被3整除

# coding=utf-8
while 1:
    try:
        start,end=map(int,raw_input().split())
        count=0
        #left=0
        def count_3(num):
            if num%3==0:
                count=(num/3)*2
            elif num%3==1:
                count=(num/3)*2
            elif num%3==2:
                count=(num/3)*2+1
            return count
        print count_3(end)-count_3(start-1)
        break
    except:
        break
做了很久最后发现蠢是原罪，找规律就好了，三个数中，×√√，所以就不会超出内存。刚开始做的时候一直往求和能否被3整除上面想，即是每逢3清零重新count还是会超出内存只通过百分之七十

核心思想

• 第一步：所有位上的数字之和能够被3整除，则这个数能够被3整除。
• 第二步：所有位数之和能被3整除的这个验证过程再简化，我们能够发现：

1            
     1%3 = 1     
     1%3 = 1
12            
    (1+2)%3 = 0  
    ((1%3)+2%3)%3 = 0
123  
   (1+2+3)%3 = 0
    (((1%3)+2%3)%3+3%3)%3 = 0;
.....
......

// 这样是为了避免数字过大而超出了int范围。

import java.util.*;
public class Main{
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int count = 0;
        int start = sc.nextInt();
        int end = sc.nextInt();
        int pre = 0;
        int i = 0;
        //这里用等差数列的求和公式会超出int范围
        for(;i<start;i++){
            pre+=i%3;
            pre%=3;
        }
        for(;i<=end;i++){
            int tempMod = i%3;
            pre+=tempMod;
            if(pre%3==0){
                count++;
            }
            pre = pre%3;
        }
        System.out.println(count);
    }
}

import sys

def num(x):
    return x - (x+2)/3

l, r = [int(x) for x in sys.stdin.readline().split()]
print num(r)-num(l-1)

importjava.util.Scanner;  public class Test {public static void main(String[] args) {
        Scanner sc = newScanner(System.in);  int a = sc.nextInt();  int b = sc.nextInt();  long result = count(a ,b);    System.out.println(result);  } private static int count(int start,int end){  if(start > end){  return 0;   }  intnum =0;  for (longi = start-1; i <= end;i++) {  longyushu = (((1+i))*i/2)%3;  if (yushu==0){
            num++;   }
     }  return num;    }
}

	package tester0820;

import java.util.Scanner;

public class Main {
    private long a;
    private long b;
    
    public Main(long a, long b){
        this.a = a;
        this.b = b;
    }
    
    @SuppressWarnings("resource")
    public static void main(String[] args){
        Scanner in = new Scanner(System.in);
        long x = in.nextLong();
        long y = in.nextLong();
        Main m = new Main(x, y);
        System.out.println(m.test());
    }
    
    public int test(){
        if (a <= b) {
            int count = 0;
            for(long i=a; i<=b; i++) {
                if(i%3 != 1) {



	                count ++;
                }
            }
            return count;
        } else {
            return 0;
        }
    }
}
	

		
	

	
	

		
		

			
			

				
				

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						importjava.util.*;
					

					

						publicclassMain{
					

					

						    publicstaticvoidmain(String[] args){
					

					

						        Scanner sc = newScanner(System.in);
					

					

						        longa = sc.nextLong();
					

					

						        longb = sc.nextLong();
					

					

						        longcount = 0;
					

					

						        longsum = 0;
					

					

						        for(longk = 1; k <= a; k++){
					

					

						                sum = sum + k;
					

					

						            }
					

					

						        if(sum % 3== 0){
					

					

						            count++;
					

					

						        }
					

					

						        for(longr = a+1; r <= b; r++){
					

					

						            sum = sum + r;
					

					

						            if(sum % 3== 0){
					

					

						                    count++;
					

					

						                }
					

					

						        }
					

					

						        System.out.println(count);
					

					

						    }
					

					

						}