/*
??? 遞歸: 【逆序】從未知點推到已知點，【順序】代入已知點結果，從已知點帶入并計算到未知點，最終到終點
??? 尾遞歸: 從起點開始，依順序計算結果，并無限靠近最終目標點
??? 迭代: 從起點開始，依順序計算結果，并無限靠近最終目標點
?? ?
??? 以如上的三種方式，實現斐波拉契數列 計算
??? 斐波拉契數列： 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,
?????????? { 0,? n=0
??? f(n) = { 1,? n=1 n=2
?????????? { f(n-1) + f(n-2)
*/


#include <stdio.h>

/* 遞歸 */
unsigned int recursion(unsigned int sn)
{
??? if (0 == sn)
??? {
??????? return 0;
??? }
??? else if (?? 3 > sn
???????????? && sn > 0)
??? {
??????? return 1;
??? }
??? else
??? {
??????? return recursion(sn-1) + recursion(sn-2);
??? }

??? printf("recursion:not expect reach!\n");
??? return 0;
}

/* 尾遞歸 */
unsigned int trailRecursion(unsigned int first, unsigned int second, unsigned sn);
unsigned int trailRecursion(unsigned int first, unsigned int second, unsigned sn)
{
??? if (0 == sn)
??? {
??????? return 0;
??? }
??? if (1 == sn)
??? {
??????? return first;
??? }
??? else if (2 == sn)
??? {
??????? return second;
??? }
??? else if (3 == sn)
??? {
??????? return first + second;
??? }
??? else
??? {
??????? return trailRecursion(second, first+second, sn-1);
??? }
}
/* 迭代 */
unsigned int iteration(unsigned int sn)
{
??? unsigned int first = 1;
??? unsigned int second = 1;
??? unsigned int curr = 0;

??? if (0 == sn)
??? {
??????? return 0;
??? }
??? else if (1 == sn)
??? {
??????? return first;
??? }
??? else if (2 == sn)
??? {
??????? return second;
??? }
?? ?
??? while(sn-- > 2)
??? {
??????? curr = first + second;
??????? first = second;
??????? second = curr;
??? }
?? ?
??? return curr;
}
/* 測試程序 */
int main(void)
{
??? unsigned int value = 0;
??? unsigned int sn = 10;

??? value = recursion(sn);
??? printf("fibonacciSequency-recursion-%u: %u\n", sn, value);

??? value = trailRecursion(1, 1, 10);
??? printf("fibonacciSequency-trailRecursion-%u: %u\n", sn, value);

??? value = iteration(10);
??? printf("fibonacciSequency-iteration-%u: %u\n", sn, value);

??? return 0;
}

轉載于:https://www.cnblogs.com/tedani/p/10004512.html

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