2 的幂与所需的和
给定一个整数 N，任务是找到数，当这些数被提升到 2 的幂，最后相加，得到整数 N
示例:
Input : 71307
Output : 0, 1, 3, 7, 9, 10, 12, 16
Explanation :
71307 = 2^0 + 2^1 + 2^3 + 2^7 +
2^9 + 2^10 + 2^12 + 2^16
Input : 1213
Output : 0, 2, 3, 4, 5, 7, 10
Explanation :
1213 = 2^0 + 2^2 + 2^3 + 2^4 +
2^5 + 2^7 + 2^10
逼近: 每个数都可以用 2 的幂来描述。 例:29 = 2^0 + 2^2 + 2^3 + 2^4. 2^0(2 的指数是' 0 ')0 2^2(2 的指数是' 2 ')1 2^3(2 的指数是' 3 ')3 2^4(2 的指数是' 4') 4 通过将给定数的余数除以 2 直到大于 0 时推到向量，将每个数转换为其二进制等价数。现在，迭代它的二进制等价物，只要有设置位，就打印第 I 个值(迭代号)。
应用: 汉明码:汉明码是一种能够检测并纠正一位错误的纠错码。这种模式也用于汉明码错误检测中，奇偶校验位在 LSB(最低有效位)的基础上存储数字的异或，其中数字以块的形式分配，您需要找到给定数字的 2 的幂和存在的块。
下图显示了带有给定数字的块。
以下是上述方法的实施:
C++
// CPP program to find the
// blocks for given number.
#include <bits/stdc++.h>
using namespace std;
void block(long int x)
{
vector<long int> v;
// Converting the decimal number
// into its binary equivalent.
cout << "Blocks for " << x << " : ";
while (x > 0)
{
v.push_back(x % 2);
x = x / 2;
}
// Displaying the output when
// the bit is '1' in binary
// equivalent of number.
for (int i = 0; i < v.size(); i++)
{
if (v[i] == 1)
{
cout << i;
if (i != v.size() - 1)
cout << ", ";
}
}
cout << endl;
}
// Driver Function
int main()
{
block(71307);
block(1213);
block(29);
block(100);
return 0;
}
Java 语言(一种计算机语言，尤用于创建网站)
// Java program to find the
// blocks for given number.
import java.util.*;
class GFG {
static void block(long x)
{
ArrayList<Integer> v = new ArrayList<Integer>();
// Convert decimal number to
// its binary equivalent
System.out.print("Blocks for "+x+" : ");
while (x > 0)
{
v.add((int)x % 2);
x = x / 2;
}
// Displaying the output when
// the bit is '1' in binary
// equivalent of number.
for (int i = 0; i < v.size(); i++)
{
if (v.get(i) == 1)
{
System.out.print(i);
if (i != v.size() - 1)
System.out.print( ", ");
}
}
System.out.println();
}
// Driver Code
public static void main(String args[])
{
block(71307);
block(1213);
block(29);
block(100);
}
}
// This code is contributed by Arnab Kundu.
Python 3
# Python3 program to find the
# blocks for given number.
def block(x):
v = []
# Converting the decimal number
# into its binary equivalent.
print ("Blocks for %d : " %x, end="")
while (x > 0):
v.append(int(x % 2))
x = int(x / 2)
# Displaying the output when
# the bit is '1' in binary
# equivalent of number.
for i in range(0, len(v)):
if (v[i] == 1):
print (i, end = "")
if (i != len(v) - 1):
print (", ", end = "")
print ("\n")
block(71307)
block(1213)
block(29)
block(100)
# This code is contributed by Manish
# Shaw (manishshaw1)
C
// C# program to find the
// blocks for given number.
using System;
using System.Collections.Generic;
class GFG {
static void block(long x)
{
List<int> v = new List<int>();
// Convert decimal number to
// its binary equivalent
Console.Write("Blocks for " + x + " : ");
while (x > 0)
{
v.Add((int)x % 2);
x = x / 2;
}
// Displaying the output when
// the bit is '1' in binary
// equivalent of number.
for (int i = 0; i < v.Count; i++)
{
if (v[i] == 1)
{
Console.Write(i);
if (i != v.Count - 1)
Console.Write(", ");
}
}
Console.WriteLine();
}
// Driver Code here
public static void Main()
{
block(71307);
block(1213);
block(29);
block(100);
}
}
// This code is contributed by Ajit.
服务器端编程语言（Professional Hypertext Preprocessor 的缩写）
<?php
// PHP program to find the
// blocks for given number.
function block($x)
{
$v = array();
// Convert decimal number to
// its binary equivalent
echo 'Blocks for ' .$x.' : ';
while ($x > 0)
{
array_push($v,intval($x % 2));
$x = intval($x / 2);
}
// Displaying the output when
// the bit is '1' in binary
// equivalent of number.
for ($i = 0; $i < sizeof($v); $i++)
{
if ($v[$i] == 1)
{
print $i;
if ($i != sizeof($v) - 1)
echo ', ';
}
}
echo "\n";
}
// Driver Code
block(71307);
block(1213);
block(29);
block(100);
// This code is contributed
// by Manish Shaw (manishshaw1)
?>
java 描述语言
<script>
// Javascript program to find the
// blocks for given number.
function block(x)
{
let v = [];
// Convert decimal number to
// its binary equivalent
document.write("Blocks for " + x + " : ");
while (x > 0)
{
v.push(x % 2);
x = parseInt(x / 2, 10);
}
// Displaying the output when
// the bit is '1' in binary
// equivalent of number.
for(let i = 0; i < v.length; i++)
{
if (v[i] == 1)
{
document.write(i);
if (i != v.length - 1)
document.write(", ");
}
}
document.write("</br>");
}
// Driver code
block(71307);
block(1213);
block(29);
block(100);
// This code is contributed by mukesh07
</script>
Output:
Blocks for 71307 : 0, 1, 3, 7, 9, 10, 12, 16
Blocks for 1213 : 0, 2, 3, 4, 5, 7, 10
Blocks for 29 : 0, 2, 3, 4
Blocks for 100 : 2, 5, 6
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