logo

הדפס את כל המספרים n ספרות שסכום הספרות שלהם שווה לסכום הנתון

מספר נתון של ספרות n הדפס את כל המספרים n ספרות שסכום הספרות שלהם מצטבר לסכום נתון. הפתרון לא צריך לשקול 0 מובילים כספרות.
דוגמאות:  
 

    Input:     N = 2 Sum = 3  
Output: 12 21 30
Input: N = 3 Sum = 6
Output: 105 114 123 132 141 150 204
213 222 231 240 303 312 321
330 402 411 420 501 510 600
Input: N = 4 Sum = 3
Output: 1002 1011 1020 1101 1110 1200
2001 2010 2100 3000


 



הזמנה מראש של חציית עץ


א פתרון פשוט יהיה ליצור את כל המספרים N-ספרות ולהדפיס מספרים שסכום הספרות שלהם שווה לסכום הנתון. המורכבות של פתרון זה תהיה אקספוננציאלית. 
פתרון טוב יותר הוא ליצור רק את אותם מספרים N-ספרות העונים על האילוצים הנתונים. הרעיון הוא להשתמש ברקורסיה. אנחנו בעצם ממלאים את כל הספרות מ-0 עד 9 במיקום הנוכחי ושומרים על סכום הספרות עד כה. לאחר מכן אנו חוזרים על הסכום שנותר ומספר הספרות שנותרו. אנו מטפלים באפסים מובילים בנפרד מכיוון שהם אינם נספרים כספרות.
להלן יישום רקורסיבי פשוט של הרעיון לעיל -
 

