顺序表查找和有序表查找

  1 #include <iostream>
  2 using namespace std;
  3 
  4 //顺序表查找（线性查找、静态表查找）  时间复杂度为O(n)
  5 int Seq_Search(int *s,int n,int key)
  6 {
  7     s[0] = key;   //设置了一个哨兵，避免了每次比较一次过后都要判断查找位置是否越界
  8     int i = n;
  9     while (s[i] != key)
 10     {
 11         --i;
 12     }
 13     return i;
 14 }
 15 
 16 //二分查找（折半查找） 前提条件：记录的关键码必须有序，必须是顺序存储   时间复杂度为O(logn)
 17 int Binary_Search(int *s,int n,int key)
 18 {
 19     int low,mid,high;
 20     low = 1;
 21     high = n;
 22     while (low <= high)
 23     {
 24         mid = (low + high)/2;
 25         if (s[mid] > key)
 26         {
 27             high = mid - 1;
 28         }else if (s[mid] < key)
 29         {
 30             low = mid + 1;
 31         }else
 32             return mid;
 33     }
 34     return 0;
 35 }
 36 
 37 //插值查找(对于表长较大，关键字分布比较均匀的查找表来说，插值查找算法的平均性能要比二分查找算法的性能高)
 38 int B_Search(int *s,int n,int key)
 39 {
 40     int low,mid,high;
 41     low = 1;
 42     high = n;
 43     while (low <= high)
 44     {
 45         mid = low + (high - low)*(key - s[low])/(s[high] - s[low]);
 46         if (s[mid] > key)
 47         {
 48             high = mid - 1;
 49         }else if (s[mid] < key)
 50         {
 51             low = mid + 1;
 52         }else
 53             return mid;
 54     }
 55     return 0;
 56 }
 57 
 58 //计算斐波那契数列
 59 void Fibonacci(int *F)
 60 {
 61     F[0]=0;
 62     F[1]=1;
 63     for(int i =2;i<10;i++)  
 64     { 
 65         F[i] = F[i-1] + F[i-2];  
 66     } 
 67 }
 68 
 69 //斐波那契查找(时间复杂度是O(logn))
 70 int Fibonacci_Search(int *s,int n,int key,int *F)
 71 {
 72     int low,high,mid,i,k;
 73     low = 1;
 74     high = n;
 75     k = 0;  //k为斐波那契数列的下标
 76     while (n > F[k] - 1)  //计算n位于斐波那契数列的位置
 77     {
 78         k++;
 79     }
 80     for (i = n;i < F[k] -1;i++)  //将不满的数值补全
 81     {
 82         s[i] = s[n];
 83     }
 84     //开始查找
 85     while (low <= high)
 86     {
 87         mid = low + F[k] - 1;
 88         if (key < s[mid])
 89         {
 90             high = mid - 1;
 91             k = k - 1;   //斐波那契数列下标减一位
 92         }else if (key > s[mid])
 93         {
 94             low = mid + 1;
 95             k = k - 2;   //斐波那契数列下标减两位
 96         }else
 97         {
 98             if (mid <= n)
 99             {
100                 return mid;
101             }else
102                 return n;   //若mid>n，说明是补全的数值，返回n
103         }
104     }
105     return 0;
106 }
107 
108 void main()
109 {
110     int s[] = {0,1,16,24,35,47,59,62,73,88,99};
111     int n = 11;
112     int m,a;
113     int Fbi[10];
114     Fibonacci(Fbi);
115 
116     cout << "输入顺序表查找要查找的数字: ";
117     cin >> m;
118     a = Seq_Search(s,n,m);
119     cout << "顺序表查找" << m <<"的位置在："<< a << endl << endl;
120 
121     cout << "输入二分查找要查找的数字: ";
122     cin >> m;
123     a = Binary_Search(s,n,m);
124     cout << "二分查找" << m <<"的位置在："<< a << endl << endl;
125 
126     cout << "输入插值查找要查找的数字: ";
127     cin >> m;
128     a = B_Search(s,n,m);
129     cout << "插值查找" << m <<"的位置在："<< a << endl << endl;
130 
131     cout << "输入斐波那契查找要查找的数字: ";
132     cin >> m;
133     a = Fibonacci_Search(s,n,m,Fbi);
134     cout << "斐波那契查找" << m <<"的位置在："<< a << endl << endl;
135 
136     system("pause");
137 }