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C のランダム関数

このトピックでは、ランダム関数と、C プログラミング言語で乱数を生成する方法について学びます。ご存知のとおり、ランダム関数は、定義された 2 つの数値の間で乱数を見つけるために使用されます。 C プログラミング言語では、ランダム関数には rand() 関数と srand() 関数という 2 つの組み込み関数があります。これらの関数をC言語で理解してみましょう。

C のランダム関数

rand()関数

の中に C プログラミング言語 , rand() 関数は、[0, RAND_MAX] の範囲の乱数を生成するライブラリ関数です。プログラムで rand() 関数を使用するときは、 stdlib.h rand() 関数が stdlib ヘッダー ファイルで定義されているためです。シード番号は含まれません。したがって、同じプログラムを何度も実行すると、同じ値が返されます。

注: srand() 関数を呼び出さずに rand() 関数を使用して乱数を生成した場合、プログラムが実行されるたびに同じ一連の数値が返されます。

構文

 int rand (void) 

rand() 関数は、0 から RAND_MAX までの範囲のランダムな整数を返します。 RAND_MAX は、stdlib.h ヘッダー ファイルで定義されるシンボリック定数で、その値は C ライブラリに応じて 32767 より大きくなりますが、32767 より小さくなります。

文字列から整数への変換

rand()関数を使用して乱数を生成する

rand()関数を使って乱数を取得するプログラムを書いてみましょう。

かどうか

 #include #include #include void main() { // use rand() function to generate the number printf (' The random number is: %d', rand()); printf ('
 The random number is: %d', rand()); printf (' 
 The random number is: %d', rand()); printf ('
 The random number is: %d', rand()); getch(); } 

出力

 The random number is: 41 The random number is: 18467 The random number is: 6334 The random number is: 26500 

