通过插入加法运算符可能的数字字符串的所有可能表达式的总和

给定一个长度为N的数字字符串str ，任务是通过在字符串的字符之间插入“+”运算符任意次数来找到所有可能表达式的总和。

例子：

Input: str = “125”
Output: 176
Explanation:
Inserting “+” after 1st index modifies str to “1+25” and value = 26
Inserting “+” after 2nd index modifies str to “12+5” and value = 17
Inserting “+” after both 1st and 2nd index modifies str to “1+2+5” and value = 8
Therefore, the total sum of all possible expression is 125 + 26 + 17 + 8 = 176

Input: str = “9999999999”
Output: 12656242944

方法：想法是以所有可能的方式在字符串的所有可能索引处插入“+”运算符并计算总和。最后，打印获得的总和。请按照以下步骤解决问题：

• 初始化一个变量，比如 sumOfExp ，通过在字符串的所有可能索引处插入“+”运算符来存储所有可能表达式的总和。
• 迭代生成所有可能的字符串索引子集。对于索引的每个子集，在子集的元素处插入“+”运算符，并将sumOfExp增加当前表达式的总和。
• 最后，打印sumOfExp的值。

下面是上述方法的实现：

Python3

# Python program to implement
# the above approach
  
# Function to find sum of all expressions by
# inserting '+' operator at all possible indices
def findSumOfExpressions(S, N):
  
    # Stores sum of all expressions by inserting
    # '+' operator at all possible indices
    sumOfExp = 0
  
    # Generate all possible subset
    # of indices iteratively
    for i in range(2 ** (N - 1)):
  
        # Stores sum of 
        # current expressions
        ans_sub = 0
  
        # Stores numbers of
        # current expressions
        subst = S[0]
  
        # Traverse the string at insert + at
        # current subset of indices
        for j in range(N - 1):
  
            # If current index exists
            # in the current subset
            if (i >> j) & 1:
  
                # Update ans_sub
                ans_sub += int(subst)
  
                # Update subst
                subst = S[j + 1]
            else:
  
                # Update subst
                subst += S[j + 1]
  
            # + can't be inserted after
            # the last index    
            if j == N - 2:
                ans_sub += int(subst)
  
        # Update ans
        sumOfExp += ans_sub
  
    # Base case     
    if N == 1:
        print(int(S))
    else:
  
        # Print answer
        print(sumOfExp)
  
# Driver Code
if __name__ == '__main__':
      
    # Given string
    S = "9999999999"
      
    # Length of the string
    N = len(S)
  
    # Function call
    findSumOfExpressions(S, N)

输出：

12656242944

时间复杂度： O(2 ^N * N)
辅助空间： O(1)