#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<int, int> 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;
int n, k, a[N], suff[N];
int dp[N], lst_dp[N], opt[N];
int lst[N][K];
int 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);
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";
}
assert(0);
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 |
Runtime error |
10 ms |
512 KB |
Execution killed with signal 11 (could be triggered by violating memory limits) |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Runtime error |
10 ms |
640 KB |
Execution killed with signal 11 (could be triggered by violating memory limits) |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Runtime error |
10 ms |
896 KB |
Execution killed with signal 11 (could be triggered by violating memory limits) |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Runtime error |
10 ms |
2304 KB |
Execution killed with signal 11 (could be triggered by violating memory limits) |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Runtime error |
29 ms |
17144 KB |
Execution killed with signal 11 (could be triggered by violating memory limits) |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Runtime error |
197 ms |
131072 KB |
Execution killed with signal 11 (could be triggered by violating memory limits) |
| 2 |
Halted |
0 ms |
0 KB |
- |
