算法竞赛相关 Java 二分模版

[方法 Arrays.binarySearch();](#方法 Arrays.binarySearch();)

找和目标值相关

复制代码

public class BinarySearchTemplate {

    // 查找大于 x 的最小值（即严格上界）
    public static int upperBound(int[] arr, int x) {
        int left = 0, right = arr.length;
        while (left < right) {
            int mid = left + (right - left) / 2;
            if (arr[mid] > x) {
                right = mid;
            } else {
                left = mid + 1;
            }
        }
        if(left<0||left>arr.length-1) {
        	return -1; // -1 表示没有找到符合条件的元素
        }else {
        	return arr[left]; 	
        }
    }

    // 查找大于等于 x 的最小值（即第一个不小于 x 的元素）
    public static int lowerBound(int[] arr, int x) {
        int left = 0, right = arr.length;
        while (left < right) {
            int mid = left + (right - left) / 2;
            if (arr[mid] >= x) {
                right = mid;
            } else {
                left = mid + 1;
            }
        }
        if(left < 0||left > arr.length-1) {
        	return -1; // -1 表示没有找到符合条件的元素
        }else {
        	return arr[left]; 	
        }
    }

    // 查找小于 x 的最大值（即严格下界）
    public static int floor(int[] arr, int x) {
        int left = -1, right = arr.length - 1;
        while (left < right) {
            int mid = left + (right - left + 1) / 2;
            if (arr[mid] < x) {
                left = mid;
            } else {
                right = mid - 1;
            }
        }
        if(left < 0||left > arr.length-1) {
        	return -1; // -1 表示没有找到符合条件的元素
        }else {
        	return arr[left]; 	
        }
    }

    // 查找小于等于 x 的最大值（即最后一个不大于 x 的元素）
    public static int ceiling(int[] arr, int x) {
        int left = -1, right = arr.length - 1;
        while (left < right) {
            int mid = left + (right - left + 1) / 2;
            if (arr[mid] <= x) {
                left = mid;
            } else {
                right = mid - 1;
            }
        }
        if(left < 0||left > arr.length-1) {
        	return -1; // -1 表示没有找到符合条件的元素
        }else {
        	return arr[left]; 	
        }
    }

    // 测试示例
    public static void main(String[] args) {
        int[] arr = {1, 3, 5, 7, 9, 11};
        int x = 6;
        System.out.println("大于 " + x + " 的最小值: " + upperBound(arr, x)); // 输出 7
        System.out.println("大于等于 " + x + " 的最小值: " + lowerBound(arr, x)); // 输出 7
        System.out.println("小于 " + x + " 的最大值: " + floor(arr, x)); // 输出 5
        System.out.println("小于等于 " + x + " 的最大值: " + ceiling(arr, x)); // 输出 5
    }
}

方法 Arrays.binarySearch();

例题 P2249 【深基13.例1】查找 - 洛谷

题解

复制代码

// @github https://github.com/Dddddduo
// @github https://github.com/Dddddduo/acm-java-algorithm
// @github https://github.com/Dddddduo/Dduo-mini-data_structure
import java.util.*;
import java.io.*;
import java.math.*;
import java.lang.*;
import java.time.*;

/**
 * 题目地址
 *
 */

// xixi♡西
public class Main {

    static IoScanner sc = new IoScanner();
    static final int mod = (int) (1e9 + 7);
//    static final int mod = (int) (1e9 + 7);

//    static int n;
//    static int arr[];
//    static boolean visited[];
//    static ArrayList<ArrayList<Integer>> adj = new ArrayList<>();

    /**
     * @throws IOException
     */
    
    private static void solve() throws IOException {
        // todo
    	int n=sc.nextInt();
    	int m=sc.nextInt();
    	long arr[]=new long[n];
    	for(int i=0;i<n;i++) {
    		arr[i]=sc.nextLong();
    	}
    	
    	StringBuilder sb=new StringBuilder("");
    	
    	for(int i=0;i<m;i++) {
    		long target=sc.nextLong();
            int index = Arrays.binarySearch(arr, target);
            if (index >= 0) {
                while (index > 0 && arr[index - 1]==target) {
                    index--;
                }
            } 
            index+=1;
            if(index<1||index>n) {
            	sb.append("-1 ");
            }else {
            	sb.append(index+" ");
            }
    	}
    	dduoln(sb);
    	
    }
    
    public static void main(String[] args) throws Exception {
        int t = 1;
//        t = sc.nextInt();
        while (t-- > 0) {
            solve();
        }
    }

    static <T> void dduo(T t) {
        System.out.print(t);
    }

    static <T> void dduoln() {
        System.out.println("");
    }

    static <T> void dduoln(T t) {
        System.out.println(t);
    }
}

/**
 * IoScanner类
 *
 * @author Dduo
 * @version 1.0
 * @description 通过IO流操作缓冲区减少了与底层输入输出设备的交互次数，旨在简化 Java 中的标准输入读取操作。
 */
class IoScanner {
    BufferedReader bf;
    StringTokenizer st;
    BufferedWriter bw;

    public IoScanner() {
        bf = new BufferedReader(new InputStreamReader(System.in));
        st = new StringTokenizer("");
        bw = new BufferedWriter(new OutputStreamWriter(System.out));
    }

    public String nextLine() throws IOException {
        return bf.readLine();
    }

    public String next() throws IOException {
        while (!st.hasMoreTokens()) {
            st = new StringTokenizer(bf.readLine());
        }
        return st.nextToken();
    }

    public char nextChar() throws IOException {
        return next().charAt(0);
    }

    public int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    public long nextLong() throws IOException {
        return Long.parseLong(next());
    }

    public double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }

    public float nextFloat() throws IOException {
        return Float.parseFloat(next());
    }

    public BigInteger nextBigInteger() throws IOException {
        return new BigInteger(next());
    }

    public BigDecimal nextDecimal() throws IOException {
        return new BigDecimal(next());
    }
}

二分答案模版

复制代码

    	long left=0;
    	long right=(long) 1e9;
    	long mid=0;
    	while(left<right) {
    		mid =left+(right-left)/2;
    		if(judge(mid)==true) {
    			right = mid;
    		}else {
    			left = mid+1;
    		}
    	}
    	dduoln(left);