1702. Maximum Binary String After Change

Description

You are given a binary string binary consisting of only 0's or 1's. You can apply each of the following operations any number of times:

  • Operation 1: If the number contains the substring "00", you can replace it with "10".
    <ul>
	<li>For example, <code>&quot;<u>00</u>010&quot; -&gt; &quot;<u>10</u>010</code>&quot;</li>
</ul>
</li>
<li>Operation 2: If the number contains the substring <code>&quot;10&quot;</code>, you can replace it with <code>&quot;01&quot;</code>.
<ul>
	<li>For example, <code>&quot;000<u>10</u>&quot; -&gt; &quot;000<u>01</u>&quot;</code></li>
</ul>
</li>

Return the maximum binary string you can obtain after any number of operations. Binary string x is greater than binary string y if x's decimal representation is greater than y's decimal representation.

 

Example 1:

Input: binary = "000110"
Output: "111011"
Explanation: A valid transformation sequence can be:
"000110" -> "000101" 
"000101" -> "100101" 
"100101" -> "110101" 
"110101" -> "110011" 
"110011" -> "111011"

Example 2:

Input: binary = "01"
Output: "01"
Explanation: "01" cannot be transformed any further.

 

Constraints:

  • 1 <= binary.length <= 105
  • binary consist of '0' and '1'.

Solutions

Solution 1: Quick Thinking

We observe that operation 2 can move all $1$s to the end of the string, and operation 1 can change all 0000..000 strings to 111..110.

Therefore, to get the maximum binary string, we should move all $1$s that are not at the beginning to the end of the string, making the string in the form of 111..11...00..11, and then use operation 1 to change the middle 000..00 to 111..10. In this way, we can finally get a binary string that contains at most one $0$, which is the maximum binary string we are looking for.

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

Python Code
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class Solution:
    def maximumBinaryString(self, binary: str) -> str:
        k = binary.find('0')
        if k == -1:
            return binary
        k += binary[k + 1 :].count('0')
        return '1' * k + '0' + '1' * (len(binary) - k - 1)

Java Code
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class Solution {
    public String maximumBinaryString(String binary) {
        int k = binary.indexOf('0');
        if (k == -1) {
            return binary;
        }
        int n = binary.length();
        for (int i = k + 1; i < n; ++i) {
            if (binary.charAt(i) == '0') {
                ++k;
            }
        }
        char[] ans = binary.toCharArray();
        Arrays.fill(ans, '1');
        ans[k] = '0';
        return String.valueOf(ans);
    }
}

C++ Code
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class Solution {
public:
    string maximumBinaryString(string binary) {
        int k = binary.find('0');
        if (k == binary.npos) return binary;
        int n = binary.size();
        for (int i = k + 1; i < n; ++i) {
            if (binary[i] == '0') {
                ++k;
            }
        }
        return string(k, '1') + '0' + string(n - k - 1, '1');
    }
};

Go Code
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func maximumBinaryString(binary string) string {
	k := strings.IndexByte(binary, '0')
	if k == -1 {
		return binary
	}
	for _, c := range binary[k+1:] {
		if c == '0' {
			k++
		}
	}
	ans := []byte(binary)
	for i := range ans {
		ans[i] = '1'
	}
	ans[k] = '0'
	return string(ans)
}