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POJ 3250 Bad Hair Day

Bad Hair Day
Time Limit: 2000MS Memory Limit: 65536K
Total Submissions: 17727 Accepted: 5981

Description

Some of Farmer John‘s N cows (1 ≤ N ≤ 80,000) are having a bad hair day! Since each cow is self-conscious about her messy hairstyle, FJ wants to count the number of other cows that can see the top of other cows‘ heads.

Each cow i has a specified height hi (1 ≤ hi ≤ 1,000,000,000) and is standing in a line of cows all facing east (to the right in our diagrams). Therefore, cow i can see the tops of the heads of cows in front of her (namely cows i+1, i+2, and so on), for as long as these cows are strictly shorter than cow i.

Consider this example:

        =
=       =
=   -   =         Cows facing right -->
=   =   =
= - = = =
= = = = = =
1 2 3 4 5 6

Cow#1 can see the hairstyle of cows #2, 3, 4
Cow#2 can see no cow‘s hairstyle
Cow#3 can see the hairstyle of cow #4
Cow#4 can see no cow‘s hairstyle
Cow#5 can see the hairstyle of cow 6
Cow#6 can see no cows at all!

Let ci denote the number of cows whose hairstyle is visible from cow i; please compute the sum of c1 through cN.For this example, the desired is answer 3 + 0 + 1 + 0 + 1 + 0 = 5.

Input

Line 1: The number of cows, N. 
Lines 2..N+1: Line i+1 contains a single integer that is the height of cow i.

Output

Line 1: A single integer that is the sum of c1 through cN.

Sample Input

610374122

Sample Output

5

Source

USACO 2006 November Silver
 
    所以的牛都是面朝右边的,牛 i 能看到牛 j 当且仅当 i<j,h[ i ] > h[k], k=i , i+1, .. ,j。
    维护一个单调栈,从左往右扫描h[i],(1) 当栈为空时,把h[i]压入栈中;(2)当栈非空时,不断弹出栈顶元素,知道当前h[i]小于栈顶元素,把h[i]压入栈。 这样,h[i]被压入栈前栈的大小,就是能看到第 i 头牛的其它牛数量,累加即可。
 
 1 #include <iostream> 2 #include <algorithm> 3 #include <map> 4 #include <vector> 5 #include <functional> 6 #include <string> 7 #include <cstring> 8 #include <queue> 9 #include <stack>10 #include <set>11 #include <cmath>12 #include <cstdio>13 using namespace std;14 #define IOS ios_base::sync_with_stdio(false)15 typedef long long LL;16 const int INF = 0x3f3f3f3f;17 const double PI=4.0*atan(1.0);18 19 const int maxn=80000;20 LL ans;21 int n,h;22 int main()23 {24     while(scanf("%d",&n)!=EOF){25         stack<int> s;26         ans=0;27         for(int i=0;i<n;i++){28             scanf("%d",&h);29             while(!s.empty()&&h>=s.top()) s.pop();30             ans+=s.size();31             s.push(h);32         }33         printf("%lld\n",ans);34     }35 }

 

POJ 3250 Bad Hair Day