# 二分搜尋

December 11, 2021

## 解法思路

[3 24 57 57 67 68 83 90 92 95]

3 24 57 57 67 [68 83 90 92 95]

3 24 57 57 67 68 83 90 [92 95]

## 程式實作

``````#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#define MAX 10
#define SWAP(x,y) {int t; t = x; x = y; y = t;}

void quickSort(int[], int, int);
int binarySearch(int[], int);

int main(void) {
srand(time(NULL));

int number[MAX] = {0};

int i;
for(i = 0; i < MAX; i++) {
number[i] = rand() % 100;
}

quickSort(number, 0, MAX-1);

printf("數列：");
for(i = 0; i < MAX; i++)
printf("%d ", number[i]);

int find;
printf("\n輸入尋找對象：");
scanf("%d", &find);

if((i = binarySearch(number, find)) >= 0)
printf("找到數字於索引 %d ", i);
else
printf("\n找不到指定數");

printf("\n");

return 0;
}

int binarySearch(int number[], int find) {
int low = 0;
int upper = MAX - 1;
while(low <= upper) {
int mid = (low+upper) / 2;
if(number[mid] < find)
low = mid+1;
else if(number[mid] > find)
upper = mid - 1;
else
return mid;
}
return -1;
}

void quickSort(int number[], int left, int right) {
if(left < right) {
int s = number[(left+right)/2];
int i = left - 1;
int j = right + 1;

while(1) {
while(number[++i] < s) ;  // 向右找
while(number[--j] > s) ;  // 向左找
if(i >= j)
break;
SWAP(number[i], number[j]);
}

quickSort(number, left, i-1);   // 對左邊進行遞迴
quickSort(number, j+1, right);  // 對右邊進行遞迴
}
}
``````
``````public class Search {
public static int binary(int[] number, int des) {
int low = 0;
int upper = number.length - 1;

while(low <= upper) {
int mid = (low+upper) / 2;
if(number[mid] < des)
low = mid+1;
else if(number[mid] > des)
upper = mid - 1;
else
return mid;
}

return -1;
}

public static void main(String[] args) {
int[] number = {1, 2, 3, 4, 6, 7, 8};
int find = Search.binary(number, 2);
System.out.println(find >= 0 ? "找到數值於索引" + find : "找不到數值");
}
}
``````
``````def search(number, des):
low = 0
upper = len(number) - 1
while low <= upper:
mid = (low + upper) // 2
if number[mid] < des:
low = mid + 1
elif number[mid] > des:
upper = mid - 1
else:
return mid
return -1

number = [1, 4, 2, 6, 7, 3, 9, 8]
number.sort()
find = search(number, 2)
print("找到數值於索引 " + str(find) if find >= 0 else "找不到數值")
``````
``````object Search {
def binary(number: Array[Int], des: Int) = {
var low = 0
var upper = number.length - 1
var result = -1
var isContinue = true
while(isContinue && low <= upper) {
val mid = (low + upper) / 2
if(number(mid) < des) {
low = mid + 1
}
else if(number(mid) > des) {
upper = mid - 1
}
else {
result = mid
isContinue = false
}
}
result
}
}

val number = Array(1, 2, 3, 4, 6, 7, 8)
val find = Search.binary(number, 3)
println(if(find >= 0) "找到數值於索引 " + find else "找不到數值")
``````
``````# encoding: UTF-8
def search(number, des)
low = 0
upper = number.length - 1
while low <= upper
mid = (low + upper) / 2
if number[mid] < des
low = mid + 1
elsif number[mid] > des
upper = mid - 1
else
return mid
end
end
-1
end

number = [1, 4, 2, 6, 7, 3, 9, 8]
number.sort!
find = search(number, 2)
print find >= 0 ? "找到數值於索引 " + find.to_s : "找不到數值", "\n"
``````
``````function search(lt, n) {
let low = 0
let upper = lt.length - 1;
while(low <= upper) {
let mid = Math.floor((low + upper) / 2);
if(lt[mid] < n) {
low = mid + 1;
}
else if(lt[mid] > n) {
upper = mid - 1;
}
else {
return mid;
}
}
return -1;
}

lt = [1, 4, 2, 6, 7, 3, 9, 8];
lt.sort((a, b) => a - b);
console.log(search(lt, 2));
``````
``````binarySearch [] _ = -1
binarySearch lt n = _search lt n 0 (length lt - 1)
where
_search lt n low upper =
if low > upper then -1
else
let mid = (low + upper) `div` 2
elem = lt !! mid
in
if elem == n then mid
else
if elem < n then _search lt n (mid + 1) upper
else _search lt n low (mid - 1)

main = print \$ binarySearch [3, 5, 8, 9, 10, 13, 15] 13
``````