使用 C 的 DSA - 二分搜索
二分搜索是一种非常快速的搜索算法。此搜索算法基于分而治之的原则。为了使此算法正常工作,数据集合应为排序形式。
二分搜索通过比较集合中最中间的项目来搜索特定项目。如果匹配,则返回项目的索引。如果中间项目大于项目,则在中间项目右侧的子数组中搜索项目,否则在中间项目左侧的子数组中搜索项目。此过程也在子数组上继续,直到子数组的大小减小到零。
二分搜索将可搜索的项目减半,从而将要进行的比较次数减少到非常少。
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("=
");
}
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
" , (comparisons +1) );
printf("lowerBound : %d, intArray[%d] = %d
",
lowerBound,lowerBound,intArray[lowerBound]);
printf("upperBound : %d, intArray[%d] = %d
",
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("]
");
}
main(){
printf("Input Array: ");
display();
printline(50);
//find location of 1
int location = find(55);
// if element was found
if(location != -1)
printf("
Element found at location: %d" ,(location+1));
else
printf("
Element not found.");
}
输出
如果我们编译并运行上述程序,则会产生以下输出 −
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
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