study from:
https://www.cnblogs.com/flashhu/p/9480669.html
3.斜率dp
study from:http://www.cnblogs.com/MashiroSky/p/6009685.html
或单减
https://www.luogu.org/problemnew/show/P3195
study from:http://www.cnblogs.com/MashiroSky/p/5968118.html
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1 #include <cstdio>
2 #include <cstdlib>
3 #include <cmath>
4 #include <cstring>
5 #include <time.h>
6 #include <string> 7 #include <set> 8 #include <map> 9 #include <list> 10 #include <stack> 11 #include <queue> 12 #include <vector> 13 #include <bitset> 14 #include <ext/rope> 15 #include <algorithm> 16 #include <iostream> 17 using namespace std; 18 #define ll long long 19 #define minv 1e-6 20 #define inf 1e9 21 #define pi 3.1415926536 22 #define E 2.7182818284 23 const ll mod=1e9+7;//998244353 24 const int maxn=5e4+10; 25 26 ll sum[maxn],a[maxn],f[maxn],L; 27 int q[maxn]; 28 29 double slope(int j,int k) 30 { 31 return (f[k]-f[j]+(a[k]+L+1)*(a[k]+L+1)-(a[j]+L+1)*(a[j]+L+1)) 32 /2.0/(a[k]-a[j]); 33 } 34 35 int main() 36 { 37 int n,l,r,i; 38 ll s; 39 scanf("%d%lld",&n,&L); 40 sum[0]=0; 41 l=1,r=1; 42 f[0]=0; 43 q[1]=0; 44 for (i=1;i<=n;i++) 45 { 46 scanf("%lld",&s); 47 sum[i]=sum[i-1]+s; 48 a[i]=sum[i]+i; 49 while (r>l && slope(q[l],q[l+1])<=a[i]) //have = 50 l++; 51 f[i]=f[q[l]]+pow(i-q[l]-1+sum[i]-sum[q[l]]-L,2); 52 while (r>l && slope(q[r-1],q[r])>slope(q[r],i))//have no = 53 r--; 54 q[++r]=i; 55 } 56 printf("%lld",f[n]); 57 return 0; 58 }
https://www.luogu.org/problemnew/show/P2900
1 #include <cstdio>
2 #include <cstdlib>
3 #include <cmath>
4 #include <cstring>
5 #include <time.h>
6 #include <string> 7 #include <set> 8 #include <map> 9 #include <list> 10 #include <stack> 11 #include <queue> 12 #include <vector> 13 #include <bitset> 14 #include <ext/rope> 15 #include <algorithm> 16 #include <iostream> 17 using namespace std; 18 #define ll long long 19 #define minv 1e-6 20 #define inf 1e9 21 #define pi 3.1415926536 22 #define nl 2.7182818284 23 const ll mod=1e9+7;//998244353 24 const int maxn=5e4+10; 25 26 struct node 27 { 28 ll x,y; 29 }s[maxn],d[maxn]; 30 31 ll f[maxn]; 32 int q[maxn]; 33 34 int cmp(node a,node b) 35 { 36 if (a.y==b.y) 37 return a.x>b.x; 38 else 39 return a.y>b.y; 40 } 41 42 double slope(int j,int k) 43 { 44 return 1.0*(f[k]-f[j])/(d[j+1].y-d[k+1].y); 45 } 46 47 int main() 48 { 49 int n,i,m,k,l,r; 50 scanf("%d",&n); 51 for (i=1;i<=n;i++) 52 scanf("%lld%lld",&s[i].x,&s[i].y); 53 sort(s+1,s+n+1,cmp); 54 m=0; 55 k=0; 56 for (i=1;i<=n;i++) 57 if (s[i].x>k) 58 { 59 d[++m]=s[i]; 60 k=s[i].x; 61 } 62 63 f[0]=0; 64 q[1]=0; 65 l=1,r=1; 66 for (i=1;i<=m;i++) 67 { 68 while (l<r && slope(q[l],q[l+1])<=d[i].x) 69 l++; 70 f[i]=f[q[l]]+d[q[l]+1].y*d[i].x; 71 while (l<r && slope(q[r-1],q[r])>slope(q[r],i)) 72 r--; 73 q[++r]=i; 74 } 75 printf("%lld",f[m]); 76 return 0;77 }