范围 [L, R] 中两个数字的最大可能按位或

给定一个范围[L, R] ，任务是从给定范围中找到某个对(a, b)的最大按位或。
例子：

Input: L = 10, R = 20 
Output: 31
Input: L = 56, R = 77 
Output: 127 
 

方法：首先，将给定的整数L和R都转换为它们的二进制表示。现在，如果L的位数少于R，则将零压入L的 MSB 侧，以使L和R的位数相等。
现在从 MSB 端比较L和R的各个位。由于R大于L ，我们会发现R 的^第i位为1且L 的^第i位为0 的情况。所以在^第i位之后，使L 的所有位都为1 。这确保在L的位中所做的修改不会超过R ，因此它将仅在L和R之间。这样做也确保了最大的按位或。
下面是上述方法的实现：

C++

// C++ implementation of the approach
#include 
using namespace std;
 
// Function to return the maximum bitwise
// OR of any pair from the given range
long long int max_bitwise_or(long long int L, long long int R)
{
    vector v1, v2, v3;
    long long int z = 0, i, ans = 0, cnt = 1;
 
    // Converting L to its binary representation
    while (L > 0) {
        v1.push_back(L % 2);
        L = L / 2;
    }
 
    // Converting R to its binary representation
    while (R > 0) {
        v2.push_back(R % 2);
        R = R / 2;
    }
 
    // In order to make the number
    // of bits of L and R same
    while (v1.size() != v2.size()) {
 
        // Push 0 to the MSB
        v1.push_back(0);
    }
 
    for (i = v2.size() - 1; i >= 0; i--) {
 
        // When ith bit of R is 1
        // and ith bit of L is 0
        if (v2[i] == 1 && v1[i] == 0 && z == 0) {
 
            z = 1;
            continue;
        }
 
        // From MSB side set all bits of L to be 1
        if (z == 1) {
 
            // From (i+1)th bit, all bits
            // of L changed to be 1
            v1[i] = 1;
        }
    }
 
    for (i = 0; i < v2.size(); i++) {
        v3.push_back(v2[i] | v1[i]);
    }
 
    for (i = 0; i < v2.size(); i++) {
        if (v3[i] == 1) {
            ans += cnt;
        }
        cnt *= 2;
    }
    return ans;
}
 
// Driver code
int main()
{
    long long int L = 10, R = 20;
 
    cout << max_bitwise_or(L, R);
 
    return 0;
}

Java

// Java implementation of the approach
import java.util.*;
class GFG
{
 
// Function to return the maximum bitwise
// OR of any pair from the given range
static int max_bitwise_or(int L, int R)
{
    Vector v1 = new Vector(),
                    v2 = new Vector(),
                    v3 = new Vector();
 
    int z = 0, i, ans = 0, cnt = 1;
 
    // Converting L to its binary representation
    while (L > 0)
    {
        v1.add(L % 2);
        L = L / 2;
    }
 
    // Converting R to its binary representation
    while (R > 0)
    {
        v2.add(R % 2);
        R = R / 2;
    }
 
    // In order to make the number
    // of bits of L and R same
    while (v1.size() != v2.size())
    {
 
        // Push 0 to the MSB
        v1.add(0);
    }
 
    for (i = v2.size() - 1; i >= 0; i--)
    {
 
        // When ith bit of R is 1
        // and ith bit of L is 0
        if (v2.get(i) == 1 && v1.get(i) == 0 && z == 0)
        {
            z = 1;
            continue;
        }
 
        // From MSB side set all bits of L to be 1
        if (z == 1)
        {
 
            // From (i+1)th bit, all bits
            // of L changed to be 1
            v1.remove(i);
            v1.add(i,1);
        }
    }
 
    for (i = 0; i < v2.size(); i++)
    {
        v3.add(v2.get(i) | v1.get(i));
    }
 
    for (i = 0; i < v2.size(); i++)
    {
        if (v3.get(i) == 1)
        {
            ans += cnt;
        }
        cnt *= 2;
    }
    return ans;
}
 
// Driver code
public static void main(String []args)
{
    int L = 10, R = 20;
 
    System.out.println(max_bitwise_or(L, R));
}
}
 
// This code is contributed by PrinciRaj1992

Python3

# Python3 implementation of the approach
 
# Function to return the maximum bitwise
# OR of any pair from the given range
def max_bitwise_or(L, R):
    v1 = []
    v2 = []
    v3 = []
    z = 0
    i = 0
    ans = 0
    cnt = 1
 
