C语言求Fibonacci数列

方法有三种甚至更多，但核心思想都是一个数列的通项公式：F(n)=F(n-1)+F(n-2)。核心代码放在最后。

方法一：普通法

#include <stdio.h>
#include <stdlib.h>
unsigned long Fibonacci(unsigned n);/*打印Fibonacci*/int main(void)
{unsigned int q;int count;printf("This program is using for Fibonacci.");printf("Please enter a number that you want to see the Fibonacci:");while (scanf("%u", &q) == 1){for (count = 1; count <= q; count++)printf("%lu ", Fibonacci(count));printf("\n\aPlease enter the next number:");continue;}printf("\aThank you for you using.");return EXIT_SUCCESS;
}unsigned long Fibonacci(unsigned n)
{int a = 1, b = 1;int i, temp;if (n > 2)for (i = 3; i <= n; i++){temp = a + b; /*交换数值*/a = b;b = temp;}elseb = 1;return b;
}

方法二：利用数组

#include <stdio.h>
#include <stdlib.h>
#define upper 57
unsigned int Fibonacci(unsigned int a); /*打印Fibonacci*/
unsigned int check(void);               /*检查输入是否为数字的错误*/int main(void)
{unsigned int num; /*Fibonacci数列的项数*/printf("This program is using for Fibonacci array.\n");printf("Please enter the number that you want to see the ""Fibonacci(more than 0,less than 4294967295)"" (For your computer's speed of operation considerations,""generally do not recommend more than 10000):");/*因为用的是unsigned int类型，所以建议输入大于0小于4294967295*/while (1) /*无条件进入循环*/{num = check();Fibonacci(num);/*准备开始第n(n>1)次循环*/printf("This program is using for Fibonacci array.\n");printf("Please enter the number that you want to see ""the Fibonacci(less than 4294967295)"" (For your computer's speed of operation ""considerations, generally do not recommend ""more than 10000)");}printf("Done!");return EXIT_SUCCESS;
}unsigned int Fibonacci(unsigned int a) /*Fibonacii数列求解运算*/
{unsigned int arr[a];arr[0] = 1;arr[1] = 1;if (a > 2) /*求出第3项及以后的结果*/{printf("%u %u", arr[0], arr[1]);for (int i = 2; i < a; i++){arr[i] = arr[i - 1] + arr[i - 2];printf("  %u", arr[i]);if (i == (a - 1)){printf("\n");}}}else /*处理当输入1 or 2时的情况*/{if (a == 1){printf("%u\n", arr[1]);}if (a == 2){printf("%u %u\n", arr[1], arr[1]);}}
}unsigned int check(void)
{unsigned int input;char ch;while (scanf("%u", &input) != 1){while ((ch = getchar()) != '\n')putchar(ch); /*处理错误输入*/printf(" is not an integer.Please enter a right number"" (like1,50 or 8950,but less than 4294967295:");}return input;
}

方法三：递归求解

#include <stdio.h>
#include <stdlib.h>
#define upper 57
unsigned int Fibonacci(unsigned int a); /*打印Fibonacci*/
unsigned int check(void);               /*检查输入是否为数字的错误*/int main(void)
{unsigned int num; /*Fibonacci数列的项数*/printf("This program is using for Fibonacci array.\n");printf("Please enter the number that you want to see the ""Fibonacci(more than 0,less than 4294967295)"" (For your computer's speed of operation considerations,""generally do not recommend more than 10000):");/*因为用的是unsigned int类型，所以建议输入大于0小于4294967295*/while (1) /*无条件进入循环*/{num = check();for (int i = 1; i <=num; i++){printf("%u  ", Fibonacci(i));}/*准备开始第n(n>1)次循环*/printf("This program is using for Fibonacci array.\n");printf("Please enter the number that you want to see ""the Fibonacci(less than 4294967295)"" (For your computer's speed of operation ""considerations, generally do not recommend ""more than 10000)");}printf("Done!");return EXIT_SUCCESS;
}unsigned int Fibonacci(unsigned int a) /*Fibonacii数列求解运算*//*递归*/
{if (a > 2)  /*F(n)=F(n-1)+F(n-2)*/return Fibonacci(a - 1) + Fibonacci(a - 2);elsereturn 1;
}unsigned int check(void)
{unsigned int input;char ch;while (scanf("%u", &input) != 1){while ((ch = getchar()) != '\n')putchar(ch); /*处理错误输入*/printf(" is not an integer.Please enter a right number"" (like1,50 or 8950,but less than 4294967295:");}return input;
}

核心代码：
普通法：

unsigned long Fibonacci(unsigned n)
{int a = 1, b = 1;int i, temp;if (n > 2)for (i = 3; i <= n; i++){temp = a + b; /*交换数值*/a = b;b = temp;}elseb = 1;return b;
}

数组法：

unsigned int Fibonacci(unsigned int a) /*Fibonacii数列求解运算*/
{unsigned int arr[a];arr[0] = 1;arr[1] = 1;if (a > 2) /*求出第3项及以后的结果*/{printf("%u %u", arr[0], arr[1]);for (int i = 2; i < a; i++){arr[i] = arr[i - 1] + arr[i - 2];printf("  %u", arr[i]);if (i == (a - 1)){printf("\n");}}}else /*处理当输入1 or 2时的情况*/{if (a == 1){printf("%u\n", arr[1]);}if (a == 2){printf("%u %u\n", arr[1], arr[1]);}}
}

递归法：

unsigned int Fibonacci(unsigned int a) /*Fibonacii数列求解运算*//*递归*/
{if (a > 2)  /*F(n)=F(n-1)+F(n-2)*/return Fibonacci(a - 1) + Fibonacci(a - 2);elsereturn 1;
}

显而易见的是，普通法最简单，但代码可读性不高；数组法难易度居中；递归法最难，代码最简洁，但同时占用内存也多。

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