给定整数N ,任务是找到比设置位数最大的N小的最大数。
例子:
Input : N = 345
Output : 255
Explanation:
345 in binary representation is 101011001 with 5 set bits, and 255 is 11111111 with maximum number of set bits less than the integer N.
Input : N = 2
Output : 1
Explanation:
2 in binary representation is 10 with 1 set bit, and 1 has maximum number of set bits less than the integer N.
天真的方法:
解决上述问题的简单方法是迭代直到整数N并找到每个数字的设置位数,并在每个步骤中存储具有最大设置位数的位数。
下面是上述方法的实现:
C++
// C++ implementation to Find the
// largest number smaller than integer
// N with maximum number of set bits
#include
using namespace std;
// Function to return the largest
// number less than N
int largestNum(int n)
{
int num = 0;
int max_setBits = 0;
// Iterate through all the numbers
for (int i = 0; i <= n; i++) {
// Find the number of set bits
// for the current number
int setBits = __builtin_popcount(i);
// Check if this number has the
// highest set bits
if (setBits >= max_setBits) {
num = i;
max_setBits = setBits;
}
}
// Return the result
return num;
}
// Driver code
int main()
{
int N = 345;
cout << largestNum(N);
return 0;
}
Java
// Java implementation to Find the
// largest number smaller than integer
// N with maximum number of set bits
class GFG
{
/* Function to get no of set
bits in binary representation
of positive integer n */
static int countSetBits(int n)
{
int count = 0;
while (n > 0)
{
count += n & 1;
n >>= 1;
}
return count;
}
// Function to return the largest
// number less than N
static int largestNum(int n)
{
int num = 0;
int max_setBits = 0;
// Iterate through all the numbers
for (int i = 0; i <= n; i++)
{
// Find the number of set bits
// for the current number
int setBits = countSetBits(i);
// Check if this number has the
// highest set bits
if (setBits >= max_setBits)
{
num = i;
max_setBits = setBits;
}
}
// Return the result
return num;
}
// Driver code
public static void main (String[] args)
{
int N = 345;
System.out.println(largestNum(N));
}
}
// This code is contributed by AnkitRai01
Python3
# Python3 implementation to find the
# largest number smaller than integer
# N with maximum number of set bits
# Function to return the largest
# number less than N
def largestNum(n):
num = 0;
max_setBits = 0;
# Iterate through all the numbers
for i in range(n + 1):
# Find the number of set bits
# for the current number
setBits = bin(i).count('1');
# Check if this number has the
# highest set bits
if (setBits >= max_setBits):
num = i;
max_setBits = setBits;
# Return the result
return num;
# Driver code
if __name__ == "__main__" :
N = 345;
print(largestNum(N));
# This code is contributed by AnkitRai01
C#
// C# implementation to Find the
// largest number smaller than integer
// N with a maximum number of set bits
using System;
class GFG{
// Function to get no of set
// bits in binary representation
// of positive integer n
static int countSetBits(int n)
{
int count = 0;
while (n > 0)
{
count += n & 1;
n >>= 1;
}
return count;
}
// Function to return the largest
// number less than N
static int largestNum(int n)
{
int num = 0;
int max_setBits = 0;
// Iterate through all the numbers
for(int i = 0; i <= n; i++)
{
// Find the number of set bits
// for the current number
int setBits = countSetBits(i);
// Check if this number has
// the highest set bits
if (setBits >= max_setBits)
{
num = i;
max_setBits = setBits;
}
}
// Return the result
return num;
}
// Driver code
public static void Main(String[] args)
{
int N = 345;
Console.Write(largestNum(N));
}
}
// This code is contributed by shivanisinghss2110
Javascript
C++
// C++ implementation to Find the
// largest number smaller than integer
// N with maximum number of set bits
#include
using namespace std;
// Function to return the largest
// number less than N
int largestNum(int n)
{
int num = 0;
// Iterate through all possible values
for (int i = 0; i <= 32; i++)
{
// Multiply the number by 2 i times
int x = (1 << i);
if ((x - 1) <= n)
num = (1 << i) - 1;
else
break;
}
// Return the final result
return num;
}
// Driver code
int main()
{
int N = 345;
cout << largestNum(N);
return 0;
}
Java
// Java implementation to Find the
