根据给定条件从数组构造一个K长的二进制字符串

给定一个由N个整数和整数K组成的数组arr [] ，任务是构造一个满足以下条件的长度为K的二进制字符串：

1. 如果可以从数组中形成总和为i的子集，则^第i^个索引处的字符为’ 1′ 。
2. 否则，第i^个索引处的字符为‘0’ 。

例子：

Input: arr[] = {1, 4}, K = 5
Output: 10011
Explanation: 
Character at 1st index can be made by ‘1’ considering the subset {1}. 
Character at 4th index can be made by ‘1’ considering the subset {4}. 
Character at 5th index can be made by ‘1’ considering the subset {1, 4}.

Input: arr[] = {1, 6, 1}, K = 8
Output: 11000111

方法：这个想法是使用贪婪的方法来解决这个问题。步骤如下：

• 初始化一个大小为10 ⁵ + 5的位集，例如bit [] ，并将bit [0] = 1设置为1。
• 遍历数组，对于每个数组元素arr [i] ，如果可以将p作为子集总和获得，则将位更新为位| =位<< << arr [i]以具有位p 。
• 在^第i^次迭代中，位[i]存储初始总和，并且在执行位<< << arr [i]之后，所有位均移位arr [i] 。因此，位p变为p + arr [i]。
• 最后一点| (bit << arr [i])合并这两种情况，无论是否考虑第i^个位置。
• 从1迭代到K，然后将每个值bit [i]打印为所需的二进制字符串。

下面是上述方法的实现：

C++

// C++ program for the above approach
 
#include 
using namespace std;
 
// To construct the
// required binary string
bitset<100003> bit;
 
// Function to construct binary string
// according to the given conditions
void constructBinaryString(int arr[],
                           int N, int K)
{
    // Initialize with 1
    bit[0] = 1;
 
    // Traverse the array
    for (int i = 0; i < N; i++) {
 
        // To check if the i-th integer
        // needs to be considered or not
        bit |= bit << arr[i];
    }
 
    // Print the binary string
    for (int i = 1; i <= K; i++) {
        cout << bit[i];
    }
}
 
// Driver Code
int main()
{
    // Given array
    int arr[] = { 1, 6, 1 };
 
    // Size of the array
    int N = sizeof(arr) / sizeof(arr[0]);
 
    // Given K
    int K = 8;
 
    constructBinaryString(arr, N, K);
}

Python3

# Python program for the above approach
 
# To construct the
# required binary string
#bit = [0]*100003
 
# Function to construct binary string
# according to the given conditions
def constructBinaryString(arr,N, K):
     
    # Initialize with 1
    bit = 1
     
    # Traverse the array
    for i in range(0, N):
       
        # To check if the i-th eger
        # needs to be considered or not
        bit |= bit << arr[i]
     
    # Print the binary string
    #for i in range(1,K):
    #    print(bit[i])
    bit = bin(bit).replace("0b", "")
    print(bit[1:K + 1])
     
# Driver Code
# Given array
arr = [1, 6, 1]
 
# Size of the array
N = len(arr)
 
# Given K
K = 8
 
constructBinaryString(arr, N, K)
 
# This code is contributed by shubhamsingh10

输出：

11000111

时间复杂度： O(N)
辅助空间： O(N)