rand()関数を使用して5つの乱数を生成します

C言語のrand()関数を使って5つの乱数を生成するプログラムを考えてみましょう。

ランダム.c

 #include #include int main() { int i; /* It returns the same sequence of random number on every execution of the program. */ printf(' Random Numbers are: 
&apos;); for (i = 0; i <5; i++) { printf(' %d', rand()); } return 0; < pre> <p> <strong>Output</strong> </p> <pre> Random Numbers are: 41 18467 6334 26500 19169 </pre> <p> <strong>2nd execution of the program:</strong> </p> <pre> Random Numbers are: 41 18467 6334 26500 19169 </pre> <p> <strong>3rd execution of the program</strong> </p> <pre> Random Numbers are: 41 18467 6334 26500 19169 </pre> <p>As we can see in the above output, it returns the same sequence of random numbers on every execution of the programming code.</p> <h3>Generate 10 random numbers from 1 to 100 using rand() function</h3> <p>Let&apos;s consider a program to find the random number in C using rand() function.</p> <p> <strong>rand_num.c</strong> </p> <pre> #include #include #include int main() { // declare the local variables int i, num; printf (&apos; Program to get the random number from 1 to 100 
&apos;); for (i = 1; i <= 100 10; i++) { num="rand()" % + 1; use rand() function to get the random number printf (' %d ', num); getch(); } < pre> <p> <strong>Output</strong> </p> <pre> Program to get the random number from 1 to 100 42 68 35 1 70 25 79 59 63 65 </pre> <h2>srand() function</h2> <p>The srand() function is a C library function that determines the initial point to generate different series of pseudo-random numbers. A srand() function cannot be used without using a rand() function. The srand() function is required to set the value of the seed only once in a program to generate the different results of random integers before calling the rand() function.</p> <h3>Syntax</h3> <pre> int srand (unsigned int seed) </pre> <p> <strong>seed</strong> : It is an integer value that contains a seed for a new sequence of pseudo-random numbers.</p> <h3>Generate the random numbers using srand() function</h3> <p>Let&apos;s write a program to get the random numbers using srand() function in C.</p> <p> <strong>srandNum.c</strong> </p> <pre> #include #include #include // use time.h header file to use time int main() { int num, i; time_t t1; // declare time variable printf(&apos; Enter a number to set the limit for a random number 
&apos;); scanf (&apos; %d&apos;, &amp;num); /* define the random number generator */ srand ( (unsigned) time (&amp;t1)); // pass the srand() parameter printf(&apos;
&apos;); // print the space /* generate random number between 0 to 50 */ for (i = 0; i <num; i++) { printf( '%d 
', rand() % 50); } return 0; < pre> <p> <strong>Output</strong> </p> <pre> Enter a number to set the limit for a random number 10 44 32 23 35 6 33 1 4 22 18 </pre> <p> <strong>2nd execution of the program:</strong> </p> <pre> Enter a number to set the limit for a random number 15 13 30 24 27 4 30 28 35 36 13 44 39 21 5 7 </pre> <p>As we can see in the above Output, it returns different sequences of random numbers on every execution of the programming code.</p> <h3>Generate the random numbers using srand() and time() function</h3> <p>Let&apos;s write a program to get the random numbers using srand() with time() function.