Ideas
This question is a modified version of the longest ascending subsequence. To ensure strict increase,
a [j] − a [i] >= j − ia[j]-a[i]>=jia[j]−a[i]>=j−i,化简得 a [ j ] − j > a [ i ] − i a[j]-j>a[i]-i a[j]−j>a[i]−i , so we only need to obtain the LIS of sequence b (b [i] = a [i] − ib[i]=a[i]-ib[i]=a[i]−i ), but if you write it in dynamic programming, it will drop T. For LIS, you need to use the greedy + bisection solution. If you don’t understand, you can look atthe two complexity solutions of the longest ascending subsequence
Code
- Use upper_bound() version
#pragma GCC optimize(2)
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long ul;
typedef unsigned long long ull;
#define pi acos(-1.0)
#define e exp(1.0)
#define pb push_back
#define mk make_pair
#define fir first
#define sec second
#define scf scanf
#define prf printf
typedef pair<ll,ll> pa;
const ll INF=0x3f3f3f3f3f3f3f3f;
const ll MAX_T=12;
const ll MAX_N=1e5+7;
ll T,N;
ll A[MAX_N],B[MAX_N];
ll do_LIS(){
ll i,j,k,cnt=0;
for(i=0;i<N;i++){
ll pos=upper_bound(B,B+cnt,A[i])-B;
if(pos==cnt){
cnt++;
}
B[pos]=A[i];
}
return cnt;
}
int main()
{
// freopen(".../.txt","w",stdout);
// freopen(".../.txt","r",stdin);
// ios::sync_with_stdio(false);
ll i,j,k=0;
scf("%lld",&T);
while(T--){
scf("%lld",&N);
for(i=0;i<N;i++){
scf("%lld",&A[i]);
A[i]-=i;
}
ll res=N-do_LIS();
prf("Case #%lld:\n",++k);
prf("%lld\n",res);
}
return 0;
}
- This is a handwritten bisection version
#pragma GCC optimize(2)
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long ul;
typedef unsigned long long ull;
#define pi acos(-1.0)
#define e exp(1.0)
#define pb push_back
#define mk make_pair
#define fir first
#define sec second
#define scf scanf
#define prf printf
typedef pair<ll,ll> pa;
const ll INF=0x3f3f3f3f3f3f3f3f;
const ll MAX_T=12;
const ll MAX_N=1e5+7;
ll T,N;
ll A[MAX_N],B[MAX_N];
ll do_LIS(){
ll i,j,k,cnt=0;
for(i=0;i<N;i++){
ll L=0,R=cnt-1,mid,res=-1;
while(L<=R){
mid=L+(R-L)/2;
if(B[mid]>A[i]){
res=mid;
R=mid-1;
}
else{
L=mid+1;
}
}
if(res==-1){
B[cnt]=A[i];
cnt++;
}
else
B[res]=A[i];
}
return cnt;
}
int main()
{
// freopen(".../.txt","w",stdout);
// freopen(".../.txt","r",stdin);
// ios::sync_with_stdio(false);
ll i,j,k=0;
scf("%lld",&T);
while(T--){
scf("%lld",&N);
for(i=0;i<N;i++){
scf("%lld",&A[i]);
A[i]-=i;
}
ll res=N-do_LIS();
prf("Case #%lld:\n",++k);
prf("%lld\n",res);
}
return 0;
}