Day03

试题A 门牌制作

#include<stdio.h>
int main() {
	int count = 0;
	int a, b, c, d;
	for (int i = 0; i <= 2020; i++) {
		a = i / 1000;
		b = (i / 100) % 10;
		c = (i / 10) % 10;
		d = i % 10;
		if (a == 2) {
			count++;
		}
		if (b == 2) {
			count++;
		}
		if (c == 2) {
			count++;
		}
		if (d == 2) {
			count++;
		}
	}
	printf("%d", count);
	return 0;
}

答案：624

试题B 既约分数

最大公约数百度百科

/*
 辗转相除法
 */

#include<stdio.h>
int main() {
	int quotient = 0; //商
	int remainder = 1; //余数
	int count = 0; //计数
	int tempA = 0, tempB = 0; //临时变量

	for (int numerator = 1; numerator <= 2020; numerator++) { //分子
		for (int denominator = 1; denominator <= 2020; denominator++) { //分母
			tempA = numerator;
			tempB = denominator;
			while (remainder != 0) {
				quotient = tempA / tempB;
				remainder = tempA % tempB;
				tempA = tempB;
				tempB = remainder;
			}
			if (tempA == 1) {
				count++;
			}
			remainder = 1;
		}
	}
	printf("%d", count);
	return 0;
}

答案：2481215

/*
  更相损减术
 */
#include<stdio.h>
#include<math.h>
int main() {
    int count1 = 0; //计数：有几个既约分数
    int count2 = 0; //计数：共约去几个2
    int tempA = 0, tempB = 0; //临时变量 
    int difference = 1; //差
    int temp;
    for (int numerator = 1; numerator <= 2020; numerator++) {
        for (int denominator = 1; denominator <= 2020; denominator++) {
            tempA = numerator;
            tempB = denominator;
            while ((tempA % 2 == 0) && (tempB % 2 == 0)) {
                tempA = tempA / 2;
                tempB = tempB / 2;
                count2++;
            }
            while (difference != 0) {
                if (tempA < tempB) {
                    temp = tempA;
                    tempA = tempB;
                    tempB = temp;
                }
                difference = tempA - tempB;
                tempA = difference;
            }
            if ((tempB * int(pow(2, count2))) == 1) {
                count1++;
            }
            difference = 1;
            count2 = 0;
        }
    }
    printf("%d", count1);
    return 0;
}

答案：2481215

试题C 蛇形填数

#include<stdio.h>
#define M 40 //填完有a[19][19]斜行最多有第40行第40列的元素
int main() {
	int a[M][M] = { 0 };
	int count = 1; //给数组赋值，依次加一
	int i, j;
	for (int k = 0;k < 780; k++) { //下角标的和，填完有a[19][19]斜行最多到780
		for (i = 0; i < M; i++) {
			for (j = 0; j < M; j++) {
				//反对角线方向填数字
				//偶数行反对角线，下角标加起来和为奇数
				if (i + j == k && k % 2 == 1) {
					a[i][j] = count;
					count++;
				}
				//奇数行反对角线，下角标加起来和为偶数
				if (i + j == k && k % 2 == 0) {
					a[j][i] = count;
					count++;
				}
			}
		}
	}
	printf("%d\n", a[19][19]); //容易出错，第20行第20列
	return 0;
}

找规律

试题D 跑步锻炼

#include<stdio.h>
int main() {
	int year = 2000, month = 1, day = 1, week = 5;
	int d[13] = { 0, 31, 0, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31 };
	int answer = 0;
	for (; year <= 2020; year++) {
		if ((year % 4 == 0 && year % 100 != 0) || year % 400 == 0) {
			d[2] = 29;
		} 
		for (; month <= 12; month++) {
			if (year == 2020 && month == 10) {
				goto outloop;
			}
			for (; day <= d[month]; day++) {
				week = (week + 1) % 7;
				if (week == 1 || day == 1) {
					answer = answer + 2;
				}
				else {
					answer++;
				}
			}
			day = 1;
		}
		month = 1;
		d[2] = 28; 
	}
	outloop:
	printf("%d", answer + 2);
	return 0;
}

答案：8879

https://blog.csdn.net/qq_43738331/article/details/110729821这个博客代码写的更清晰