</p> <p> <strong>srand_time.c</strong> </p> <pre> #include #include int main() { int random = rand(); // assign the rand() function to random variable srand( time(0)); printf( &apos; Seed = %d&apos;, time(0)); printf( &apos; Random number = %d&apos;, random); return 0; } </pre> <p> <strong>Output</strong> </p> <pre> Seed = 1619450091 Random number = 41 </pre> <h3>Get a seeding value and print the random numbers using srand() function</h3> <p>Let&apos;s write a program to get the seed value and random numbers using srand() function.</p> <p> <strong>srand_time.c</strong> </p> <pre> #include #include int main() { int count; unsigned int seed; // use for randomize number printf(&apos; Enter the Seeding value: 
&apos;); scanf(&apos; %u&apos;, &amp;seed); srand (seed); // pass parameter // generate random number between 1 to 6 for (count = 1; count <= 1 5="=" 10; ++count) { printf(' %5d', + (rand () % 6)); if (count 0) print the number in next line puts(' '); } return 0; < pre> <p> <strong>Output</strong> </p> <pre> Enter the Seeding value: 10 6 4 3 3 6 3 3 1 3 4 </pre> <p> <strong>2nd execution of the program:</strong> </p> <pre> Enter the Seeding value: 20 2 4 2 4 5 4 3 5 1 4 </pre> <p> <strong>3rd execution of the program:</strong> </p> <pre> Enter the Seeding value: 25 1 6 1 6 4 4 1 4 1 3 </pre> <p>As we can see in the above Output, when we executed the same program again and again with different seeds values, it displays the different sequences of a random number from 1 to 6.</p> <h3>Generate the random number using the random function</h3> <p>Let&apos;s create a program to use stadlib header file to get the random number using random function in C.</p> <p> <strong>func.c</strong> </p> <pre> #include #include #include int main() { int i, num, max, temp; printf (&apos; Enter a number to set the limit of random numbers 
&apos;); scanf (&apos;%d&apos;, num); printf (&apos; Enter the maximum number from you want to get the random number: 
&apos;); scanf (&apos;%d&apos;, max); printf (&apos; %d random number from 0 to %d number are: 
&apos;, num, max); randomize(); for (i = 1; i <= num; i++) { temp="random(max)" * use random() function to get the random number printf (' %d ', temp); print } getch(); < pre> <p> <strong>Output</strong> </p> <pre> Enter a number to set the limit of random numbers 17 Enter the maximum number from you want to get the random number: 100 15 random number from 0 to 100 number are: 42 68 35 1 70 25 79 59 63 28 75 89 90 43 7 4 65 </pre> <h2>Program to generate float random numbers</h2> <p>Let&apos;s consider a program to print the float random numbers in C.</p> <p> <strong>random1.c</strong> </p> <pre> #include #include #include int main() { srand( (unsigned int) time(NULL)); float f1 = 5.0; int i; printf(?Float random numbers are: 
?); for (i = 0; i<10; i++) { printf('%f', ((float) rand() rand_max) * f1); printf('
'); } return 0; < pre> <p> <strong>Output</strong> </p> <pre> Float random numbers are: 1.208075 1.658376 4.645070 2.298807 3.117161 0.961486 4.115573 4.336223 2.894833 2.249825 </pre> <hr></10;></pre></=></pre></=></pre></num;></pre></=></pre></5;>

プログラムの 2 回目の実行:

