C 中的 DSA - 插值查詢

概述

插值查詢是二分查詢的改進變體。此搜尋演算法處理所需值探查位置。為使此演算法正常工作，資料收集應採用已排序形式。

插值查詢透過計算探查位置來搜尋特定專案。最初探查位置是集合最中間專案的的位置。如果發生匹配，則返回專案索引。如果中間專案大於專案，則再次在中間專案右側的子陣列中計算探查位置，否則在中間專案左側的子陣列中搜索專案。此過程繼續在子陣列中進行，直到子陣列大小減小到零。

插值查詢的示例是詞典查詢，其中從 X 開始搜尋單詞，我們在字典末尾附近搜尋，從而插入探查位置，依此類推。

演算法

Interpolation Search ( A: array of item, n: total no. of items 
   ,x: item to be searched)
Step 1: Set lowerBound = 0
Step 2: Set upperBound = n - 1
Step 3: if lowerBound  = upperBound or A[lowerBound] = A[upperBound] go to step 12
Step 4: set midPoint = lowerBound + 
   ((upperBound -lowerBound) / (A[upperBound] - A[lowerBound])) 
   * (x - A[lowerBound])
Step 5: if A[midPoint] < x
Step 6: set from = midPoint + 1
Step 7: if A[midPoint] > x
Step 8: set to = midPoint - 1 
Step 9: if A[midPoint] = x go to step 11
Step 10: Go to Step 3
Step 11: Print Element x Found at index midPoint and go to step 13
Step 12: Print element not found
Step 13: Exit

示例

#include <stdio.h>
#include <math.h>
#define MAX 20

// array of items on which linear search will be conducted. 
int intArray[MAX] = {1,2,3,4,6,7,9,11,12,14,15,16,17,19,33,34,43,45,55,66};

void printline(int count){
   int i;
   for(i=0;i <count-1;i++){
      printf("=");
   }
   printf("=\n");
}
int find(int data){
   int lowerBound = 0;
   int upperBound = MAX -1;
   int midPoint = -1;
   int comparisons = 0;      
   int index = -1;
   while(lowerBound <= upperBound){
      printf("Comparison %d\n" , (comparisons +1) ) ;
      printf("lowerBound : %d, intArray[%d] = %d\n",
         lowerBound,lowerBound,intArray[lowerBound]);
      printf("upperBound : %d, intArray[%d] = %d\n",
         upperBound,upperBound,intArray[upperBound]);
      comparisons++;
      // probe the mid point 
      midPoint = lowerBound + 
      round((double)(upperBound - lowerBound) 
         / (intArray[upperBound] - intArray[lowerBound]) 
         *  (data - intArray[lowerBound]));
      printf("midPoint = %d\n",midPoint);
      // data found 
      if(intArray[midPoint] == data){
         index = midPoint;
         break;
      } else {
         // if data is larger 
         if(intArray[midPoint] < data){
            // data is in upper half 
            lowerBound = midPoint + 1;
         }
         // data is smaller 
         else{           
            // data is in lower half 
            upperBound = midPoint -1;
         }
      }
   }
   printf("Total comparisons made: %d" , comparisons);
   return index;
}
void display(){
   int i;
   printf("[");
   // navigate through all items 
   for(i=0;i<MAX;i++){
      printf("%d ",intArray[i]);
   }
   printf("]\n");
}
int main(){
   printf("Input Array: ");
   display();
   printline(50);
   
   //find location of 1
   int location = find(55);

   // if element was found 
   if(location != -1)
      printf("\nElement found at location: %d" ,(location+1));
   else
      printf("Element not found.");
}

輸出

如果我們編譯並執行上述程式，它將產生以下輸出 −

Input Array: [1 2 3 4 6 7 9 11 12 14 15 16 17 19 33 34 43 45 55 66 ]
==================================================
Comparison 1
lowerBound : 0, intArray[0] = 1
upperBound : 19, intArray[19] = 66 midPoint = 16 Comparison 2
lowerBound : 17, intArray[17] = 45
upperBound : 19, intArray[19] = 66
midPoint = 18
Total comparisons made: 2
Element found at location: 19