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282. Expression Add Operators

Difficulty Topics

Description

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.

 

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

Solution

expression-add-operators.py
class Solution:
    def addOperators(self, s: str, target: int) -> List[str]:
        n = len(s)
        res = []

        def backtrack(i, path, curr, prev):
            if i == n:
                if curr == target:
                    res.append(path)
                return

            for j in range(i, n):
                if j > i and s[i] == '0': break
                num = int(s[i : j + 1])

                if i == 0:
                    backtrack(j + 1, path + str(num), curr + num, num)
                else:
                    backtrack(j + 1, path + "+" + str(num), curr + num, num)
                    backtrack(j + 1, path + "-" + str(num), curr - num, -num)
                    backtrack(j + 1, path + "*" + str(num), curr - prev + prev * num, prev * num)

        backtrack(0, "", 0, 0)
        return res