 Random Numbers are: 41 18467 6334 26500 19169 

プログラムの 3 回目の実行

Javaは文字を文字列に変換します
 Random Numbers are: 41 18467 6334 26500 19169 

上記の出力でわかるように、プログラミング コードが実行されるたびに同じ乱数のシーケンスが返されます。

rand()関数を使用して1から100までの10個の乱数を生成します

C言語でrand()関数を使って乱数を求めるプログラムを考えてみましょう。

rand_num.c

 #include #include #include int main() { // declare the local variables int i, num; printf (&apos; Program to get the random number from 1 to 100 
&apos;); for (i = 1; i <= 100 10; i++) { num="rand()" % + 1; use rand() function to get the random number printf (\' %d \', num); getch(); } < pre> <p> <strong>Output</strong> </p> <pre> Program to get the random number from 1 to 100 42 68 35 1 70 25 79 59 63 65 </pre> <h2>srand() function</h2> <p>The srand() function is a C library function that determines the initial point to generate different series of pseudo-random numbers. A srand() function cannot be used without using a rand() function. The srand() function is required to set the value of the seed only once in a program to generate the different results of random integers before calling the rand() function.</p> <h3>Syntax</h3> <pre> int srand (unsigned int seed) </pre> <p> <strong>seed</strong> : It is an integer value that contains a seed for a new sequence of pseudo-random numbers.</p> <h3>Generate the random numbers using srand() function</h3> <p>Let&apos;s write a program to get the random numbers using srand() function in C.</p> <p> <strong>srandNum.c</strong> </p> <pre> #include #include #include // use time.h header file to use time int main() { int num, i; time_t t1; // declare time variable printf(&apos; Enter a number to set the limit for a random number 
&apos;); scanf (&apos; %d&apos;, &amp;num); /* define the random number generator */ srand ( (unsigned) time (&amp;t1)); // pass the srand() parameter printf(&apos;
&apos;); // print the space /* generate random number between 0 to 50 */ for (i = 0; i <num; i++) { printf( \'%d 
\', rand() % 50); } return 0; < pre> <p> <strong>Output</strong> </p> <pre> Enter a number to set the limit for a random number 10 44 32 23 35 6 33 1 4 22 18 </pre> <p> <strong>2nd execution of the program:</strong> </p> <pre> Enter a number to set the limit for a random number 15 13 30 24 27 4 30 28 35 36 13 44 39 21 5 7 </pre> <p>As we can see in the above Output, it returns different sequences of random numbers on every execution of the programming code.</p> <h3>Generate the random numbers using srand() and time() function</h3> <p>Let&apos;s write a program to get the random numbers using srand() with time() function.</p> <p> <strong>srand_time.c</strong> </p> <pre> #include #include int main() { int random = rand(); // assign the rand() function to random variable srand( time(0)); printf( &apos; Seed = %d&apos;, time(0)); printf( &apos; Random number = %d&apos;, random); return 0; } </pre> <p> <strong>Output</strong> </p> <pre> Seed = 1619450091 Random number = 41 </pre> <h3>Get a seeding value and print the random numbers using srand() function</h3> <p>Let&apos;s write a program to get the seed value and random numbers using srand() function.</p> <p> <strong>srand_time.c</strong> </p> <pre> #include #include int main() { int count; unsigned int seed; // use for randomize number printf(&apos; Enter the Seeding value: 
&apos;); scanf(&apos; %u&apos;, &amp;seed); srand (seed); // pass parameter // generate random number between 1 to 6 for (count = 1; count <= 1 5="=" 10; ++count) { printf(\' %5d\', + (rand () % 6)); if (count 0) print the number in next line puts(\' \'); } return 0; < pre> <p> <strong>Output</strong> </p> <pre> Enter the Seeding value: 10 6 4 3 3 6 3 3 1 3 4 </pre> <p> <strong>2nd execution of the program:</strong> </p> <pre> Enter the Seeding value: 20 2 4 2 4 5 4 3 5 1 4 </pre> <p> <strong>3rd execution of the program:</strong> </p> <pre> Enter the Seeding value: 25 1 6 1 6 4 4 1 4 1 3 </pre> <p>As we can see in the above Output, when we executed the same program again and again with different seeds values, it displays the different sequences of a random number from 1 to 6.</p> <h3>Generate the random number using the random function</h3> <p>Let&apos;s create a program to use stadlib header file to get the random number using random function in C.</p> <p> <strong>func.c</strong> </p> <pre> #include #include #include int main() { int i, num, max, temp; printf (&apos; Enter a number to set the limit of random numbers 
&apos;); scanf (&apos;%d&apos;, num); printf (&apos; Enter the maximum number from you want to get the random number: 
&apos;); scanf (&apos;%d&apos;, max); printf (&apos; %d random number from 0 to %d number are: 
&apos;, num, max); randomize(); for (i = 1; i <= num; i++) { temp="random(max)" * use random() function to get the random number printf (\' %d \', temp); print } getch(); < pre> <p> <strong>Output</strong> </p> <pre> Enter a number to set the limit of random numbers 17 Enter the maximum number from you want to get the random number: 100 15 random number from 0 to 100 number are: 42 68 35 1 70 25 79 59 63 28 75 89 90 43 7 4 65 </pre> <h2>Program to generate float random numbers</h2> <p>Let&apos;s consider a program to print the float random numbers in C.</p> <p> <strong>random1.c</strong> </p> <pre> #include #include #include int main() { srand( (unsigned int) time(NULL)); float f1 = 5.0; int i; printf(?Float random numbers are: 
?); for (i = 0; i<10; i++) { printf(\'%f\', ((float) rand() rand_max) * f1); printf(\'
\'); } return 0; < pre> <p> <strong>Output</strong> </p> <pre> Float random numbers are: 1.208075 1.658376 4.645070 2.298807 3.117161 0.961486 4.115573 4.336223 2.894833 2.249825 </pre> <hr></10;></pre></=></pre></=></pre></num;></pre></=>

