# Split Two Strings to Make Palindrome

You are given two strings `a` and `b` of the same length. Choose an index and split both strings **at the same index**, splitting `a` into two strings: `aprefix` and `asuffix` where `a = aprefix + asuffix`, and splitting `b` into two strings: `bprefix` and `bsuffix` where `b = bprefix + bsuffix`. Check if `aprefix + bsuffix` or `bprefix + asuffix` forms a palindrome.

When you split a string `s` into `sprefix` and `ssuffix`, either `ssuffix` or `sprefix` is allowed to be empty. For example, if `s = "abc"`, then `"" + "abc"`, `"a" + "bc"`, `"ab" + "c"` , and `"abc" + ""` are valid splits.

Return `true` _if it is possible to form a palindrome string, otherwise return_ `false`.

**Notice** that `x + y` denotes the concatenation of strings `x` and `y`.

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**Example 1:**

<pre><code><strong>Input: a = "x", b = "y"
</strong><strong>Output: true
</strong><strong>Explaination: If either a or b are palindromes the answer is true since you can split in the following way:
</strong>aprefix = "", asuffix = "x"
bprefix = "", bsuffix = "y"
Then, aprefix + bsuffix = "" + "y" = "y", which is a palindrome.
</code></pre>

**Example 2:**

<pre><code><strong>Input: a = "xbdef", b = "xecab"
</strong><strong>Output: false
</strong></code></pre>

**Example 3:**

<pre><code><strong>Input: a = "ulacfd", b = "jizalu"
</strong><strong>Output: true
</strong><strong>Explaination: Split them at index 3:
</strong>aprefix = "ula", asuffix = "cfd"
bprefix = "jiz", bsuffix = "alu"
Then, aprefix + bsuffix = "ula" + "alu" = "ulaalu", which is a palindrome.
</code></pre>

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**Constraints:**

* `1 <= a.length, b.length <= 105`
* `a.length == b.length`
* `a` and `b` consist of lowercase English letters



### Answer:

```java
class Solution {
    public int maxPalindromeFromCenter(String str, int s, int e) {
        int len = 0;
        while (s >= 0 && str.charAt(s) == str.charAt(e)) {
            len++;
            s--;
            e++;
        }
        return len;
    }

    // Find max common prefix & suffix between the 2 strings
    public int maxCommon(String a, String b, int n) {
        int s = 0, e = n - 1;
        int len1 = 0;
        while (s <= e) {
            if (a.charAt(s) == b.charAt(e))
                len1++;
            else
                break;
            s++;
            e--;
        }
        int len2 = 0;
        s = 0;
        e = n - 1;
        while (s <= e) {
            if (b.charAt(s) == a.charAt(e))
                len2++;
            else
                break;
            s++;
            e--;
        }
        return Math.max(len1, len2);
    }

    public boolean checkPalindromeFormation(String a, String b) {
        int n = a.length();
        int P1 = maxPalindromeFromCenter(a, (int) Math.floor((n - 1) / 2.0), (int) Math.ceil((n - 1) / 2.0));
        int P2 = maxPalindromeFromCenter(b, (int) Math.floor((n - 1) / 2.0), (int) Math.ceil((n - 1) / 2.0));
        int common = maxCommon(a, b, n);
        return common + Math.max(P1, P2) >= (n + 1) / 2;
    }
}
```
