题意
一个扫地机器人要按顺序收集所有垃圾,求最小步数
组数T
机器人容量 Cap
垃圾数目 n
垃圾坐标和重量 x y c
转移方程
\( d(i)=min\{d(j)+dis2org(j+1)+dis(j+1,i)|j<i,cap(j+1,i)<=Cap\}+dis2org(i) \)
令 \(dis(j+1,i)=dis(i)-dis(j)\),则有\( d(i)=min\{d(j)+dis2org(j+1)-dis(j+1)\}+dis(i)+dis2org(i) \)
1 /* 2 author:jxy 3 lang:C/C++ 4 university:China,Xidian University 5 **If you need to reprint,please indicate the source** 6 */ 7 #include <iostream> 8 #include <cstdio> 9 #include <cstdlib> 10 #include <cstring> 11 #include <algorithm> 12 using namespace std; 13 int Cap,n; 14 int dis2org[100005]; //到原点距离 15 int dis[100005],cap[100005];//从0到i的距离 16 int abs(int x){return x>0?x:-x;} 17 int ans[100005]; 18 int que[100005]; 19 int calc(int i) 20 { 21 return ans[i]+dis2org[i+1]-dis[i+1]; 22 } 23 int main() 24 { 25 int T; 26 scanf("%d",&T); 27 while(T--) 28 { 29 scanf("%d%d",&Cap,&n); 30 int i,x,y,c,lx=0,ly=0,l,r; 31 dis[0]=cap[0]=0; 32 for(i=1;i<=n;i++) 33 { 34 scanf("%d%d%d",&x,&y,&c); 35 dis2org[i]=abs(x)+abs(y); 36 cap[i]=cap[i-1]+c; 37 dis[i]=dis[i-1]+abs(x-lx)+abs(y-ly); 38 lx=x;ly=y; 39 } 40 l=r=0; 41 ans[0]=0; 42 for(i=1;i<=n;i++) 43 { 44 while(l<r&&cap[i]-cap[que[l]]>Cap)l++; 45 while(l<r&&calc(i-1)<=calc(que[r-1]))r--;//维护单调队列 46 que[r++]=i-1; 47 ans[i]=calc(que[l])+dis[i]+dis2org[i]; 48 } 49 printf("%d\n",ans[n]); 50 if(T)puts(""); 51 } 52 }
原文:http://www.cnblogs.com/czjxy881/p/3536493.html