数据结构考研分类复习真题 第五章 答案[38]

．二项式(a+b）n展开式的系数的递归定义为

C(nk)=

()int BiForm(int nk) //二项式展开式的系数的递归算法

{if(n< || k< || k>=n) {printf(参数错误\n );exit();}

if(k== || k==n) return();

else return(BiForm(nk)+BiForm(nk);

}

()C()的递归树

()计算C(nk)(<=k<=n)的非递归算法

int cnk(int nint k)

{int i; long x=y=;

for (i=;i<=k;i++) x*=i;

for (i=nk+;i<=n;i++) y*=i;

return(y/x)

}//cnk

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