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 _DEBUG
getchar();
#endif

}