מספר נקרא שמח אם הוא מוביל ל-1 לאחר רצף של שלבים שבו כל מספר צעד מוחלף בסכום הריבועים של הספרה שלו, כלומר אם נתחיל במספר שמח ונמשיך להחליף אותו בסכום ריבועי ספרתי נגיע ל-1.
דוגמאות:
Input: n = 19
Output: True
19 is Happy Number
1^2 + 9^2 = 82
8^2 + 2^2 = 68
6^2 + 8^2 = 100
1^2 + 0^2 + 0^2 = 1
As we reached to 1 19 is a Happy Number.
Input: n = 20
Output: False
מספר לא יהיה Happy Number כאשר הוא עושה לולאה ברצף שלו כלומר הוא נוגע במספר ברצף שכבר נגעו בו. אז כדי לבדוק אם מספר שמח או לא, נוכל לשמור סט אם אותו מספר יחזור שוב, אנו מסמנים את התוצאה כלא מאושרת. פונקציה פשוטה בגישה לעיל יכולה להיכתב כדלקמן -
סוגי מחשביםC++
// method return true if n is Happy Number int numSquareSum(int n) {  int num = 0;  while (n != 0) {  int digit = n % 10;  num += digit * digit;  n /= 10;  }  return num; } int isHappyNumber(int n) {  set<int> st;  while (1)  {  n = numSquareSum(n);  if (n == 1)  return true;  if (st.find(n) != st.end())  return false;  st.insert(n);  } } 
 Java // method return true if n is Happy Number public static int numSquareSum(int n) {  int num = 0;  while (n != 0) {  int digit = n % 10;  num += digit * digit;  n /= 10;  }  return num; } static boolean isHappyNumber(int n) {  HashSet<Integer> st = new HashSet<>();  while (true) {  n = numSquareSum(n);  if (n == 1)  return true;  if (st.contains(n))  return false;  st.add(n);  } } // This code is contributed by Princi Singh 
 Python # method return true if n is Happy Number def numSquareSum(n): num = 0 while(n): digit = n % 10 num = num + digit*digit n = n // 10 return num def isHappyNumber(n): st = set() while (1): n = numSquareSum(n) if (n == 1): return True if n not in st: return False st.insert(n) 
 C# // Method return true if n is Happy Number static int numSquareSum(int n) {  int num = 0;  while (n != 0) {  int digit = n % 10;  num += digit * digit;  n /= 10;  }  return num; } static int isHappyNumber(int n) {  HashSet<int> st = new HashSet<>();  while (1) {  n = numSquareSum(n);  if (n == 1)  return true;  if (st.Contains(n))  return false;  st.Add(n);  } } // This code is contributed by 29AjayKumar 
 JavaScript <script> // method return true if n is Happy Number  function numSquareSum(n) {  let num = 0;  while (n !== 0) {  let digit = n % 10;  num += digit * digit;  n = Math.floor(n / 10);  }  return num;  }  let st = new Set();  while (1)  {  n = numSquareSum(n);  if (n == 1)  return true;  if (st.has(n))  return false;  st.add(n);  } } //This code is contributed by Mayank Tyagi </script> 
 ניתוח מורכבות:
    מורכבות זמן:   O(n*log(n)).   
    מרחב עזר:   O(n) מאז שימוש בסט נוסף לאחסון
ערך של מחרוזת
אנחנו יכולים לפתור בעיה זו מבלי להשתמש בשטח נוסף וניתן להשתמש בטכניקה הזו גם בבעיות דומות אחרות. אם נתייחס לכל מספר כצומת והחלפה בספרת סכום ריבועי כקישור אז הבעיה הזו זהה ל מציאת לולאה ברשימת קישורים :
אז בתור פתרון מוצע מהקישור לעיל נשמור על שני מספרים איטיים ומהירים שניהם אתחול ממספר נתון איטי מוחלף צעד אחד בכל פעם ומהיר מוחלף שני שלבים בכל פעם. אם הם נפגשים ב-1 אז המספר הנתון הוא Happy Number אחרת לא.
