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Given a numeric string str of length N, determine the sum of all possible expressions that can be formed by inserting the '+' operator between the characters of the string in all possible ways. Each way of inserting the '+' operator creates a unique expression, and the task is to compute the sum of the evaluated values of all such distinct expressions.
For example, with the string "125", there are four possible expressions: "125" (no operators), "1+25", "12+5", and "1+2+5". The sum of all these expressions is 125 + 26 + 17 + 8 = 176.
Input:
str (String): A numeric string consisting of digits (0-9) only. The string length is N where 1 ≤ N ≤ 10.Output:
long or unsigned long long to handle large sums.Example 1:
Input: str = "125"
Output: 176
Explanation:
Example 2:
Input: str = "9999999999"
Output: 12656242944
Explanation: There are 2^9 = 512 possible ways to insert '+' operators in the 10-digit string. Each combination yields a different expression value. The sum of all 512 expression values equals 12656242944.
unsigned long long in C++, long in Java, or appropriate type in other languages)Use bit manipulation with subset enumeration: Iterate through all possible integers from 0 to 2^(N-1) - 1. Each integer represents a binary bitmask indicating positions where '+' operators should be inserted. For each bitmask, construct the corresponding expression and evaluate it by parsing segments between operator positions, then accumulate the sum.