第五课

for循环

1.阶乘

n!=1×2×3×4×5×…×n

输入n，输出n！

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#include <stdio.h>

int main()
{
    int n;
    
    scanf("%d", &n);
    int fact = 1;
    
    int i = 1;
    while ( i<= n) {
        fact *= i;
        i++;
    }
    
    printf("%d!=%d\n", n, fact);
    
    return 0;
}

等同于

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#include <stdio.h>

int main()
{
    int n;
    
    scanf("%d", &n);
    int fact = 1;
    
    int i = 1;
    for ( i=1; i<=n; i++ ) {
        fact *= i;
    }
    
    printf("%d!=%d\n", n, fact);
    
    return 0;
}

正着来

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#include <stdio.h>

int main()
{
    int n;
    
    scanf("%d", &n);
    int fact = 1;
    
    int i = 1;
    for ( i=n; i>1; i-- ) {
        fact *= i;
    }
    
    printf("%d!=%d\n", n, fact);
    
    return 0;
}

反着来

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#include <stdio.h>

int main()
{
    int n;
    
    scanf("%d", &n);
    int fact = 1;
    
    int i = n;
    for ( n=n; i>1; i-- ) {
        fact *= n;
    }
    
    printf("%d!=%d\n", i, fact);
    
    return 0;
}

for ( i=1; i<=n; i++ )

三个表达式：

①初始条件

②循环继续的条件

③循环每一轮要做的事情

for循环像一个计数循环，设定一个计数器，初始化它，然后在计数器到达某值之前，重复执行循环体，而每执行一轮循环，计数器值以一定步进进行调整，比如加1或者减1

结构

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for ( i=a; i<b; i = i+c ) {
    printf("%d", i)
}

读成:对于一开始的i=a，当i<b时，重复做循环体，每一轮循环在做完循环体内语句后，使得i=i+c。

※做求和的程序时，记录结果的变量应该初始化为0，而做求积的变量时，记录结果的变量应该初始化为1

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#include <stdio.h>

int main()
{
    int n;
    
    scanf("%d", &n);
    int fact = 1;
    
    int i = 1;
    for ( int i=1; i<=n; i++ ) {
        fact *= i;
    }
    
    printf("%d!=%d\n", n, fact);
    
    return 0;
}

（只能在C99里）

2.循环次数

for ( i=0; i<n; i++ )

则循环的次数是n，而循环结束以后，i的值是n。循环的控制变量i，是选择从0开始还是从1开始，是判断i<n还是判断i<=n,对循环的次数，循环结束后变量的值都有影响。

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#include <stdio.h>

int main()
{
    int 1;
    
    for ( i=0; i<n; i++ ) {
        printf("i=%d", i);
    }
    printf("\n最后i=%d", i);
    
    return 0;
}

输出：

i=0 i=1 i=2 i=3 i=4 … i=n-1

最后i=n

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#include <stdio.h>

int main()
{
    int 1;
    
    for ( i=1; i<=n; i++ ) {
        printf("i=%d", i);
    }
    printf("\n最后i=%d", i);
    
    return 0;
}

输出：

i=1 i=2 i=3 i=4 … i=n

最后i=n+1

for==while

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for ( int i=1; i<=n; i++ ) {
    fact *= i;
}

等同于

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int i=1;
while ( i<=n ) {
    fact *= i;
    i++;
}

任何一个for循环都可以改写成一个while循环

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for (初始动作; 条件; 每轮的动作) {
    
}

for (;条件;) == while (条件)

