[USACO06NOV]Bad Hair Day S(栈)

Posted 2023-05-27 markun0

题目大意:

按顺序给出n头牛的身高,每头牛可以看见它到后出现的牛中第一头身高高过(大于等于)它的牛之间的所有牛,求所有牛总共能看到的牛数

解题思路:

从后往前遍历查看每头牛能看到的牛数,每次进行的比较数量的太多,但我们可以用栈来存储关键信息以减少不必要的比较

代码如下:

#include <bits/stdc++.h>
#include<algorithm>
using namespace std;
#define ll long long
#define N 80005
int a[N];
//每头牛的身高和所能看到的别的牛的头发的数量
struct P 
    int x, num=0;
    P(int x, int num) :x(x), num(num)
;
stack<P>ans;
ll sum = 0;
int main()

    ios::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    int n,w; cin >> n;
    for (int i = 1; i <= n; i++)
    
        cin >> a[i]; 
	
    for (int i = n; i; i--) 
        int num = 0;
        while (!ans.empty() && a[i] > ans.top().x) 
            num += ans.top().num+1;
            //去掉冗杂元素
            ans.pop();
        
        sum += num;
        //存入该头牛的信息
        ans.push(P(a[i],num));
    
    cout << sum;

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 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

6
10
3
7
4
12
2

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 }