C++// C++ program to check a number is a Happy number or not #include     using namespace std; // Utility method to return sum of square of digit of n int numSquareSum(int n) {  int squareSum = 0;  while (n) {  squareSum += (n % 10) * (n % 10);  n /= 10;  }  return squareSum; } // method return true if n is Happy number bool isHappynumber(int n) {  int slow fast;  // initialize slow and fast by n  slow = fast = n;  do {  // move slow number by one iteration  slow = numSquareSum(slow);  // move fast number by two iteration  fast = numSquareSum(numSquareSum(fast));  } while (slow != fast);  // if both number meet at 1 then return true  return (slow == 1); } // Driver code to test above methods int main() {  int n = 13;  if (isHappynumber(n))  cout << n << ' is a Happy numbern';  else  cout << n << ' is not a Happy numbern'; } // This code is contributed by divyeshrabadiya07 
 C // C program to check a number is a Happy number or not #include   #include   // Utility method to return sum of square of digit of n int numSquareSum(int n) {  int squareSum = 0;  while (n) {  squareSum += (n % 10) * (n % 10);  n /= 10;  }  return squareSum; } // method return true if n is Happy number bool isHappynumber(int n) {  int slow fast;  // initialize slow and fast by n  slow = fast = n;  do {  // move slow number by one iteration  slow = numSquareSum(slow);  // move fast number by two iteration  fast = numSquareSum(numSquareSum(fast));  } while (slow != fast);  // if both number meet at 1 then return true  return (slow == 1); } // Driver code to test above methods int main() {  int n = 13;  if (isHappynumber(n))  printf('%d is a Happy numbern' n);  else  printf('%d is not a Happy numbern' n); } // This code is contributed by Sania Kumari Gupta // (kriSania804) 
 Java // Java program to check a number is a Happy // number or not class GFG {   // Utility method to return sum of square of // digit of n static int numSquareSum(int n) {  int squareSum = 0;  while (n!= 0)  {  squareSum += (n % 10) * (n % 10);  n /= 10;  }  return squareSum; }   // method return true if n is Happy number static boolean isHappynumber(int n) {  int slow fast;    // initialize slow and fast by n  slow = fast = n;  do  {  // move slow number  // by one iteration  slow = numSquareSum(slow);    // move fast number  // by two iteration  fast = numSquareSum(numSquareSum(fast));    }  while (slow != fast);    // if both number meet at 1  // then return true  return (slow == 1); }   // Driver code to test above methods public static void main(String[] args) {  int n = 13;  if (isHappynumber(n))  System.out.println(n +   ' is a Happy number');  else  System.out.println(n +   ' is not a Happy number'); } } 
 Python # Python3 program to check if a number is a Happy number or not # Utility method to return the sum of squares of digits of n def num_square_sum(n): square_sum = 0 while n: square_sum += (n % 10) ** 2 n //= 10 return square_sum # Method returns True if n is a Happy number def is_happy_number(n): # Initialize slow and fast pointers slow = n fast = n while True: # Move slow pointer by one iteration slow = num_square_sum(slow) # Move fast pointer by two iterations fast = num_square_sum(num_square_sum(fast)) if slow != fast: continue else: break # If both pointers meet at 1 then return True return slow == 1 # Driver Code n = 13 if is_happy_number(n): print(n 'is a Happy number') else: print(n 'is not a Happy number') 
 C# // C# program to check a number // is a Happy number or not using System; class GFG { // Utility method to return  // sum of square of digit of n static int numSquareSum(int n) {  int squareSum = 0;  while (n!= 0)  {  squareSum += (n % 10) *   (n % 10);  n /= 10;  }  return squareSum; } // method return true if // n is Happy number static bool isHappynumber(int n) {  int slow fast;  // initialize slow and  // fast by n  slow = fast = n;  do  {    // move slow number  // by one iteration  slow = numSquareSum(slow);  // move fast number  // by two iteration  fast = numSquareSum(numSquareSum(fast));  }  while (slow != fast);  // if both number meet at 1  // then return true  return (slow == 1); } // Driver code public static void Main() {  int n = 13;  if (isHappynumber(n))  Console.WriteLine(n +   ' is a Happy number');  else  Console.WriteLine(n +   ' is not a Happy number'); } } // This code is contributed by anuj_67. 
 JavaScript <script> // Javascript program to check a number is a Happy // number or not // Utility method to return sum of square of // digit of n function numSquareSum(n) {  var squareSum = 0;  while (n!= 0)  {  squareSum += (n % 10) * (n % 10);  n = parseInt(n/10);  }  return squareSum; }   // method return true if n is Happy number function isHappynumber(n) {  var slow fast;    // initialize slow and fast by n  slow = fast = n;  do  {  // move slow number  // by one iteration  slow = numSquareSum(slow);    // move fast number  // by two iteration  fast = numSquareSum(numSquareSum(fast));    }  while (slow != fast);    // if both number meet at 1  // then return true  return (slow == 1); }   // Driver code to test above methods var n = 13; if (isHappynumber(n))  document.write(n +   ' is a Happy number'); else  document.write(n +   ' is not a Happy number');   // This code contributed by Princi Singh  </script> 
 PHP  // PHP program to check a number // is a Happy number or not // Utility method to return  // sum of square of digit of n function numSquareSum( $n) { $squareSum = 0; while ($n) { $squareSum += ($n % 10) * ($n % 10); $n /= 10; } return $squareSum; } // method return true if // n is Happy number function isHappynumber( $n) { $slow; $fast; // initialize slow  // and fast by n $slow = $n; $fast = $n; do { // move slow number // by one iteration $slow = numSquareSum($slow); // move fast number // by two iteration $fast = numSquareSum(numSquareSum($fast)); } while ($slow != $fast); // if both number meet at 1  // then return true return ($slow == 1); } // Driver Code $n = 13; if (isHappynumber($n)) echo $n  ' is a Happy numbern'; else echo n  ' is not a Happy numbern'; // This code is contributed by anuj_67. ?>  פלט:
13 is a Happy Numberניתוח מורכבות:
    מורכבות זמן:   O(n*log(n)).  
