蓝桥杯——递归二：典型递归模型（2017.2.20）

1. 递归法实现折半查找

源代码：

法一：

#include <stdio.h>#define maxn 1010int Find(int a[],int k,int low,int high){int i,mid;if(low>high)i=-1;else{mid=(low+high)/2;if(a[mid]==k)i=mid;else if(a[mid]<k)i=Find(a,k,mid+1,high);elsei=Find(a,k,low,mid-1);}return i;}int main(){int a[maxn];int i,n,k;int low,high,index;while(scanf("%d",&n)!=EOF){for(i=0;i<n;i++)scanf("%d",&a[i]);scanf("%d",&k);low=0,high=n-1;index=Find(a,k,low,high);if(index>=0)printf("%d\n",index+1);elseprintf("Not found!\n");}return 0;}

法二：

#include <stdio.h>#define maxn 1010void Find(int a[],int k,int low,int high){int i,mid;if(low>high)printf("Not found!\n");else{mid=(low+high)/2;if(a[mid]==k)printf("%d\n",mid+1);else if(a[mid]<k)Find(a,k,mid+1,high);elseFind(a,k,low,mid-1);}}int main(){int a[maxn];int i,n,k;int low,high,index;while(scanf("%d",&n)!=EOF){for(i=0;i<n;i++)scanf("%d",&a[i]);scanf("%d",&k);low=0,high=n-1;Find(a,k,low,high);}return 0;}

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2. 递归法求Fibonacci数列的第n项，其中1<=n<=40

源代码：

#include <stdio.h>#define maxn 1010int fib(int n){if(n==1 || n==2)return 1;elsereturn fib(n-1)+fib(n-2);}int main(){int i,n;while(scanf("%d",&n)!=EOF)printf("fib(%d)=%d\n",n,fib(n));return 0;}

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3. 汉诺塔问题

源代码：

#include <stdio.h>int step=0;void print(char x,char y){printf("%c->%c\n",x,y);step++; }void move(int n,char s1,char s2,char s3)    //s1-起点 s2-经过的柱 s3-终点 {int step=0;if(n==1)print(s1,s3);else{move(n-1,s1,s3,s2);print(s1,s3);move(n-1,s2,s1,s3);}}int main(){int n;while(scanf("%d",&n)!=EOF){move(n,'A','B','C');                //将n个盘子从A柱移到C柱printf("step=%d\n",step);step=0;}return 0;}

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4. 几种排序算法的递归实现

（1）冒泡排序

源代码：

#include <stdio.h>#include <string.h>#define maxn 1010void bubblesort(int a[],int start,int end){int i,t;if(start<=end){for(i=start;i<end;i++){if(a[i]<a[i+1]){t=a[i];a[i]=a[i+1];a[i+1]=t;}}printf("%d ",a[end]);end--;bubblesort(a,start,end);}}int main(){int i,n,a[maxn]={0};int start,end;while(scanf("%d",&n)!=EOF){for(i=0;i<n;i++)scanf("%d",&a[i]);start=0,end=n-1;bubblesort(a,start,end);printf("\n");memset(a,0,sizeof(n));}return 0;}

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（2）选择排序

源代码：

#include <stdio.h>#define maxn 1010void SelectSort(int a[],int start,int end){int i,j,k;int t,index;if(start<end){t=a[start];index=start;for(i=start+1;i<end+1;i++){if(a[index]>a[i])index=i;}if(start!=index){t=a[start];a[start]=a[index];a[index]=t;}start++;SelectSort(a,start,end);}}int main(){int n,a[maxn];int i,start,end;while(scanf("%d",&n)!=EOF){for(i=0;i<n;i++)scanf("%d",&a[i]);start=0,end=n-1;SelectSort(a,start,end);for(i=0;i<n;i++)printf("%d ",a[i]);printf("\n");}return 0;}

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（3）快速排序

源代码：

#include <stdio.h>#define maxn 1010void Quicksort(int a[],int left,int right){int i=left,j=right;int tmp;if(left<right){tmp=a[left];while(i!=j){while(j>i && a[j]>=tmp)j--;a[i]=a[j];while(i<j && a[i]<=tmp)i++;a[j]=a[i];}a[i]=tmp;Quicksort(a,left,i-1);Quicksort(a,i+1,right);}}int main(){int i,n,left,right;int a[maxn];while(scanf("%d",&n)!=EOF){for(i=0;i<n;i++)scanf("%d",&a[i]);left=0,right=n-1;Quicksort(a,left,right);for(i=0;i<n;i++)printf("%d ",a[i]);printf("\n");}return 0;}

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5. 递归打印杨辉三角形

源代码：

#include <stdio.h>int fun(int x,int y){if(y==0 || y==x)return 1;elsereturn (fun(x-1,y-1)+fun(x-1,y));}int main(){int i,j,n;while(scanf("%d",&n)!=EOF){for(i=0;i<n;i++){for(j=0;j<=i;j++)printf("%4d",fun(i,j));printf("\n");}}return 0;}

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附各题思路分析及要点整理：