洛谷 P2970 [USACO09DEC]Selfish Grazing S

题目描述

Each of Farmer John's N (1 <= N <= 50,000) cows likes to graze in a certain part of the pasture, which can be thought of as a large one-dimeensional number line. Cow i's favorite grazing range starts at location S_i and ends at location E_i (1 <= S_i < E_i; S_i < E_i <= 100,000,000).

Most folks know the cows are quite selfish; no cow wants to share any of its grazing area with another. Thus, two cows i and j can only graze at the same time if either S_i >= E_j or E_i <= S_j. FJ would like to know the maximum number of cows that can graze at the same time for a given set of cows and their preferences.

Consider a set of 5 cows with ranges shown below:

  ... 1    2    3    4    5    6    7    8    9   10   11   12   13 ...
  ... |----|----|----|----|----|----|----|----|----|----|----|----|----
Cow 1:      <===:===>          :              :              :
Cow 2: <========:==============:==============:=============>:
Cow 3:          :     <====>   :              :              :
Cow 4:          :              :     <========:===>          :
Cow 5:          :              :     <==>     :              :

These ranges represent (2, 4), (1, 12), (4, 5), (7, 10), and (7, 8), respectively.

For a solution, the first, third, and fourth (or fifth) cows can all graze at the same time. If the second cow grazed, no other cows could graze. Also, the fourth and fifth cows cannot graze together, so it is impossible for four or more cows to graze.

约翰有N(1≤N≤50000)头牛约翰的草地可以认为是一条直线．每只牛只喜欢在某个特定的范围内吃草．第i头牛喜欢在区间(SiEi)吃草1≤Si<Ei≤1,000,000,00.

奶牛们都很自私他们不喜欢和其他奶牛共享自己喜欢吃草的领域因此约翰要保证任意

两头牛都不会共享他们喜欢吃草昀领域．如果奶牛i和奶牛J想要同时吃草那么要满足Si>=Ej或者Ei≤Sj．约翰想知道在同一时刻最多可以有多少头奶牛同时吃草

输入格式

* Line 1: A single integer: N

* Lines 2..N+1: Line i+1 contains the two space-separated integers: S_i and E_i

输出格式

* Line 1: A single integer representing the maximum number of cows that can graze at once.

输入输出样例

输入 #1

5 
2 4 
1 12 
4 5 
7 10 
7 8 

输出 #1

3 

看到这道题

很容易想到的排序方式就是左端点排序跨度值排序

可是这道题

恰恰相反

是右端点排序

因为他要看n个区间内哪些是不重合的

所以需要把右端点排序然后才能和上一个区间比较

其他的就没什么难点了

AC代码:

# include <iostream>
# include <cstdio>
# include <algorithm>
using namespace std;
# define int long long
int n,r=1,cnt;//r右边界 
struct node{
	int s;
	int e;
}a[50005];
bool cmp(node x,node y){
	return x.e<y.e;
}
signed main(){
	scanf("%lld",&n);
	for (int i=1;i<=n;i++){
		scanf("%lld%lld",&a[i].s,&a[i].e);
	}
	sort(a+1,a+1+n,cmp);
	for (int i=1;i<=n;i++){
		if (r<=a[i].s){
			cnt++;
			r=a[i].e;
		}
	}
	printf("%lld",cnt);
	return 0;
}