866

Author: lzl124631x

leetcode/866. Prime Palindrome/README.md

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+# [866. Prime Palindrome (Medium)](https://leetcode.com/problems/prime-palindrome/)
+
+<p>Find the smallest prime palindrome greater than or equal to <code>N</code>.</p>
+
+<p>Recall that a&nbsp;number is <em>prime</em> if it's only divisors are 1 and itself, and it is greater than 1.&nbsp;</p>
+
+<p>For example, 2,3,5,7,11 and 13 are&nbsp;primes.</p>
+
+<p>Recall that a number is a <em>palindrome</em> if it reads the same from left to right as it does from right to left.&nbsp;</p>
+
+<p>For example, 12321 is a palindrome.</p>
+
+<p>&nbsp;</p>
+
+<div>
+<p><strong>Example 1:</strong></p>
+
+<pre><strong>Input: </strong><span id="example-input-1-1">6</span>
+<strong>Output: </strong><span id="example-output-1">7</span>
+</pre>
+
+<div>
+<p><strong>Example 2:</strong></p>
+
+<pre><strong>Input: </strong><span id="example-input-2-1">8</span>
+<strong>Output: </strong><span id="example-output-2">11</span>
+</pre>
+
+<div>
+<p><strong>Example 3:</strong></p>
+
+<pre><strong>Input: </strong><span id="example-input-3-1">13</span>
+<strong>Output: </strong><span id="example-output-3">101</span></pre>
+</div>
+</div>
+</div>
+
+<p>&nbsp;</p>
+
+<p><strong>Note:</strong></p>
+
+<ul>
+	<li><code>1 &lt;= N &lt;= 10^8</code></li>
+	<li>The answer is guaranteed to exist and be less than <code>2 * 10^8</code>.</li>
+</ul>
+
+
+**Related Topics**:  
+[Math](https://leetcode.com/tag/math/)
+
+## Solution 1.
+
+```cpp
+// OJ: https://leetcode.com/problems/prime-palindrome/
+// Author: github.com/lzl124631x
+// Time: O(N)
+// Space: O(logN)
+// Ref: https://leetcode.com/problems/prime-palindrome/solution/
+class Solution {
+    bool isPrime(int x) {
+        if (x < 2) return false;
+        for (int d = 2, R = sqrt(x); d <= R; ++d) {
+            if (x % d == 0) return false;
+        }
+        return true;
+    }
+public:
+    int primePalindrome(int N) {
+        for (int L = 1; L <= 5; ++L) {
+            for (int root = pow(10, L - 1); root < pow(10, L); ++root) { // check for odd-length palindromes
+                auto s = to_string(root);
+                for (int k = L - 2; k >= 0; --k) s += s[k];
+                int x = stoi(s);
+                if (x >= N && isPrime(x)) return x;
+            }
+            for (int root = pow(10, L - 1); root < pow(10, L); ++root) {
+                auto s = to_string(root);
+                for (int k = L - 1; k >= 0; --k) s += s[k];
+                int x = stoi(s);
+                if (x >= N && isPrime(x)) return x;
+            }
+        }
+        return -1;
+    }
+};
+```
+
+## Solution 2. Brute Force with Mathematical Shortcut
+
+```cpp
+// OJ: https://leetcode.com/problems/prime-palindrome/
+// Author: github.com/lzl124631x
+// Time: O(N)
+// Space: O(1)
+// Ref: https://leetcode.com/problems/prime-palindrome/solution/
+class Solution {
+    bool isPrime(int x) {
+        if (x < 2) return false;
+        for (int d = 2, R = sqrt(x); d <= R; ++d) {
+            if (x % d == 0) return false;
+        }
+        return true;
+    }
+    int reverse(int N) {
+        int ans = 0;
+        while (N > 0) {
+            ans = 10 * ans + (N % 10);
+            N /= 10;
+        }
+        return ans;
+    }
+public:
+    int primePalindrome(int N) {
+        while (true) {
+            if (N == reverse(N) && isPrime(N)) return N;
+            ++N;
+            if (1e7 < N && N < 1e8) N = 1e8;
+        }
+    }
+};
+```