    # Converting L to its binary representation
    while (L > 0):
        v1.append(L % 2)
        L = L // 2
 
    # Converting R to its binary representation
    while (R > 0):
        v2.append(R % 2)
        R = R // 2
 
    # In order to make the number
    # of bits of L and R same
    while (len(v1) != len(v2)):
 
        # Push 0 to the MSB
        v1.append(0)
 
    for i in range(len(v2) - 1, -1, -1):
 
        # When ith bit of R is 1
        # and ith bit of L is 0
        if (v2[i] == 1 and
            v1[i] == 0 and z == 0):
            z = 1
            continue
 
        # From MSB side set all bits of L to be 1
        if (z == 1):
 
            # From (i+1)th bit, all bits
            # of L changed to be 1
            v1[i] = 1
 
    for i in range(len(v2)):
        v3.append(v2[i] | v1[i])
 
    for i in range(len(v2)):
        if (v3[i] == 1):
            ans += cnt
        cnt *= 2
 
    return ans
 
# Driver code
L = 10
R = 20
 
print(max_bitwise_or(L, R))
 
# This code is contributed by Mohit Kumar

C#

// C# implementation of the approach
using System;
using System.Collections.Generic;
     
class GFG
{
 
// Function to return the maximum bitwise
// OR of any pair from the given range
static int max_bitwise_or(int L, int R)
{
    List v1 = new List(),
              v2 = new List(),
              v3 = new List();
 
    int z = 0, i, ans = 0, cnt = 1;
 
    // Converting L to its binary representation
    while (L > 0)
    {
        v1.Add(L % 2);
        L = L / 2;
    }
 
    // Converting R to its binary representation
    while (R > 0)
    {
        v2.Add(R % 2);
        R = R / 2;
    }
 
    // In order to make the number
    // of bits of L and R same
    while (v1.Count != v2.Count)
    {
 
        // Push 0 to the MSB
        v1.Add(0);
    }
 
    for (i = v2.Count - 1; i >= 0; i--)
    {
 
        // When ith bit of R is 1
        // and ith bit of L is 0
        if (v2[i] == 1 && v1[i] == 0 && z == 0)
        {
            z = 1;
            continue;
        }
 
        // From MSB side set all bits of L to be 1
        if (z == 1)
        {
 
            // From (i+1)th bit, all bits
            // of L changed to be 1
            v1.RemoveAt(i);
            v1.Insert(i, 1);
        }
    }
 
    for (i = 0; i < v2.Count; i++)
    {
        v3.Add(v2[i] | v1[i]);
    }
 
    for (i = 0; i < v2.Count; i++)
    {
        if (v3[i] == 1)
        {
            ans += cnt;
        }
        cnt *= 2;
    }
    return ans;
}
 
// Driver code
public static void Main(String []args)
{
    int L = 10, R = 20;
 
    Console.WriteLine(max_bitwise_or(L, R));
}
}
 
// This code is contributed by Rajput-Ji

Javascript

 
// JavaScript implementation of the approach
 
// Function to return the maximum bitwise
// OR of any pair from the given range
function max_bitwise_or(L, R)
{
    let v1 = [], v2 = [], v3 = [];
    let z = 0, i, ans = 0, cnt = 1;
 
    // Converting L to its binary representation
    while (L > 0) {
        v1.push(L % 2);
        L = parseInt(L / 2);
    }
 
    // Converting R to its binary representation
    while (R > 0) {
        v2.push(R % 2);
        R = parseInt(R / 2);
    }
 
    // In order to make the number
    // of bits of L and R same
    while (v1.length != v2.length) {
 
        // Push 0 to the MSB
        v1.push(0);
    }
 
    for (i = v2.length - 1; i >= 0; i--) {
 
        // When ith bit of R is 1
        // and ith bit of L is 0
        if (v2[i] == 1 && v1[i] == 0 && z == 0) {
 
            z = 1;
            continue;
        }
 
        // From MSB side set all bits of L to be 1
        if (z == 1) {
 
            // From (i+1)th bit, all bits
            // of L changed to be 1
            v1[i] = 1;
        }
    }
 
    for (i = 0; i < v2.length; i++) {
        v3.push(v2[i] | v1[i]);
    }
 
    for (i = 0; i < v2.length; i++) {
        if (v3[i] == 1) {
            ans += cnt;
        }
        cnt *= 2;
    }
    return ans;
}
 
// Driver code
    let L = 10, R = 20;
 
    document.write(max_bitwise_or(L, R));
 

输出：

31

时间复杂度： O(logR + logL)
辅助空间： O(logR + logL)

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