srand() 関数

srand() 関数は、さまざまな一連の擬似乱数を生成するための開始点を決定する C ライブラリ関数です。 srand() 関数は、 rand() 関数を使用せずに使用することはできません。 srand() 関数は、rand() 関数を呼び出す前に、ランダムな整数のさまざまな結果を生成するために、プログラム内でシードの値を 1 回だけ設定する必要があります。

構文

 int srand (unsigned int seed) 

シード : これは、新しい擬似乱数シーケンスのシードを含む整数値です。

srand() 関数を使用して乱数を生成する

Cのsrand()関数を使って乱数を取得するプログラムを書いてみましょう。

srandNum.c

 #include #include #include // use time.h header file to use time int main() { int num, i; time_t t1; // declare time variable printf(&apos; Enter a number to set the limit for a random number 
&apos;); scanf (&apos; %d&apos;, &amp;num); /* define the random number generator */ srand ( (unsigned) time (&amp;t1)); // pass the srand() parameter printf(&apos;
&apos;); // print the space /* generate random number between 0 to 50 */ for (i = 0; i <num; i++) { printf( \'%d 
\', rand() % 50); } return 0; < pre> <p> <strong>Output</strong> </p> <pre> Enter a number to set the limit for a random number 10 44 32 23 35 6 33 1 4 22 18 </pre> <p> <strong>2nd execution of the program:</strong> </p> <pre> Enter a number to set the limit for a random number 15 13 30 24 27 4 30 28 35 36 13 44 39 21 5 7 </pre> <p>As we can see in the above Output, it returns different sequences of random numbers on every execution of the programming code.</p> <h3>Generate the random numbers using srand() and time() function</h3> <p>Let&apos;s write a program to get the random numbers using srand() with time() function.</p> <p> <strong>srand_time.c</strong> </p> <pre> #include #include int main() { int random = rand(); // assign the rand() function to random variable srand( time(0)); printf( &apos; Seed = %d&apos;, time(0)); printf( &apos; Random number = %d&apos;, random); return 0; } </pre> <p> <strong>Output</strong> </p> <pre> Seed = 1619450091 Random number = 41 </pre> <h3>Get a seeding value and print the random numbers using srand() function</h3> <p>Let&apos;s write a program to get the seed value and random numbers using srand() function.</p> <p> <strong>srand_time.c</strong> </p> <pre> #include #include int main() { int count; unsigned int seed; // use for randomize number printf(&apos; Enter the Seeding value: 
&apos;); scanf(&apos; %u&apos;, &amp;seed); srand (seed); // pass parameter // generate random number between 1 to 6 for (count = 1; count <= 1 5="=" 10; ++count) { printf(\' %5d\', + (rand () % 6)); if (count 0) print the number in next line puts(\' \'); } return 0; < pre> <p> <strong>Output</strong> </p> <pre> Enter the Seeding value: 10 6 4 3 3 6 3 3 1 3 4 </pre> <p> <strong>2nd execution of the program:</strong> </p> <pre> Enter the Seeding value: 20 2 4 2 4 5 4 3 5 1 4 </pre> <p> <strong>3rd execution of the program:</strong> </p> <pre> Enter the Seeding value: 25 1 6 1 6 4 4 1 4 1 3 </pre> <p>As we can see in the above Output, when we executed the same program again and again with different seeds values, it displays the different sequences of a random number from 1 to 6.</p> <h3>Generate the random number using the random function</h3> <p>Let&apos;s create a program to use stadlib header file to get the random number using random function in C.</p> <p> <strong>func.c</strong> </p> <pre> #include #include #include int main() { int i, num, max, temp; printf (&apos; Enter a number to set the limit of random numbers 
&apos;); scanf (&apos;%d&apos;, num); printf (&apos; Enter the maximum number from you want to get the random number: 
&apos;); scanf (&apos;%d&apos;, max); printf (&apos; %d random number from 0 to %d number are: 
&apos;, num, max); randomize(); for (i = 1; i <= num; i++) { temp="random(max)" * use random() function to get the random number printf (\' %d \', temp); print } getch(); < pre> <p> <strong>Output</strong> </p> <pre> Enter a number to set the limit of random numbers 17 Enter the maximum number from you want to get the random number: 100 15 random number from 0 to 100 number are: 42 68 35 1 70 25 79 59 63 28 75 89 90 43 7 4 65 </pre> <h2>Program to generate float random numbers</h2> <p>Let&apos;s consider a program to print the float random numbers in C.</p> <p> <strong>random1.c</strong> </p> <pre> #include #include #include int main() { srand( (unsigned int) time(NULL)); float f1 = 5.0; int i; printf(?Float random numbers are: 
?); for (i = 0; i<10; i++) { printf(\'%f\', ((float) rand() rand_max) * f1); printf(\'
\'); } return 0; < pre> <p> <strong>Output</strong> </p> <pre> Float random numbers are: 1.208075 1.658376 4.645070 2.298807 3.117161 0.961486 4.115573 4.336223 2.894833 2.249825 </pre> <hr></10;></pre></=></pre></=></pre></num;>

プログラムの 2 回目の実行:

 Enter a number to set the limit for a random number 15 13 30 24 27 4 30 28 35 36 13 44 39 21 5 7 

上記の出力でわかるように、プログラミング コードが実行されるたびに、異なる乱数シーケンスが返されます。

srand() 関数と time() 関数を使用して乱数を生成します。

srand() と time() 関数を使用して乱数を取得するプログラムを書いてみましょう。

VLCでYouTubeをダウンロード

srand_time.c

 #include #include int main() { int random = rand(); // assign the rand() function to random variable srand( time(0)); printf( &apos; Seed = %d&apos;, time(0)); printf( &apos; Random number = %d&apos;, random); return 0; } 

