Solution

CMakeLists.txt

@@ -0,0 +1,6 @@
+cmake_minimum_required(VERSION 3.21)
+project(max_palindromic_number)
+
+set(CMAKE_CXX_STANDARD 14)
+
+add_executable(max_palindromic_number main.cpp)

main.cpp

@@ -0,0 +1,97 @@
+#include <iostream>
+#include <bitset>
+#include <vector>
+#include <array>
+#include <cassert>
+
+// zero_number_ascii_offset is an ascii number of '0' which is the offset for all ascii digits as well
+constexpr char zero_number_ascii_offset = 48;
+
+// typedef for single digits, just a presence of a digit
+typedef std::bitset<10> singles_t;
+// typedef for counts of doubles digits
+typedef std::array<size_t, 10> doubles_t;
+
+// to_digit converts char to digit
+uint8_t to_digit(char c) {
+    return c - zero_number_ascii_offset;
+}
+
+// to_char converts digit to char
+char to_char(uint8_t n) {
+    return n + zero_number_ascii_offset;
+}
+
+/* solution
+ * let's assume the biggest palindrome has:
+ * 1. biggest single in the center (xxx9xxx > xxx8xxx);
+ * 2. biggest doubles at corners (9xxxx9 > 8xxxx8).
+ *
+ * the algorithm:
+ * 1. count all doubles and singles, takes O(N);
+ * 2. construct the result string with constant length;
+ * 3. if there is biggest single then put it to the center;
+ * 4. fill the string from the center to corners using doubles;
+ *
+ * complexity: O(N)
+ */
+std::string solution(std::string &S) {
+
+    std::bitset<10> singles{};
+    std::array<size_t, 10> doubles{};
+
+    size_t doubles_count = 0;
+    size_t doubles_sum = 0;
+
+    for (char c: S) {
+        uint8_t digit = to_digit(c);
+
+        assert(digit < 10);
+
+        if (singles.test(digit)) {
+            singles.reset(digit);
+            ++doubles[digit];
+            ++doubles_count;
+            doubles_sum += digit;
+        } else {
+            singles.set(digit);
+        }
+    }
+
+    char biggest_single = 0;
+    for (uint8_t i = 10; i > 0; i--) {
+        if (singles.test(i - 1)) {
+            biggest_single = to_char(i - 1);
+            break;
+        }
+    }
+
+    bool has_single = biggest_single > 0;
+    size_t single_offset = (has_single ? 1 : 0);
+    size_t result_len = doubles_count * 2 + single_offset;
+    if (doubles_sum == 0) {
+        result_len = 1;
+        biggest_single = biggest_single > 0 ? biggest_single : '0';
+    }
+
+    std::string result(result_len, biggest_single);
+
+    if (doubles_sum > 0) {
+        size_t iter = 0;
+        for (uint8_t i = 0; i < 10; i++) {
+            size_t count = doubles[i];
+            while (count-- > 0) {
+                result[result_len / 2 - 1 - iter] = to_char(i);
+                result[result_len / 2 + single_offset + iter] = to_char(i);
+                iter++;
+            }
+        }
+    }
+
+    return result;
+}
+
+int main() {
+    std::cout << solution("090") << std::endl;
+    return 0;
+}