POJ 3250：Bad Hair Day 好玩的单调栈

Bad Hair Day

Time Limit: 2000MS Memory Limit: 65536KTotal Submissions: 15699 Accepted: 5255

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 h_i (1 ≤ h_i ≤ 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 c_i denote the number of cows whose hairstyle is visible from cow i; please compute the sum of c₁ through c_N.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 c_N.

Sample Input

610374122

Sample Output

5

题意是站着一排牛，牛从左往右看能看到比自己身高小的牛的发型，但是如果碰到牛的身高比自己高了，那么到此为止。

转换一下思维，想象一下牛是从右往左看只能看到比自己身高大的牛，然后如果身高变小，那么到此为止。

很好玩的题目，用单调栈来做，从左往右读，栈内元素从栈底到栈顶是递增的，这样如果遇到元素比栈顶元素大，那么弹出。然后计算此时栈内元素的个数，相加即得到结果。

代码：

#include <iostream>  #include <algorithm>  #include <cmath>  #include <vector>  #include <string>  #include <cstring>  #pragma warning(disable:4996)  using namespace std;#define N 80002long long a[N], stack[N], top;int main(){//freopen("i.txt", "r", stdin);//freopen("o.txt", "w", stdout);long long ans, tmp;int i, j, n;scanf("%d", &n);for (i = 1; i <= n; i++){scanf("%lld", a + i);}a[++n] = 1e9 + 7;top = 0;ans = 0;for (i = 1; i <= n; i++){while (top >= 1 && a[i] >= a[stack[top - 1]]){--top;}ans = ans + top;if (top == 0 || a[i] < a[stack[top - 1]]){stack[top++] = i;}}printf("%lld\n", ans);//system("pause");  return 0;}