Dano število števk n izpiši vsa n-mestna števila, katerih vsota števk je seštevek dane vsote. Rešitev ne sme obravnavati začetnih ničel kot števk.
Primeri:
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
execvp
A preprosta rešitev bi bilo ustvariti vsa N-mestna števila in natisniti števila, katerih vsota števk je enaka dani vsoti. Kompleksnost te rešitve bi bila eksponentna.
Boljša rešitev je ustvariti samo tista N-mestna števila, ki izpolnjujejo podane omejitve. Ideja je uporaba rekurzije. V bistvu zapolnimo vse števke od 0 do 9 v trenutno pozicijo in ohranimo dosedanjo vsoto števk. Nato rekurziramo za preostalo vsoto in število preostalih števk. Vodilne ničle obravnavamo ločeno, ker se ne štejejo kot števke.
Spodaj je preprosta rekurzivna izvedba zgornje ideje –
// 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] = '