【Light OJ 1414】February 29（容斥原理）

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本文介绍了一个计算两个指定日期之间闰日数量的程序。通过容斥原理确定给定年份是否为闰年，并据此计算闰日总数。文章提供了一段C++代码实现，包括日期输入解析及闰年判断。

February 29

Time Limit: 1000MS

Memory Limit: 32768KB

64bit IO Format: %lld & %llu

Submit Status

Description

It is 2012, and it's a leap year. So there is a "February 29" in this year, which is called leap day. Interesting thing is the infant who will born in this February 29, will get his/her birthday again in 2016, which is another leap year. So February 29 only exists in leap years. Does leap year comes in every 4 years? Years that are divisible by 4 are leap years, but years that are divisible by 100 are not leap years, unless they are divisible by 400 in which case they are leap years.

In this problem, you will be given two different date. You have to find the number of leap days in between them.

Input

Input starts with an integer T (≤ 550), denoting the number of test cases.

Each of the test cases will have two lines. First line represents the first date and second line represents the second date. Note that, the second date will not represent a date which arrives earlier than the first date. The dates will be in this format - "month day, year", See sample input for exact format. You are guaranteed that dates will be valid and the year will be in between 2 * 10³ to 2 * 10⁹. For your convenience, the month list and the number of days per months are given below. You can assume that all the given dates will be a valid date.

Output

For each case, print the case number and the number of leap days in between two given dates (inclusive).

Sample Input

January 12, 2012

March 19, 2012

August 12, 2899

August 12, 2901

August 12, 2000

August 12, 2005

February 29, 2004

February 29, 2012

Sample Output

Case 1: 1

Case 2: 0

Case 3: 1

Case 4: 3

容斥原理求该年之前闰年的个数

#include<cstdio>
#include<iostream>
#include<cstring>
#include<cmath>
#include<map>
#include<algorithm>
using namespace std;
map<string,int>mp;
void init() {
	int flag=1;
	mp["January"]=flag++;
	mp["February"]=flag++;
	mp["March"]=flag++;
	mp["April"]=flag++;
	mp["May"]=flag++;
	mp["June"]=flag++;
	mp["July"]=flag++;
	mp["August"]=flag++;
	mp["September"]=flag++;
	mp["Ocober"]=flag++;
	mp["November"]=flag++;
	mp["December"]=flag++;
}
bool judge(int n) {
	if(n%400==0||n%4==0&&n%100!=0)
		return true;
	return false;
}
int main() {
	int T,casen=0,ans;
	char c1[20],c2[20];
	int year1,year2,day1,day2;
	scanf("%d",&T);
	init();
	while(T--) {
		int ans=0;
		scanf("%s%d,%d",c1,&day1,&year1);
		scanf("%s%d,%d",c2,&day2,&year2);
		int cnt1,cnt2;
		cnt1=year1/4-year1/100+year1/400;                //容斥原理
		cnt2=year2/4-year2/100+year2/400;
		if(judge(year1)){
			if(mp[c1]==1||mp[c1]==2){		//只有月份大于2时year1年之前的2.29个数才不减 
				cnt1--;
			}
		}
		if(judge(year2)){
			if(mp[c2]==1||mp[c2]==2&&day2<=28){
				cnt2--;
			}
		}
		ans=cnt2-cnt1;
		printf("Case %d: %d\n",++casen,ans);
	}
	return 0;
}