累和真的是你想的这么简单吗

来自面试官的拷问 图片.png 结果 图片.png

到底是我的a,b和他的m,n不对应还是我没有进行非法判断呢?后来我想了下都不是,这题应该考的效率,于是:

import org.junit.Test;

import java.util.Date;

public class TestSum {

    //普通for循环累和
    public int sum1(int m, int n){
        int sum=0;
        for (int i = m; i <= n; i++) {
            sum += i;
        }
        return sum;
    }

    //高斯算法累和
    public int sum2(int m, int n){
        return (m+n)*(n-m+1)/2;
    }
    
    //递归累和
    public int sum3(int m, int n) {
        if (m > n) return 0;
        if (m == n) return m;
        return m + n + sum3(m + 1, n - 1);
    }

    @Test
    public void test1(){

        //普通循环效率最低
        Date start = new Date();
        int sum = sum1(0, 100000000);
        Date end = new Date();
        System.out.println("普通for循环结果"+sum);
        System.out.println("普通for循环耗时"+(end.getTime()-start.getTime()));
        System.out.println("==================================");


        //高斯运算最优
        start = new Date();
        sum = sum2(0, 100000000);
        end = new Date();
        System.out.println("高斯运算结果"+sum);
        System.out.println("高斯运算耗时"+(end.getTime()-start.getTime()));
        System.out.println("==================================");


        //递归运算效率不错,但在数字过大时后会内存溢出
        /*start = new Date();
        sum = sum3(0, 90000);
        end = new Date();
        System.out.println("递归运算结果"+sum);
        System.out.println("递归运算耗时"+(end.getTime()-start.getTime()));*/
    }

}

图片.png

算法理解:

图片.png