問題：
????????? 一只剛出生的小牛，4年后生一只小牛，以后每年生一只。現有一只剛出生的小牛，問N年后共有牛多少只？


1.原始笨方法
private?int?Comput(int?years)
????????{
????????????//初始化為1頭牛
????????????int?count?=?1;
????????????if?(years?<?4)
??????????{
????????????????return?count;
????????????}
????????????
????????????while?(years?-?3?>?0)
????????????{
????????????????count?=?count?+?Comput(years?-?3);
????????????????years--;
????????????}
????????????return?count;


????????} 特點:容易理解,不過效率太低.不具有實用價值.

2.采用HashTable優化方案
Hashtable?table?=?new?Hashtable();
????????public?long?Compute(int?years)
????????{
????????????//初始化為1頭牛
????????????long?count?=?1;
????????????if?(years?<=?3)
??????????{
????????????????return?count;
????????????}
????????????int?i?=?4;
????????????while?(i?<=?years)
????????????{
????????????????int?subYears?=?i?-?3;
????????????????if?(table.ContainsKey(subYears))
??????????????{
????????????????????count?=?(long)table[subYears];
????????????????}
????????????????else
??????????????{
????????????????????count?+=?Compute((int)(subYears));
????????????????}
????????????????if?(!table.ContainsKey(subYears))
??????????????{
????????????????????table.Add(subYears,?count);
????????????????}
????????????????i++;
????????????}
????????????return?(long)count;
????????} 特點:在第一種方案的基礎上性能有了大幅度的提高.采用HashTable存儲老牛的生育曲線,從而達到以后的小牛重復利用老牛的生育曲線.(直接取其生產數量)

3.采用數組的方式描述
public?int?Compute(int?years)
????????{
??????????int[]?age?=?new?int[4]?{?1,?0,?0,?0?};
????????????for?(int?i?=?2;?i?<=?years;?i++)
????????????{
????????????????age[3]?+=?age[2];??????????????age[2]?=?age[1];?
????????????????age[1]?=?age[0];
????????????????age[0]?=?age[3];?????????????????

????????????}
????????????return?(age[0]?+?age[1]?+?age[2]?+?age[3]);
????????}
特點:只采用一個循環搞定,效率極高.

3.采用優化遞歸公式實現
?f(n) ? = ? f(n-1)+f(n-3)??[n ? > ? 3]???
?f(n) ? = ? 1???????????????????[0 ? < ? n ? <= ? 3]??
public?int?Comput(int?x)
??????{
????????????if?(x?<?4)?return?1;
????????????else?return?Comput(x?-?1)?+?Comput(x?-?3);
????????}???
特點:代碼簡潔,功能簡單實現,但使用遞歸當然會犧牲一定的效率作為代價.

前些天在網絡上偶然發現的生產小牛問題.于是搜集整理了一下,方便大家共同研究學習使用.
有好的算法大家共同研究^_^

轉載于:https://www.cnblogs.com/symbol441/archive/2008/02/19/1073291.html

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