C++
// A C++ recursive program to print all n-digit // numbers whose sum of digits equals to given sum #include    using namespace std; // Recursive function to print all n-digit numbers // whose sum of digits equals to given sum // n sum --> value of inputs // out --> output array // index --> index of next digit to be filled in // output array void findNDigitNumsUtil(int n int sum char* out  int index) {  // Base case  if (index > n || sum < 0)  return;  // If number becomes N-digit  if (index == n)  {  // if sum of its digits is equal to given sum  // print it  if(sum == 0)  {  out[index] = '';  cout << out << ' ';  }  return;  }  // Traverse through every digit. Note that  // here we're considering leading 0's as digits  for (int i = 0; i <= 9; i++)  {  // append current digit to number  out[index] = i + '0';  // recurse for next digit with reduced sum  findNDigitNumsUtil(n sum - i out index + 1);  } } // This is mainly a wrapper over findNDigitNumsUtil. // It explicitly handles leading digit void findNDigitNums(int n int sum) {  // output array to store N-digit numbers  char out[n + 1];  // fill 1st position by every digit from 1 to 9 and  // calls findNDigitNumsUtil() for remaining positions  for (int i = 1; i <= 9; i++)  {  out[0] = i + '0';  findNDigitNumsUtil(n sum - i out 1);  } } // Driver program int main() {  int n = 2 sum = 3;  findNDigitNums(n sum);  return 0; } 
Java
// Java recursive program to print all n-digit // numbers whose sum of digits equals to given sum import java.io.*; class GFG  {  // Recursive function to print all n-digit numbers  // whose sum of digits equals to given sum    // n sum --> value of inputs  // out --> output array  // index --> index of next digit to be   // filled in output array  static void findNDigitNumsUtil(int n int sum char out[]  int index)  {  // Base case  if (index > n || sum < 0)  return;    // If number becomes N-digit  if (index == n)  {  // if sum of its digits is equal to given sum  // print it  if(sum == 0)  {  out[index] = '' ;  System.out.print(out);  System.out.print(' ');  }  return;  }    // Traverse through every digit. Note that  // here we're considering leading 0's as digits  for (int i = 0; i <= 9; i++)  {  // append current digit to number  out[index] = (char)(i + '0');    // recurse for next digit with reduced sum  findNDigitNumsUtil(n sum - i out index + 1);  }  }    // This is mainly a wrapper over findNDigitNumsUtil.  // It explicitly handles leading digit  static void findNDigitNums(int n int sum)  {  // output array to store N-digit numbers  char[] out = new char[n + 1];    // fill 1st position by every digit from 1 to 9 and  // calls findNDigitNumsUtil() for remaining positions  for (int i = 1; i <= 9; i++)  {  out[0] = (char)(i + '0');  findNDigitNumsUtil(n sum - i out 1);  }  }    // driver program to test above function  public static void main (String[] args)   {  int n = 2 sum = 3;  findNDigitNums(n sum);  } } // This code is contributed by Pramod Kumar 
Python 3
# Python 3 recursive program to print  # all n-digit numbers whose sum of  # digits equals to given sum # Recursive function to print all  # n-digit numbers whose sum of  # digits equals to given sum # n sum --> value of inputs # out --> output array # index --> index of next digit to be  # filled in output array def findNDigitNumsUtil(n sum outindex): # Base case if (index > n or sum < 0): return f = '' # If number becomes N-digit if (index == n): # if sum of its digits is equal # to given sum print it if(sum == 0): out[index] = '' for i in out: f = f + i print(f end = ' ') return # Traverse through every digit. Note  # that here we're considering leading # 0's as digits for i in range(10): # append current digit to number out[index] = chr(i + ord('0')) # recurse for next digit with reduced sum findNDigitNumsUtil(n sum - i out index + 1) # This is mainly a wrapper over findNDigitNumsUtil. # It explicitly handles leading digit def findNDigitNums( n sum): # output array to store N-digit numbers out = [False] * (n + 1) # fill 1st position by every digit  # from 1 to 9 and calls findNDigitNumsUtil()  # for remaining positions for i in range(1 10): out[0] = chr(i + ord('0')) findNDigitNumsUtil(n sum - i out 1) # Driver Code if __name__ == '__main__': n = 2 sum = 3 findNDigitNums(n sum) # This code is contributed  # by ChitraNayal 
C#
// C# recursive program to print all n-digit // numbers whose sum of digits equals to // given sum using System; class GFG {    // Recursive function to print all n-digit  // numbers whose sum of digits equals to  // given sum  // n sum --> value of inputs  // out --> output array  // index --> index of next digit to be   // filled in output array  static void findNDigitNumsUtil(int n int sum  char []ou int index)  {  // Base case  if (index > n || sum < 0)  return;  // If number becomes N-digit  if (index == n)  {  // if sum of its digits is equal to  // given sum print it  if(sum == 0)  {  ou[index] = '';  Console.Write(ou);  Console.Write(' ');  }    return;  }  // Traverse through every digit. Note  // that here we're considering leading  // 0's as digits  for (int i = 0; i <= 9; i++)  {  // append current digit to number  ou[index] = (char)(i + '0');  // recurse for next digit with  // reduced sum  findNDigitNumsUtil(n sum - i ou  index + 1);    }  }  // This is mainly a wrapper over   // findNDigitNumsUtil. It explicitly  // handles leading digit  static void findNDigitNums(int n int sum)  {    // output array to store N-digit  // numbers  char []ou = new char[n + 1];  // fill 1st position by every digit  // from 1 to 9 and calls   // findNDigitNumsUtil() for remaining   // positions  for (int i = 1; i <= 9; i++)  {  ou[0] = (char)(i + '0');  findNDigitNumsUtil(n sum - i ou 1);  }  }    // driver program to test above function  public static void Main ()   {  int n = 2 sum = 3;    findNDigitNums(n sum);  } } // This code is contributed by nitin mittal. 
JavaScript
<script> // Javascript recursive program to print all n-digit // numbers whose sum of digits equals to given sum    // Recursive function to print all n-digit numbers  // whose sum of digits equals to given sum    // n sum --> value of inputs  // out --> output array  // index --> index of next digit to be   // filled in output array  function findNDigitNumsUtil(n sum out index)  {    // Base case  if (index > n || sum < 0)  return;    // If number becomes N-digit  if (index == n)  {    // if sum of its digits is equal to given sum  // print it  if(sum == 0)  {  out[index] = '';  for(let i = 0; i < out.length; i++)    document.write(out[i]);  document.write(' ');  }  return;  }    // Traverse through every digit. Note that  // here we're considering leading 0's as digits  for (let i = 0; i <= 9; i++)  {  // append current digit to number  out[index] = String.fromCharCode(i + '0'.charCodeAt(0));    // recurse for next digit with reduced sum  findNDigitNumsUtil(n sum - i out index + 1);  }  }    // This is mainly a wrapper over findNDigitNumsUtil.  // It explicitly handles leading digit  function findNDigitNums(nsum)  {  // output array to store N-digit numbers  let out = new Array(n+1);  for(let i=0;i<n+1;i++)  {  out[i]=false;  }  // fill 1st position by every digit from 1 to 9 and  // calls findNDigitNumsUtil() for remaining positions  for (let i = 1; i <= 9; i++)  {  out[0] = String.fromCharCode(i + '0'.charCodeAt(0));  findNDigitNumsUtil(n sum - i out 1);  }  }    // driver program to test above function  let n = 2 sum = 3;  findNDigitNums(n sum);    // This code is contributed by avanitrachhadiya2155 </script> 
PHP
 // A PHP recursive program to print all  // n-digit numbers whose sum of digits  // equals to given sum // Recursive function to print all n-digit // numbers whose sum of digits equals to  // given sum // n sum --> value of inputs // out --> output array // index --> index of next digit to be  // filled in output array function findNDigitNumsUtil($n $sum $out $index) { // Base case if ($index > $n || $sum < 0) return; // If number becomes N-digit if ($index == $n) { // if sum of its digits is equal  // to given sum print it if($sum == 0) { $out[$index] = ''; foreach ($out as &$value) print($value); print(' '); } return; } // Traverse through every digit. Note  // that here we're considering leading // 0's as digits for ($i = 0; $i <= 9; $i++) { // append current digit to number $out[$index] = chr($i + ord('0')); // recurse for next digit with  // reduced sum findNDigitNumsUtil($n $sum - $i $out $index + 1); } } // This is mainly a wrapper over findNDigitNumsUtil. // It explicitly handles leading digit function findNDigitNums($n $sum) { // output array to store N-digit numbers $out = array_fill(0 $n + 1 false); // fill 1st position by every digit from  // 1 to 9 and calls findNDigitNumsUtil()  // for remaining positions for ($i = 1; $i <= 9; $i++) { $out[0] = chr($i + ord('0')); findNDigitNumsUtil($n $sum - $i $out 1); } } // Driver Code $n = 2; $sum = 3; findNDigitNums($n $sum); // This code is contributed  // by chandan_jnu ?> 

תְפוּקָה:  
 

12 21 30   

מורכבות זמן: O(n*n!)



מרחב עזר: עַל)