/*Consider the minimum element K in the array
1. Either we move it to the back immediately and solve recursively
2. Or we sort all the elemtents in front of K and then move all elements behind K from left to right in order
It can produce an optimal solution
Costs and solution can be maintained by DP with backtracking
*/
#include<iostream>
#include<queue>
#include<stack>
#include<algorithm>
using namespace std;
typedef long long ll;
const int N=1001;
#define fi first
#define se second
int n;
pair<int,int>b[1001];
int a[1001];
int p[1001];
int x[1001];
bool hv[1001];
ll pf[1001][1001];
ll pc[1001][1001];
ll dp[1001][1001];
bool way[1001][1001];
vector<pair<int,int> >d;
void track(int i,int j){
if(i==0 || j==0) return;
if(p[i]>=j){
track(i-1,j);
return;
}
int pos=pc[i][p[i]],tot=pc[i][j];
if(way[i][j]){
track(i-1,p[i]-1);
for(int k=p[i]+1; k<=j ;k++){
if(a[k]<=i) d.push_back({++pos,x[k]});
}
}
else{
d.push_back({pos,tot});
track(i-1,j);
}
}
int main(){
ios::sync_with_stdio(false);
cin >> n;
for(int i=1; i<=n ;i++){
cin >> b[i].fi;
b[i].se=i;b[i].fi*=-1;
}
sort(b+1,b+n+1);
for(int i=1; i<=n ;i++) a[b[i].se]=i,p[i]=b[i].se;
for(int i=1; i<=n ;i++){
x[i]=1;
for(int j=1; j<a[i] ;j++) x[i]+=hv[j];
hv[a[i]]=true;
}
for(int i=1; i<=n ;i++){
for(int j=1; j<=n ;j++){
pf[i][j]=pf[i][j-1]+x[j]*(a[j]<=i);
pc[i][j]=pc[i][j-1]+(a[j]<=i);
if(p[i]>=j){
dp[i][j]=dp[i-1][j];
continue;
}
int pos=pc[i][p[i]],tot=pc[i][j];
ll c1=dp[i-1][j]+pos+tot;
ll c2=dp[i-1][p[i]-1]+1LL*(pos+tot+1)*(tot-pos)/2+pf[i][j]-pf[i][p[i]];
if(c1>c2) way[i][j]=true;
dp[i][j]=min(c1,c2);
}
}
track(n,n);
cout << d.size() << '\n';
for(auto cur:d) cout << cur.fi << ' ' << cur.se << '\n';
}
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
3 ms |
512 KB |
Output is correct |
| 2 |
Correct |
3 ms |
512 KB |
Output is correct |
| 3 |
Correct |
3 ms |
512 KB |
Output is correct |
| 4 |
Correct |
4 ms |
1024 KB |
Output is correct |
| 5 |
Correct |
5 ms |
1920 KB |
Output is correct |
| 6 |
Correct |
6 ms |
3968 KB |
Output is correct |
| 7 |
Correct |
17 ms |
12672 KB |
Output is correct |
| 8 |
Correct |
23 ms |
20096 KB |
Output is correct |
| 9 |
Correct |
26 ms |
24064 KB |
Output is correct |
| 10 |
Correct |
30 ms |
24952 KB |
Output is correct |
