两个日期之间闰年数计算方法探索

由于一个项目的需要，需要计算两个日期之间的天数，计算天数就涉及到闰年的问题，如何计算两个日期之间的闰年数成为了问题的关键。

虽然使用循环可以很容易的计算出来，如下：

int CountLeapYearByLoop(int nYearS, int nYearE){int nCount = 0;for(int nYear = nYearS; nYear < nYearE; ++nYear){if (IsLeapYear(nYear)){nCount++;}}return nCount;}

这个算法的时间复杂度是（nYearE-nYearS），显然不适宜年份相差很大的计算。

在网上找了好久，也看到一些算法，但是不能够对应所有的情况，有些算法在年份比较大时，差值就不对了。

今天偶然发现了一个规律，如下:一般情况下，两个日期之间的差值除以4取整，减去重叠的部分，就是它们之间的闰年数，但是，当结束日期的余数减去开始日期的余数需要借位时，闰年数需要加1，开始日期的余数为0的情况，当做4来看。

经过测试，该算法基本正确，算法如下：

int CountYearByModBet(int nYearS, int nYearE, int nBet){int nCount = 0;int nYearDec = nYearE - nYearS;int nModS = nYearS%nBet;int nModE = nYearE%nBet;int nModD = nYearDec%nBet;if (nModS == 0 || nModE < nModS){nCount = nYearDec/nBet + 1;}else{nCount = nYearDec/nBet;}return nCount;}int CountLeapYear(int nYearS, int nYearE){int nCount = 0;nCount = CountYearByModBet(nYearS, nYearE, 4)- CountYearByModBet(nYearS, nYearE, 100)+ CountYearByModBet(nYearS, nYearE, 400);return nCount;}

完整的算法和测试用例如下:

#include <iostream>bool IsLeapYear(int nYear){if ((nYear%400 == 0) || ((nYear%100 != 0) && (nYear%4 == 0))){return true;}else{return false;}}int CountYearByModBet(int nYearS, int nYearE, int nBet){int nCount = 0;int nYearDec = nYearE - nYearS;int nModS = nYearS%nBet;int nModE = nYearE%nBet;int nModD = nYearDec%nBet;if (nModS == 0 || nModE < nModS){nCount = nYearDec/nBet + 1;}else{nCount = nYearDec/nBet;}return nCount;}int CountLeapYear(int nYearS, int nYearE){int nCount = 0;nCount = CountYearByModBet(nYearS, nYearE, 4)- CountYearByModBet(nYearS, nYearE, 100)+ CountYearByModBet(nYearS, nYearE, 400);return nCount;}int CountLeapYearByLoop(int nYearS, int nYearE){int nCount = 0;for(int nYear = nYearS; nYear < nYearE; ++nYear){if (IsLeapYear(nYear)){nCount++;}}return nCount;}int main(){std::cout << "leap year count test " << std::endl;int nCount = 0;int nCountEx = 0;int nYearS = 2001;int nYearE = 9999;std::cout << "count the leap year from " << nYearS << " to " << nYearE << std::endl;std::cout << "count = " << CountLeapYear(nYearS,nYearE) << std::endl;std::cout << "loop count = " << CountLeapYearByLoop(nYearS,nYearE) << std::endl;#ifdef _DEBUGgetchar();#endif}