蓝桥杯刷题笔记：二分查找

Posted 2022-05-17 爱敲代码的三毛

普通二分查找代码

循环

static int find(int[] arr,int target) 
        int left = 0;
        int right = arr.length-1;
        int mid = 0;
        while (left <= right) 
            mid = (right-left)/2 + left;
            if (arr[mid] > target) 
                right = mid-1;
             else if (arr[mid] < target) 
                left = mid+1;
             else 
                return mid;
            
        

        return -1;
    

递归

static int find2(int[] arr,int left,int right,int target) 
        if (left > right) 
            return -1;
        
        int mid = (right-left)/2 + left;

        if (arr[mid] > target) 
            return find2(arr,left,mid-1,target);
         else if (arr[mid] < target) 
            return find2(arr,mid+1,right,target);
         else if (arr[mid] == target) 
            return mid;
        

        return -1;
    

二分查找变形

变形1

给定有序序列，找到序列中大于或者等于 target最小的那个的数字

static int find3(int[] arr,int target) 
        int left = 0;
        int right = arr.length-1;
        int mid = 0;

        while (left <= right) 
            mid = (right-left)/2 + left;
            if (arr[mid] >= target) 
                right = mid-1;
             else 
                left = mid+1;
            
        
        if (left >= arr.length) 
            return -1;
        
        return arr[left];
    

变形2

给定有序序列，找到序列中大于 target最小的那个的数字

static int find4(int[] arr,int target) 
        int left = 0;
        int right = arr.length-1;
        int mid = 0;

        while (left <= right) 
            mid = (right-left)/2 + left;
            if (arr[mid] > target) 
                right = mid-1;
             else 
                left = mid+1;
            
        
        if (left >= arr.length) 
            return -1;
        
        return arr[left];
    

变形3

给定有序序列，找到序列中小于 target最大的那个的数字

static int find5(int[] arr,int target) 
        int left = 0;
        int right = arr.length-1;
        int mid = 0;

        while (left <= right) 
            mid = (right-left)/2 + left;
            if (arr[mid] <= target) 
                left = mid+1;
             else 
                right = mid-1;
            
        
        if (right < 0) 
            return -1;
        
        return arr[right];
    

变形4

给定一个 整数序列，让你取一个字段，使得区间和大于等于x，问这个字段最短可能长度是多少

示例：
[1,2,4,7,9] ,给定 target = 13 时应该得到 2, target = 3 时应该得到1，target 大于 23时应该不存在

暴力代码

static void shortestSubsequenceAnd(int[] arr,int target) 
        int min = Integer.MAX_VALUE;
        for (int i = 0; i < arr.length; i++) 
            int sum = 0;
            for (int j = i; j < arr.length; j++) 
                sum += arr[j];
                if (sum >= target) 
                    min = Math.min(min,j-i+1);
                    break;
                
                System.out.println("i: "+i +"   j:"+j);
            
        
        if (min == Integer.MAX_VALUE) 
            System.out.println("不存在");
         else 
            System.out.println(min);
        
    

变形5

给定一个数 num,求解第一个大于x的平方数

/**
     * 求第一个大于x的平方数
     * @return
     */
    static int isPerfectSquare(int x) 
        int n = x;


        while (true) 
            n++;
            int left = 1;
            int right = n;
            int mid = 0;
            while (left <= right) 
                mid = (right-left)/2 + left;
                if (mid*mid < n) 
                    left = mid+1;
                 else if (mid*mid > n) 
                    right = mid-1;
                 else 
                    return n;