# 2546. Apply Bitwise Operations to Make Strings Equal

## Description

You are given two 0-indexed binary strings s and target of the same length n. You can do the following operation on s any number of times:

• Choose two different indices i and j where 0 <= i, j < n.
• Simultaneously, replace s[i] with (s[i] OR s[j]) and s[j] with (s[i] XOR s[j]).

For example, if s = "0110", you can choose i = 0 and j = 2, then simultaneously replace s[0] with (s[0] OR s[2] = 0 OR 1 = 1), and s[2] with (s[0] XOR s[2] = 0 XOR 1 = 1), so we will have s = "1110".

Return true if you can make the string s equal to target, or false otherwise.

Example 1:

Input: s = "1010", target = "0110"
Output: true
Explanation: We can do the following operations:
- Choose i = 2 and j = 0. We have now s = "0010".
- Choose i = 2 and j = 1. We have now s = "0110".
Since we can make s equal to target, we return true.


Example 2:

Input: s = "11", target = "00"
Output: false
Explanation: It is not possible to make s equal to target with any number of operations.


Constraints:

• n == s.length == target.length
• 2 <= n <= 105
• s and target consist of only the digits 0 and 1.

## Solutions

Solution 1: Lateral Thinking

We notice that $1$ is actually a “tool” for number conversion. Therefore, as long as both strings either have $1$ or neither have $1$, we can make the two strings equal through operations.

The time complexity is $O(n)$, where $n$ is the length of the string. The space complexity is $O(1)$.

• class Solution {
public boolean makeStringsEqual(String s, String target) {
return s.contains("1") == target.contains("1");
}
}

• class Solution {
public:
bool makeStringsEqual(string s, string target) {
auto a = count(s.begin(), s.end(), '1') > 0;
auto b = count(target.begin(), target.end(), '1') > 0;
return a == b;
}
};

• class Solution:
def makeStringsEqual(self, s: str, target: str) -> bool:
return ("1" in s) == ("1" in target)


• func makeStringsEqual(s string, target string) bool {
return strings.Contains(s, "1") == strings.Contains(target, "1")
}

• function makeStringsEqual(s: string, target: string): boolean {
return s.includes('1') === target.includes('1');
}


• impl Solution {
pub fn make_strings_equal(s: String, target: String) -> bool {
s.contains('1') == target.contains('1')
}
}