二分法查找

原创于 2021-02-11 15:43:01 发布 · 151 阅读

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#二分法 #算法

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这篇博客介绍了二分查找的两种实现方式：循环查找和递归查找，并展示了如何使用Java实现。同时，讨论了在已排序数组中查找特定元素的最后出现位置的方法。此外，还提出了在有序数组中寻找坡峰元素的算法。这些内容涉及到数据结构和算法的基础知识，对于提升编程技能非常有帮助。

在这里插入图片描述

1、循环查找

public class BinarySearch {
    public static void main(String[] args) {
        int[] arr = {1,2,3,4,5,6,7};
        int index = binarySearch(arr,5);
        System.out.println(index);
    }

    public static int binarySearch(int[] arr,int item){
        int low = 0;
        int higt = arr.length-1;
        int index = -1;

        while (low<=higt) {
            int mid = (low + higt) / 2;
            int guess = arr[mid];
            if (guess == item) {
                index = mid;
                break;
            }
            if (guess > item) {
                higt = mid - 1;
            }
            if (guess < item) {
                low = mid + 1;
            }
        }
        return index;
    }
}

2、递归查找

public class BinarySearch02 {
    public static void main(String[] args) {
        int[] arr = {1,2,3,4,5,6,7};
        int index = binarySearch(arr,5,0, arr.length-1);
        System.out.println(index);
    }

    public static int binarySearch(int[] arr,int item,int low,int high){
        if (low>high){
            return -1;
        }
        int mid = (low+high)/2;
        int guess = arr[mid];
        if (guess == item){
            return mid;
        }
        else if (guess > item){
            return binarySearch(arr,item,low,mid-1);
        }
        else{
            return binarySearch(arr, item, mid+1, high);
        }
    }
}

实际上：Arrays有方法

		Arrays.sort(arr); //排序
        Arrays.binarySearch(arr,6); //查找

3、查找一个数的最后出现在第几位

public class lastPosition {
    public int lastPosition(int[] nums,int target){
        if(nums == null || nums.length == 0){
            return -1;
        }

        int start = 0;
        int end = nums.length-1;

        while (start+1 < end){  //start 与 end 是前后关系
            int mid = start +(start+end)/2;
            if(nums[mid] == target){
                start = mid; //如果是求第一次出现 则end = start  
            }else if(nums[mid] < target){
                start = mid;
            }else {
                end = mid;
            }
        }

        if(nums[end] == target){
            return end;
        }
        if(nums[start] == target){
            return start;
        }

        return -1;
    }
}

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3、如果确定不了数组长度

public int searchBigSortArray(ArrayReader reader,int target){

		//搜索target所在的数组长度
        int count = 1;
        while(reader.get(count -1) < target){
            count = count *2;
        }

        int start = count /2;
        int end = count-1;
        while (start+1 < end){  //start 与 end 是前后关系
            int mid = start +(start-end)/2;
            if(nums[mid] == target){
                start = mid;
            }else if(nums[mid] < target){
                start = mid;
            }else {
                end = mid;
            }
        }

        if(nums[end] == target){
            return end;
        }
        if(nums[start] == target){
            return start;
        }

        return -1;
    }

4、寻找坡峰

public class lastPosition {
    public int findPeak(int[] arr){
        if(arr == null ) return -1;
        int start = 0;
        int end = arr.length-2;

        while (start+1 < end){
            int mid = start + (end - start)/2;
            if(arr[mid+1] > arr [mid]){ //递增
                start = mid;
            }else if(arr[mid-1] > arr[mid] ){
                end = mid;
            }else {
                end = mid ;
            }
        }

        if(arr[start] > arr[end]){
            return arr[start];
        }else {return arr[end];}

    }

    public static void main(String[] args) {
        int arr[] = new int[]{1,2,1,3,4,5,7,6};
        lastPosition astPosition = new lastPosition();
        astPosition.findPeak(arr);
        System.out.println(astPosition.findPeak(arr));

    }

}