利用 C 的 DSA - 二分查詢

二分查詢是一種非常快速的搜尋演算法。此搜尋演算法的工作原理遵循分而治之原則。為了使此演算法正常工作，資料蒐集應採用已排序的形式。

二分查詢透過比較蒐集的中部專案來搜尋特定專案。如果發生匹配，則返回專案索引。如果中部專案大於專案，則在中部專案的右邊子陣列中搜索專案，否則在中部專案的左邊子陣列中搜索專案。此過程在子陣列上繼續進行，直至子陣列大小縮小為零。

二分查詢將可搜尋專案減半，從而將要進行的比較次數減少到非常少的數量。

演算法

Binary Search ( A: array of item, n: total no. of items ,x: item to be searched)
Step  1: Set lowerBound = 1
Step  2: Set upperBound = n 
Step  3: if upperBound < lowerBound go to step 12
Step  4: set midPoint = ( lowerBound + upperBound ) / 2
Step  5: if A[midPoint] < x
Step  6: set lowerBound = midPoint + 1
Step  7: if A[midPoint] > x
Step  8: set upperBound = 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>
#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++;
      // compute the mid point 
      midPoint = (lowerBound + upperBound) / 2;
      
      // 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");
}
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("\nElement not found.");
}

輸出

如果編譯並執行上述程式，它會產生以下輸出 −

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
Comparison 2
lowerBound : 10, intArray[10] = 15
upperBound : 19, intArray[19] = 66
Comparison 3
lowerBound : 15, intArray[15] = 34
upperBound : 19, intArray[19] = 66
Comparison 4
lowerBound : 18, intArray[18] = 55
upperBound : 19, intArray[19] = 66
Total comparisons made: 4
Element found at location: 19