出力

 Seed = 1619450091 Random number = 41 

srand() 関数を使用してシード値を取得し、乱数を出力します。

srand()関数を使ってシード値と乱数を取得するプログラムを書いてみましょう。

スプリングツールスイート

srand_time.c

 #include #include int main() { int count; unsigned int seed; // use for randomize number printf(&apos; Enter the Seeding value: 
&apos;); scanf(&apos; %u&apos;, &amp;seed); srand (seed); // pass parameter // generate random number between 1 to 6 for (count = 1; count <= 1 5="=" 10; ++count) { printf(\' %5d\', + (rand () % 6)); if (count 0) print the number in next line puts(\' \'); } return 0; < pre> <p> <strong>Output</strong> </p> <pre> Enter the Seeding value: 10 6 4 3 3 6 3 3 1 3 4 </pre> <p> <strong>2nd execution of the program:</strong> </p> <pre> Enter the Seeding value: 20 2 4 2 4 5 4 3 5 1 4 </pre> <p> <strong>3rd execution of the program:</strong> </p> <pre> Enter the Seeding value: 25 1 6 1 6 4 4 1 4 1 3 </pre> <p>As we can see in the above Output, when we executed the same program again and again with different seeds values, it displays the different sequences of a random number from 1 to 6.</p> <h3>Generate the random number using the random function</h3> <p>Let&apos;s create a program to use stadlib header file to get the random number using random function in C.</p> <p> <strong>func.c</strong> </p> <pre> #include #include #include int main() { int i, num, max, temp; printf (&apos; Enter a number to set the limit of random numbers 
&apos;); scanf (&apos;%d&apos;, num); printf (&apos; Enter the maximum number from you want to get the random number: 
&apos;); scanf (&apos;%d&apos;, max); printf (&apos; %d random number from 0 to %d number are: 
&apos;, num, max); randomize(); for (i = 1; i <= num; i++) { temp="random(max)" * use random() function to get the random number printf (\' %d \', temp); print } getch(); < pre> <p> <strong>Output</strong> </p> <pre> Enter a number to set the limit of random numbers 17 Enter the maximum number from you want to get the random number: 100 15 random number from 0 to 100 number are: 42 68 35 1 70 25 79 59 63 28 75 89 90 43 7 4 65 </pre> <h2>Program to generate float random numbers</h2> <p>Let&apos;s consider a program to print the float random numbers in C.</p> <p> <strong>random1.c</strong> </p> <pre> #include #include #include int main() { srand( (unsigned int) time(NULL)); float f1 = 5.0; int i; printf(?Float random numbers are: 
?); for (i = 0; i<10; i++) { printf(\'%f\', ((float) rand() rand_max) * f1); printf(\'
\'); } return 0; < pre> <p> <strong>Output</strong> </p> <pre> Float random numbers are: 1.208075 1.658376 4.645070 2.298807 3.117161 0.961486 4.115573 4.336223 2.894833 2.249825 </pre> <hr></10;></pre></=></pre></=>

プログラムの 2 回目の実行:

 Enter the Seeding value: 20 2 4 2 4 5 4 3 5 1 4 

プログラムの 3 回目の実行:

 Enter the Seeding value: 25 1 6 1 6 4 4 1 4 1 3 

上記の出力でわかるように、異なるシード値を使用して同じプログラムを何度も実行すると、1 から 6 までの異なる乱数のシーケンスが表示されます。

ランダム関数を使用して乱数を生成する

stadlibヘッダファイルを利用し、C言語のrandom関数を使って乱数を取得するプログラムを作成してみます。

機能

 #include #include #include int main() { int i, num, max, temp; printf (&apos; Enter a number to set the limit of random numbers 
&apos;); scanf (&apos;%d&apos;, num); printf (&apos; Enter the maximum number from you want to get the random number: 
&apos;); scanf (&apos;%d&apos;, max); printf (&apos; %d random number from 0 to %d number are: 
&apos;, num, max); randomize(); for (i = 1; i <= num; i++) { temp="random(max)" * use random() function to get the random number printf (\' %d \', temp); print } getch(); < pre> <p> <strong>Output</strong> </p> <pre> Enter a number to set the limit of random numbers 17 Enter the maximum number from you want to get the random number: 100 15 random number from 0 to 100 number are: 42 68 35 1 70 25 79 59 63 28 75 89 90 43 7 4 65 </pre> <h2>Program to generate float random numbers</h2> <p>Let&apos;s consider a program to print the float random numbers in C.</p> <p> <strong>random1.c</strong> </p> <pre> #include #include #include int main() { srand( (unsigned int) time(NULL)); float f1 = 5.0; int i; printf(?Float random numbers are: 
?); for (i = 0; i<10; i++) { printf(\'%f\', ((float) rand() rand_max) * f1); printf(\'
\'); } return 0; < pre> <p> <strong>Output</strong> </p> <pre> Float random numbers are: 1.208075 1.658376 4.645070 2.298807 3.117161 0.961486 4.115573 4.336223 2.894833 2.249825 </pre> <hr></10;></pre></=>

float乱数を生成するプログラム

C で浮動小数点乱数を出力するプログラムを考えてみましょう。

ランダム1.c

 #include #include #include int main() { srand( (unsigned int) time(NULL)); float f1 = 5.0; int i; printf(?Float random numbers are: 
?); for (i = 0; i<10; i++) { printf(\\'%f\\', ((float) rand() rand_max) * f1); printf(\\'
\\'); } return 0; < pre> <p> <strong>Output</strong> </p> <pre> Float random numbers are: 1.208075 1.658376 4.645070 2.298807 3.117161 0.961486 4.115573 4.336223 2.894833 2.249825 </pre> <hr></10;>