Find the number of leap years between two year (s)

The first thing to encounter is this problem, the number of a given two can be divisible by 2,3,5 at the same time, it can be found that if a number can be divisible by 2,3,5 at the same time, then it will certainly be divisible by 30. We can write a function to determine whether a number can be divisible by 30, and then iterate through the interval of a given two number to judge on a single basis.

Solution one bool isnums (int num) {if (num%30==0) return True;return false;} int calculateNums2 (int begin,int end) {int count=0;for (int i=begin;i<=end;i++) {if (Isnums (i)) count++;} return count;}

But the time complexity of this method is too high.

There is a very ingenious way, is directly to find the [0,begin-1] can be divisible by 30 number of numbers;

Then the number of numbers that can be divisible by 30 in [0,end] is calculated.

The two subtracts are the number of numbers that can be divisible by 30 between [Begin,end].

Solution two int calculateNums1 (int begin,int end) {int left= (begin-1)/30;int right=end/30;int result=right-left;return Result ;}

This is the solution to the constant time.

The number of leap years can also be solved by this method.

1. Can be divisible by 4, but not divisible by 100.
2. Can be divisible by 400.

So the number of leap years in [0,begin-1] can be solved as follows:

(begin-1)/4-(begin-1)/100+ (begin-1)/400, which is the number of multiples of 4 in [0,begin-1] minus the number of multiples of 100, plus the number of multiples of 400. This is something that needs to be well thought out. This can be solved within a constant time.

#include <iostream>using namespace Std;int leapyears (int begin,int end) {int begin4= (begin-1)/4;int begin100= ( begin-1)/100;int begin400= (begin-1)/400;int left=begin4-begin100+begin400;int END4=END/4;   int End100=end/100;int end400=end/400;int right=end4-end100+end400;int result=right-left;return result;} int main () {cout<<leapyears (1950,2050) <<endl;return 0;}

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Find the number of leap years between two year (s)