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This approach involves using a recursive backtracking algorithm to explore all possible combinations of the operators between the digits. The algorithm tries to build expressions from the input string by considering each possible position for inserting an operator. It is essential to keep track of the current value of the expression, the previous operand (to handle multiplication correctly with due precedence), and the current path (the expression string being built).
We also need to ensure that no operand in the expression starts with a zero unless the operand is zero itself to avoid leading zero issues.
Time Complexity: O(4^n), where n is the length of the input string 'num'. This accounts for the potential combinatorial explosion in choices of operations between each digit.
Space Complexity: O(n), due to the recursion call stack and the space needed to store the expressions.
1using System;
2using System.Collections.Generic;
3
4public class Solution {
5 public IList<string> AddOperators(string num, int target) {
6 List<string> result = new List<string>();
7 Helper(num, target, 0, 0, 0, "", result);
8 return result;
9 }
10
11 private void Helper(string num, int target, int pos, long eval, long multed, string path, List<string> result) {
12 if (pos == num.Length) {
13 if (eval == target) {
result.Add(path);
}
return;
}
for (int i = pos; i < num.Length; i++) {
if (i != pos && num[pos] == '0') break;
string currStr = num.Substring(pos, i - pos + 1);
long curr = long.Parse(currStr);
if (pos == 0) {
Helper(num, target, i + 1, curr, curr, currStr, result);
} else {
Helper(num, target, i + 1, eval + curr, curr, path + "+" + currStr, result);
Helper(num, target, i + 1, eval - curr, -curr, path + "-" + currStr, result);
Helper(num, target, i + 1, eval - multed + multed * curr, multed * curr, path + "*" + currStr, result);
}
}
}
public static void Main() {
Solution solution = new Solution();
IList<string> results = solution.AddOperators("123", 6);
foreach (string expr in results) {
Console.WriteLine(expr);
}
}
}The C# implementation follows a similar structure, utilizing a recursive helper method to guide exploration. The `List