    מרחב עזר:   O(1). 
  
    גישה נוספת לפתרון בעיה זו ללא מקום נוסף.     
מספר לא יכול להיות מספר שמח    אם בשלב כלשהו סכום ריבוע הספרות המתקבל הוא מספר חד ספרתי מלבד 1 או 7   . הסיבה לכך היא ש-1 ו-7 הם המספרים המאושרים החד-ספרתיים היחידים. באמצעות מידע זה נוכל לפתח גישה כפי שמוצג בקוד שלהלן - 
// C++ program to check if a number is a Happy number or // not. #include     using namespace std; // Method - returns true if the input is a happy number else // returns false bool isHappynumber(int n) {  int sum = n x = n;  // This loop executes till the sum of square of digits  // obtained is not a single digit number  while (sum > 9) {  sum = 0;  // This loop finds the sum of square of digits  while (x > 0) {  int d = x % 10;  sum += d * d;  x /= 10;  }  x = sum;  }  if (sum == 7 || sum == 1)  return true;  return false; } int main() {  int n = 13;  if (isHappynumber(n))  cout << n << ' is a Happy number';  else  cout << n << ' is not a Happy number';  return 0; } // This code is contributed by Sania Kumari Gupta 
 C // C program to check if a number is a Happy number or // not. #include   #include   // Method - returns true if the input is a happy number else // returns false bool isHappynumber(int n) {  int sum = n x = n;  // This loop executes till the sum of square of digits  // obtained is not a single digit number  while (sum > 9) {  sum = 0;  // This loop finds the sum of square of digits  while (x > 0) {  int d = x % 10;  sum += d * d;  x /= 10;  }  x = sum;  }  if (sum == 7 || sum == 1)  return true;  return false; } int main() {  int n = 13;  if (isHappynumber(n))  printf('%d is a Happy number' n);  else  printf('%d is not a Happy number' n);  return 0; } // This code is contributed by Sania Kumari Gupta 
 Java // This code is contributed by Vansh Sodhi. // Java program to check if a number is a Happy number or // not. class GFG {  // method - returns true if the input is a happy  // number else returns false  static boolean isHappynumber(int n)  {  int sum = n x = n;  // this loop executes till the sum of square of  // digits obtained is not a single digit number  while (sum > 9) {  sum = 0;  // this loop finds the sum of square of digits  while (x > 0) {  int d = x % 10;  sum += d * d;  x /= 10;  }  x = sum;  }  if (sum == 1 || sum == 7)  return true;  return false;  }  // Driver code  public static void main(String[] args)  {  int n = 13;  if (isHappynumber(n))  System.out.println(n + ' is a Happy number');  else  System.out.println(n  + ' is not a Happy number');  } } 
 Python # Python3 program to check if a number is a Happy number or not. # Method - returns true if the input is # a happy number else returns false def isHappynumber(n): Sum x = n n # This loop executes till the sum # of square of digits obtained is # not a single digit number while Sum > 9: Sum = 0 # This loop finds the sum of # square of digits while x > 0: d = x % 10 Sum += d * d x = int(x / 10) x = Sum if Sum == 1 or Sum == 7: return True return False n = 13 if isHappynumber(n): print(n 'is a Happy number') else: print(n 'is not a Happy number') # This code is contributed by mukesh07. 
 C# // C# program to check if a number // is a Happy number or not. using System; class GFG {  // Method - returns true if the input is  // a happy number else returns false  static bool isHappynumber(int n)  {  int sum = n x = n;  // This loop executes till the sum  // of square of digits obtained is  // not a single digit number  while (sum > 9) {  sum = 0;  // This loop finds the sum of  // square of digits  while (x > 0) {  int d = x % 10;  sum += d * d;  x /= 10;  }  x = sum;  }  if (sum == 1 || sum == 7)  return true;  return false;  }  // Driver code  public static void Main(String[] args)  {  int n = 13;  if (isHappynumber(n))  Console.WriteLine(n + ' is a Happy number');  else  Console.WriteLine(n + ' is not a Happy number');  } } // This code is contributed by 29AjayKumar 
 JavaScript <script> // This code is contributed by Vansh Sodhi. // javascript program to check if a number is a Happy number or not.  // method - returns true if the input is a happy  // number else returns false  function isHappynumber(n)  {  var sum = n x = n;  // this loop executes till the sum of square of  // digits obtained is not a single digit number  while(sum > 9)   {  sum = 0;  // this loop finds the sum of square of digits  while (x > 0)   {  var d = x % 10;  sum += d * d;  x /= 10;  }  x = sum;  }  if(sum == 1 || sum == 7)  return true;  return false; } // Driver code  var n = 13;  if (isHappynumber(n))  document.write(n +   ' is a Happy number');  else  document.write(n +   ' is not a Happy number');   // This code is contributed by 29AjayKumar  </script> 
   תְפוּקָה
13 is a Happy number
ניתוח מורכבות:
הצהרת java if else
    מורכבות זמן:   O(n*log(n)).  
    מרחב עזר:   O(1). 
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