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Expression Add Operators

Given a string num that contains only digits and an integer target, return all possibilities to insert the binary operators '+', '-', and/or '*' between the digits of num so that...

Given a string num that contains only digits and an integer target, return all possibilities to insert the binary operators '+', '-', and/or '*' between the digits of num so that the resultant expression evaluates to the target value.

Note that operands in the returned expressions should not contain leading zeros.

Note that a number can contain multiple digits.

Expression Add Operators diagram

Example 1

Input: num = "123", target = 6

Output: ["1*2*3","1+2+3"]

Explanation: Both "1*2*3" and "1+2+3" evaluate to 6.

Example 2

Input: num = "232", target = 8

Output: ["2*3+2","2+3*2"]

Explanation: Both "2*3+2" and "2+3*2" evaluate to 8.

Example 3

Input: num = "3456237490", target = 9191

Output: []

Explanation: There are no expressions that can be created from "3456237490" to evaluate to 9191.

Constraints

  • 1 <= num.length <= 10
  • num consists of only digits.
  • -231 <= target <= 231 - 1

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