Article-slope Optimization of hdu-3507-Print

 

My understanding:

Note: (I) represents a formula that contains only I unknowns

Status transfer is shown in the following expression:

Dp [I] = dp [j] + (j, I );

Dp [I] = dp [k] + (k, I );

Assume that j is better than k for I.

So dp [j] + (j, I)

If the preceding formula can be converted to: dp [j] + (j)-(dp [k] + (k)/(j)-(k) <(I)

Then we can use slope Optimization for optimization:

Set g [j, k] <(I) to indicate that when I is in the I state, selecting j state is better than selecting k State.

For g [I] [j]

If g [I] [j] <(I), the I state is better than the j state, and the j state is discarded.

If g [I] [j]> = (I), then g [j] [k]> = (I), the k State is better than the j state, then, discard the j state.

That is:

If g [I] [j] exists

 

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    using namespace std;#define maxn 550000struct list{    int x;    int val;} node[maxn],p;int a[maxn];int sum[maxn];int dp[maxn];int gety(int x,int y){    return dp[x]+sum[x]*sum[x]-dp[y]-sum[y]*sum[y];}int tan(int x,int y,int z){    int ay=gety(z,y);    int by=gety(y,x);    int ax=2*(sum[z]-sum[y]);    int bx=2*(sum[y]-sum[x]);    if(ay*bx<=by*ax)return 1;    return 0;}int pan(int a,int b,int c){    int ay=gety(b,a);    int ax=2*(sum[b]-sum[a]);    if(ay<=sum[c]*ax)return 1;    return 0;}int main(){    int n,m,i;    while(~scanf(%d%d,&n,&m))    {        sum[0]=0;        for(i=1; i<=n; i++)        {            scanf(%d,&a[i]);            sum[i]=sum[i-1]+a[i];        }        int head,tail;        head=1;        tail=0;        p.x=0;        node[++tail]=p;        memset(dp,0,sizeof(dp));        for(i=1; i<=n; i++)        {            p.x=i;            while(tail>head&&pan(node[head].x,node[head+1].x,i))head++;            int x=node[head].x;            dp[i]=dp[x]+m+(sum[i]-sum[x])*(sum[i]-sum[x]);            while(tail>head&&tan(node[tail-1].x,node[tail].x,i))tail--;            node[++tail]=p;        }        cout<