※

①如果有固定次数，用for

②如果必须执行一次，用do-while

③其他情况用while

二、循环控制

1.素数

只能被1和自己整除的数，不包括1的数是素数

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#include <stdio.h>

int main()
{
    int x;
    
    scanf("%d", &x);
    
    int i;
    int isPrime = 1;
    for ( i=2; i<x; i++ ) {
        if ( x % i == 0 ) {
            isPrime = 0;
            break;
        }
    }
    if ( isPrime == 1 ) {
        printf("是素数\n");
    } else {
        printf("不是素数\n");
    }
    
    return 0;
}
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#include <stdio.h>

int main()
{
    int x;
    
    scanf("%d", &x);
    
    int i;
    int isPrime = 1;
    for ( i=2; i<x; i++ ) {
        if ( x % i == 0 ) {
            break;
        }
    }
    if ( i < x ) {
        printf("不是素数\n");
    } else {
        printf("是素数\n");
    }
    
    return 0;
}

break：跳出循环

continue：跳过循环这一轮剩下的语句进入下一轮

2.循环的嵌套

循环里面的还是循环

n以内的素数

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#include <stdio.h>

int main()
{
    int x;
    
    for ( x=1; x<=n; x++ ) {
        int i;
        int isPrime = 1;
        for ( i=2; i<x; i++ ) {
            if ( x % i == 0 ) {
               isPrime = 0;
               break;
            }
        }
        if ( isPrime == 1 ) {
            printf("%d ", x);
        }
    }
    
    return 0;
}

前n的素数

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#include <stdio.h>

int main()
{
    int x;
    int cnt = 0;
    
    for ( x=1; cnt<n; x++ ) {
        int i;
        int isPrime = 1;
        for ( i=2; i<x; i++ ) {
            if ( x % i == 0 ) {
               isPrime = 0;
               break;
            }
        }
        if ( isPrime == 1 ) {
            cnt ++;
            printf("%d ", x);
        }
    }
    
    return 0;
}

等同于

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#include <stdio.h>

int main()
{
    int x;
    int cnt = 0;
    
    x = 1;
    while ( cnt < 50 ) {
        int i;
        int isPrime = 1;
        for ( i=2; i<x; i++ ) {
            if ( x % i == 0 ) {
               isPrime = 0;
               break;
            }
        }
        if ( isPrime == 1 ) {
            cnt ++;
            printf("%d ", x);
        }
        x++;
    }
    
    return 0;
}

排一排不舒服

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#include <stdio.h>

int main()
{
    int x;
    int cnt = 0;
    
    x = 1;
    while ( cnt < 50 ) {
        int i;
        int isPrime = 1;
        for ( i=2; i<x; i++ ) {
            if ( x % i == 0 ) {
               isPrime = 0;
               break;
            }
        }
        if ( isPrime == 1 ) {
            cnt ++;
            printf("%d ", x);
            if ( cnt %5 == 0 ) {
                printf("\n");
            }
        }
        x++;
    }
    
    return 0;
}

每5个一行

没对齐不舒服

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#include <stdio.h>

int main()
{
    int x;
    int cnt = 0;
    
    x = 1;
    while ( cnt < 50 ) {
        int i;
        int isPrime = 1;
        for ( i=2; i<x; i++ ) {
            if ( x % i == 0 ) {
               isPrime = 0;
               break;
            }
        }
        if ( isPrime == 1 ) {
            cnt ++;
            printf("%d\t", x);
            if ( cnt %5 == 0 ) {
                printf("\n");
            }
        }
        x++;
    }
    
    return 0;
}

对齐

3.从嵌套循环跳出

凑硬币

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#include <stdio.h>

int main()
{
    int x;
    int one, two, five;
    
    scanf("%d", &x);
    for ( one = 1; one < x*10; one++ ) {
        for ( two = 1; two < x*10/2; two++ ) {
            for ( five = 1; five < x*10/5; five++ ) {
                if( one + two*2 + five*5 == x*10 ) {
                    printf("可以用%d个1角加%d个2角加%d个5角得到%d元\n", one, two, five, x);
                } 
            }
        }
    }
    
    return 0;
}

得到一种结果

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#include <stdio.h>

int main()
{
    int x;
    int one, two, five;
    int exit = 0;
    
    scanf("%d", &x);
    for ( one = 1; one < x*10; one++ ) {
        for ( two = 1; two < x*10/2; two++ ) {
            for ( five = 1; five < x*10/5; five++ ) {
                if( one + two*2 + five*5 == x*10 ) {
                    printf("可以用%d个1角加%d个2角加%d个5角得到%d元\n", one, two, five, x);
                    exit = 1;
                    break;
                } 
            }
            if ( exit == 1 ) break;
        }
        if ( exit == 1 ) break;
    }
    
