贪心+TreapBZOJ1691-[Usaco2007 Dec]挑剔的美食家

Posted 2020-08-05 Yiyi

【题目大意】

有n头奶牛m种牧草，每种牧草有它的价格和鲜嫩度。每头奶牛要求它的牧草的鲜嫩度要不低于一个值，价格也不低于一个值。每种牧草只会被一头牛选择。问最少要多少钱？

【思路】

显然的贪心，把奶牛和牧草都按照鲜嫩度由大到小排序，对于每奶牛把鲜嫩度大于它的都扔进treap，然后找出后继。

不过注意后继的概念是大于它且最小的，然而我们这里是可以等于的，所以应该是找cow[i].fresh-1的后继，注意一下……

  1 #include<iostream>
  2 #include<cstdio>
  3 #include<cstring>
  4 #include<algorithm>
  5 #include<cmath>
  6 using namespace std;
  7 typedef long long ll;
  8 const int MAXN=100000+50;
  9 const int INF=0x7fffffff;
 10 struct node
 11 {
 12     int fresh,price;
 13     bool operator < (const node &x) const
 14     {
 15         return (fresh>x.fresh);//注意是由大到小排序 
 16     }
 17 }cow[MAXN],grass[MAXN];
 18 struct treap
 19 {
 20     int key,cnt,priority;
 21     treap* lson;
 22     treap* rson;
 23     treap()
 24     {
 25         cnt=1;
 26         priority=rand();
 27         lson=rson=NULL;
 28     }
 29 };
 30 treap* root=NULL;
 31 int n,m;
 32 
 33 void RightRotate(treap* &rt)
 34 {
 35     treap* tmp=rt->lson;
 36     rt->lson=tmp->rson;
 37     tmp->rson=rt;
 38     rt=tmp;
 39 }
 40 
 41 void LeftRotate(treap* &rt)
 42 {
 43     treap* tmp=rt->rson;
 44     rt->rson=tmp->lson;
 45     tmp->lson=rt;
 46     rt=tmp;
 47 }
 48 
 49 void insert(treap* &rt,int x)
 50 {
 51     if (rt==NULL) 
 52     {
 53         rt=new treap;//不要忘记了新建 
 54         rt->key=x;
 55     } 
 56     else if (rt->key==x) rt->cnt++;
 57     else
 58     {
 59         if (rt->key>x)
 60         {
 61             insert(rt->lson,x);
 62             if (rt->lson->priority>rt->priority) RightRotate(rt);
 63         }
 64         if (rt->key<x)
 65         {
 66             insert(rt->rson,x);
 67             if (rt->rson->priority>rt->priority) LeftRotate(rt);
 68         }
 69     }
 70 }
 71 
 72 void del(treap* &rt,int x)
 73 {
 74     if (rt->key==x)
 75     {
 76         if (rt->cnt>1) rt->cnt--;
 77             else
 78             {
 79                 treap* tmp=rt;
 80                 if (rt->lson==NULL)
 81                 {
 82                     rt=rt->rson;
 83                     delete tmp;
 84                 }
 85                 else if (rt->rson==NULL)
 86                 {
 87                     rt=rt->lson;
 88                     delete tmp;
 89                 }
 90                 else
 91                 {
 92                     if (rt->lson->priority>rt->rson->priority) RightRotate(rt),del(rt->rson,x);
 93                         else LeftRotate(rt),del(rt->lson,x);
 94                 }
 95             }
 96     }
 97     else
 98     {
 99         if (x<rt->key) del(rt->lson,x);
100             else del(rt->rson,x);
101     }
102 }
103 
104 int suc(treap* &rt,int x)
105 {
106     int ans=INF;
107     treap* tmp=rt;
108     while (tmp)
109     {
110         if (tmp->key>x)
111         {
112             ans=min(ans,tmp->key);
113             tmp=tmp->lson;
114         }
115         else tmp=tmp->rson;
116     }
117     return ans;
118 }
119 
120 void init()
121 {
122     scanf("%d%d",&n,&m);
123     for (int i=1;i<=n;i++) scanf("%d%d",&cow[i].price,&cow[i].fresh);
124     for (int i=1;i<=m;i++) scanf("%d%d",&grass[i].price,&grass[i].fresh);
125     sort(cow+1,cow+n+1);
126     sort(grass+1,grass+m+1);
127 }
128 
129 ll solve()
130 {
131     int j=1;
132     ll ans=0;
133     for (int i=1;i<=n;i++)
134     {
135         while (grass[j].fresh>=cow[i].fresh && j<=m)
136         {
137             insert(root,grass[j].price);//这里一开始把j打成i了 
138             j++;
139         }
140         int find=suc(root,cow[i].price-1);//注意由于这里是不低于，也就是≥，并不是取cow[i].price的后继，而是cow[i].price-1的 
141         if (find==INF) return(-1);
142             else
143             {
144                 ans+=(ll)find;
145                 del(root,find);
146             }
147     }
148     return ans;
149 }
150 
151 int main()
152 {
153     init();
154     printf("%lld",solve());
155     return 0;
156 }