// largest number smaller than integer
// N with maximum number of set bits
import java.util.*;
class GFG{
// Function to return the largest
// number less than N
static int largestNum(int n)
{
int num = 0;
// Iterate through all possible values
for (int i = 0; i <= 32; i++)
{
// Multiply the number by 2 i times
int x = (1 << i);
if ((x - 1) <= n)
num = (1 << i) - 1;
else
break;
}
// Return the final result
return num;
}
// Driver code
public static void main(String args[])
{
int N = 345;
System.out.print(largestNum(N));
}
}
// This code is contributed by Akanksha_Rai
Python3
# Python3 implementation to find the
# largest number smaller than integer
# N with the maximum number of set bits
# Function to return the largest
# number less than N
def largestNum(n):
num = 0;
# Iterate through all possible
# values
for i in range(32):
# Multiply the number by
# 2 i times
x = (1 << i);
if ((x - 1) <= n):
num = (1 << i) - 1;
else:
break;
# Return the final result
return num;
# Driver code
if __name__ == "__main__":
N = 345;
print(largestNum(N));
# This code is contributed by AnkitRai01
C#
// C# implementation to Find the
// largest number smaller than integer
// N with maximum number of set bits
using System;
class GFG{
// Function to return the largest
// number less than N
static int largestNum(int n)
{
int num = 0;
// Iterate through all possible values
for (int i = 0; i <= 32; i++)
{
// Multiply the number by 2 i times
int x = (1 << i);
if ((x - 1) <= n)
num = (1 << i) - 1;
else
break;
}
// Return the final result
return num;
}
// Driver code
public static void Main()
{
int N = 345;
Console.Write(largestNum(N));
}
}
// This code is contributed by Nidhi_Biet
Javascript
输出:
255
高效方法:要优化上述解决方案,我们必须观察到设置位最高的数肯定是2 k – 1的形式。因此,我们只需要遍历k的可能值并找到最高值刚好小于整数N。由于我们要遍历指数变量,因此最多将需要log(N)个步骤。
下面是上述方法的实现:
C++
// C++ implementation to Find the
// largest number smaller than integer
// N with maximum number of set bits
#include
using namespace std;
// Function to return the largest
// number less than N
int largestNum(int n)
{
int num = 0;
// Iterate through all possible values
for (int i = 0; i <= 32; i++)
{
// Multiply the number by 2 i times
int x = (1 << i);
if ((x - 1) <= n)
num = (1 << i) - 1;
else
break;
}
// Return the final result
return num;
}
// Driver code
int main()
{
int N = 345;
cout << largestNum(N);
return 0;
}
Java
// Java implementation to Find the
// largest number smaller than integer
// N with maximum number of set bits
import java.util.*;
class GFG{
// Function to return the largest
// number less than N
static int largestNum(int n)
{
int num = 0;
// Iterate through all possible values
for (int i = 0; i <= 32; i++)
{
// Multiply the number by 2 i times
int x = (1 << i);
if ((x - 1) <= n)
num = (1 << i) - 1;
else
break;
}
// Return the final result
return num;
}
// Driver code
public static void main(String args[])
{
int N = 345;
System.out.print(largestNum(N));
}
}
// This code is contributed by Akanksha_Rai
Python3
# Python3 implementation to find the
# largest number smaller than integer
# N with the maximum number of set bits
# Function to return the largest
# number less than N
def largestNum(n):
num = 0;
# Iterate through all possible
# values
for i in range(32):
# Multiply the number by
# 2 i times
x = (1 << i);
if ((x - 1) <= n):
num = (1 << i) - 1;
else:
break;
# Return the final result
return num;
# Driver code
if __name__ == "__main__":
N = 345;
print(largestNum(N));
# This code is contributed by AnkitRai01
C#
// C# implementation to Find the
// largest number smaller than integer
// N with maximum number of set bits
using System;
class GFG{
// Function to return the largest
// number less than N
static int largestNum(int n)
{
int num = 0;
// Iterate through all possible values
for (int i = 0; i <= 32; i++)
{
// Multiply the number by 2 i times
int x = (1 << i);
if ((x - 1) <= n)
num = (1 << i) - 1;
else
break;
}
// Return the final result
return num;
}
// Driver code
public static void Main()
{
int N = 345;
Console.Write(largestNum(N));
}
}
// This code is contributed by Nidhi_Biet
Java脚本
输出:
255
时间复杂度: O(log N)