【Java】零基础蓝桥杯算法学习——二分查找

算法模板一:

java 复制代码

// 数组arr的区间[0,left-1]满足arr[i]<k,[left,n-1]满足arr[i]>=k;
		Scanner scan = new Scanner(System.in);
		int[] arr = {1,2,3,4,5};
		int left = 0,right = arr.length-1;
		int k = scan.nextInt();
		while(left<right) {//left==right时退出循环
			int mid = (left+right)/2;//当区间长度为偶数时，mid取区间靠左端点
			if(arr[mid]>=k) right = mid;
			else left = mid+1;
		}

算法模板二：

java 复制代码

// 数组arr的区间[0,left]满足arr[i]<=k,[left+1,n-1]满足arr[i]>k;
		Scanner scan = new Scanner(System.in);
		int[] arr = {1,2,3,4,5,6};
		int left = 0,right = arr.length-1;
		int k = scan.nextInt();
		while(left<right) {//left==right时退出循环
			int mid = (left+right+1)/2;//当区间长度为偶数时，mid取区间靠右端点
			if(arr[mid]>k) right = mid-1;
			else left = mid;
		}

例题一：蓝桥杯2018真题：递增三元组

输入示例:

1 1 1

2 2 2

3 3 3

输出示例：27

代码示例：

java 复制代码

import java.util.Arrays;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        int n = scan.nextInt();
        int[] a = new int[n];
        int[] b = new int[n];
        int[] c = new int[n];
        for(int i=0;i<n;i++) a[i] = scan.nextInt();
        for(int i=0;i<n;i++) b[i] = scan.nextInt();
        for(int i=0;i<n;i++) c[i] = scan.nextInt();
        Arrays.sort(a);
        Arrays.sort(b);
        Arrays.sort(c);
        int[] B = new int[n];
        for(int i=0;i<n;i++) {
        	int l=0,r=n-1;
        	while(l<r) {
             int mid = (l+r)/2;
             if(c[mid]>b[i]) r=mid;
             else l=mid+1;
        	}
        	if(c[l]>b[i]) B[i]=n-l;
        }
        long[] sum = new long[n+1];
        for(int i=1;i<=n;i++) sum[i]=sum[i-1]+B[i-1];
        long ans=0;
        for(int i=0;i<n;i++) {
        	int l=0,r=n-1;
        	while(l<r) {
             int mid = (l+r)/2;
             if(b[mid]>a[i]) r=mid;
             else l=mid+1;
        	}
        	if(b[l]>a[i]) ans+=(sum[n]-sum[l]);
        }
        System.out.println(ans);
        scan.close();
    }
}

例题二：蓝桥杯2017真题：分巧克力

输出：2

代码示例：

java 复制代码

import java.util.Scanner;
public class Main {
     public static void main(String[] args)  {
        Scanner scan = new Scanner(System.in);
        int n = scan.nextInt();
        int k = scan.nextInt();
        int[] h = new int[n];
        int[] w = new int[n];
        for(int i=0;i<n;i++) {
        	h[i]=scan.nextInt();
        	w[i]=scan.nextInt();
        }
        int l=0,r=(int)1e5;
        while(l<r) {
        	int mid=(l+r+1)/2;
        	if(check(mid,h,w,k))  l=mid;
        	else r=mid-1;
        }
        System.out.println(l);
        scan.close();
    }
    public static boolean check(int mid,int[] h,int[] w,int k) {
    	int ans=0;
    	for(int i=0;i<h.length;i++) {
    		int res = (h[i]/mid)*(w[i]/mid);
    		ans+=res;
    	}
    	return ans>=k;
    }
}