    return 0;
}

等同于

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#include <stdio.h>

int main()
{
    int x;
    int one, two, five;
    
    scanf("%d", &x);
    for ( one = 1; one < x*10; one++ ) {
        for ( two = 1; two < x*10/2; two++ ) {
            for ( five = 1; five < x*10/5; five++ ) {
                if( one + two*2 + five*5 == x*10 ) {
                    printf("可以用%d个1角加%d个2角加%d个5角得到%d元\n", one, two, five, x);
                    goto out;
                    
                } 
            }
        }
    }
out:
    
    return 0;
}

三、应用

1.前n项求和

f(n) = 1+1/2+1/3+1/4+…+1/n

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#include <stdio.h>

int main()
{
    int n;
    int i;
    double sum = 0.0;
    
    scanf("%d", &n);
    for ( i = 1; i<=n; i++ ) {
        sum += 1.0/i;
    }
    
    printf("f(%d)=%f\n", n, sum);
    
    return 0;
}

f(n) = 1-1/2+1/3-1/4+…+1/n

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#include <stdio.h>

int main()
{
    int n;
    int i;
    double sum = 0.0;
    int sign = 1;
    
    scanf("%d", &n);
    for ( i = 1; i<=n; i++ ) {
        sum += sign*1.0/i;
        sign = -sign;
    }
    
    printf("f(%d)=%f\n", n, sum);
    
    return 0;
}

或者

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#include <stdio.h>

int main()
{
    int n;
    int i;
    double sum = 0.0;
    double sign = 1;
    
    scanf("%d", &n);
    for ( i = 1; i<=n; i++ ) {
        sum += sign/i;
        sign = -sign;
    }
    
    printf("f(%d)=%f\n", n, sum);
    
    return 0;
}

2.最大公约数

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#include <stdio.h>

int main()
{
    int a,b;
    int min;
    
    scanf("%d %d", &a, &b);
    if ( a<b ) {
        min = a;
    } else {
        min = b;
    }
    int ret = 0;
    int i;
    for ( i = 1; i < min; i++ ) {
        if ( a%i == 0 ) {
            if ( b%i == 0 ) {
                ret = i;
            }
        }
    }
    printf("%d和%d的最大公约数是%d.\n", a, b, ret);
    
    return 0;
}

等同于

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#include <stdio.h>
int main()
{
    int a,b;
    int t;
    scanf("%d %d", &a, &b);
    
    while ( b!=0 ) {
        t = a%b;
        a=b;
        b=t;
    }
    print("gcd=%d\n", a);
    
    return 0;
}

3.整数分解

反向输出

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#include <stdio.h>

int main()
{
    int x;
    scanf("%d", &x);
    
    do {
        int d = x % 10;
        printf("%d", d);
        if ( x > 9 ) {
            printf(" ");
        }
        x /= 10;
    } while ( x > 0 );
    printf("\n");
    
    return 0;
}

正向输出

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#include <stdio.h>

int main()
{
    int x;
    scanf("%d", &x);
    
    int t=0;
    do {
        int d = x%10;
        t = t*10+d;
        x /= 10;
    } while ( x>0 );
    x = t;
    do {
        int d = x % 10;
        printf("%d", d);
        if ( x > 9 ) {
            printf(" ");
        }
        x /= 10;
    } while ( x > 0 );
    printf("\n");
    
    return 0;
}

（末尾不能有0）

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#include <stdio.h>

int main()
{
    int x;
    scanf("%d", &x);
    
    int cnt = 0;
    int mask = 1;
    while ( x>9 ) {
        x/=10;
        mask *= 10;
    } 
    
    do {
        int d = x / mask;
        printf("%d", d);
        if ( mask > 9 ) {
            printf(" ");
        }
        x %= mask;
        mask /= 10;
    } while ( mask>0 );
    
    printf("\n");
    
    return 0;
}

（末尾为0）