由於一個專案的需要，需要計算兩個日期之間的天數，計算天數就涉及到閏年的問題，如何計算兩個日期之間的閏年數成為了問題的關鍵。

雖然使用迴圈可以很容易的計算出來，如下：

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

這個演算法的時間複雜度是（nYearE-nYearS

在網上找了好久，也看到一些演算法，但是不能夠對應所有的情況，有些演算法在年份比較大時，差值就不對了。

今天偶然發現了一個規律，如下:一般情況下，兩個日期之間的差值除以4取整，減去重疊的部分，就是它們之間的閏年數，但是，當結束日期的餘數減去開始日期的餘數需要借位時，閏年數需要加1，開始日期的餘數為0的情況，當做4來看。

經過測試，該演算法基本正確，演算法如下：

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; }

完整的演算法和測試用例如下:

#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 }