10 |
Correct |
3 ms |
4564 KB |
contestant found the optimal answer: 12345131038664 == 12345131038664 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
7 ms |
11672 KB |
contestant found the optimal answer: 1818678304 == 1818678304 |
| 2 |
Correct |
6 ms |
11604 KB |
contestant found the optimal answer: 1326260195 == 1326260195 |
| 3 |
Correct |
27 ms |
11648 KB |
contestant found the optimal answer: 4973126687469639 == 4973126687469639 |
| 4 |
Correct |
8 ms |
11732 KB |
contestant found the optimal answer: 3748491676694116 == 3748491676694116 |
| 5 |
Correct |
25 ms |
11572 KB |
contestant found the optimal answer: 1085432199 == 1085432199 |
| 6 |
Correct |
38 ms |
11604 KB |
contestant found the optimal answer: 514790755404 == 514790755404 |
| 7 |
Correct |
29 ms |
11604 KB |
contestant found the optimal answer: 1256105310476641 == 1256105310476641 |
| 8 |
Correct |
20 ms |
11696 KB |
contestant found the optimal answer: 3099592898816 == 3099592898816 |
| 9 |
Correct |
23 ms |
11612 KB |
contestant found the optimal answer: 1241131419367412 == 1241131419367412 |
| 10 |
Correct |
26 ms |
11648 KB |
contestant found the optimal answer: 1243084101967798 == 1243084101967798 |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
48 ms |
82208 KB |
contestant found the optimal answer: 19795776960 == 19795776960 |
| 2 |
Correct |
49 ms |
82224 KB |
contestant found the optimal answer: 19874432173 == 19874432173 |
| 3 |
Incorrect |
374 ms |
82536 KB |
Extra information in the output file |
| 4 |
Halted |
0 ms |
0 KB |
- |
