Combinations with repetitions
Combinations with repetitions are sets of M elements, in which each element of the set N can participate several times. In this case, no restrictions are imposed on the ratio of the values of M and N, and the total number of combinations with repetitions is
An example of such a problem is the choice of M postcards from N in all possible ways.
To generate combinations with repetitions, we will use the solution for generating placement with repetitions, considered. C ++ implementation
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#include <iostream>using namespace std;bool NextSet(int *a, int n, int m){ int j = m – 1; while (a == n && j >= 0) j–; if (j < 0) return false; if (a >= n) j–; a++; if (j == m – 1) return true; for (int k = j + 1; k < m; k++) a = a; return true;}void Print(int *a, int n) { static int num = 1; cout.width(3); cout << num++ << “: “; for (int i = 0; i < n; i++) cout << a << ” “; cout << endl;}int main() { int n, m, *a; cout << “N = “; cin >> n; cout << “M = “; cin >> m; int h = n > m ? n : m; // размер массива а выбирается как max(n,m) a = new int; for (int i = 0; i < h; i++) a = 1; Print(a, m); while (NextSet(a, n, m)) Print(a, m); cin.get(); cin.get(); return 0;}
The result of the above algorithm:
Algorithmization
Meaning of numbers
Here is the real picture:
1
She is loved and revered, considering successful. Many are sure: it is this figure that is the primary source of everything that exists on earth. "One" symbolizes creative energy, unity, crystal reputation and immaculate name.
The sound of the word "one" is similar to win and honor. В сочетании с другими числами значительно усиливает их и благотворно дополняет.
2
Sounds sweet and easy. It is in the "two" that the harmony of the Yin-Yang energy is so necessary for us, serving to create new life.
3
This turbulent flow of life, unprecedented development. She is in tune with growth. Which means, "Troika" carries special favorable energy in combinations with different numbers.
For instance, «3, 2, 8»Similar to the ease and accelerated development of business affairs.
4
we, without hesitation, love the "four", but the Cantonese dialect gives this figure consonance with death. For this reason, in China, they avoid it and avoid combining "4" with other numbers.. The combination of "2" and "4" speaks of an easy death, and "6" and "4" - about financial losses.
5
Sounds like "no" or "nothing". It is worth giving up digital combinations with the "five". Otherwise, she will make good things worthless, what other figures carry.
For instance, "5" and "6" are interpreted, as a lack of profitability.
6
In feng shui, it sounds similar to income, wealth.
Most consider the "six" positive, promising material well-being.
8
Cantonese pronounce it, обозначая драгоценности. This gives the G8 special luck. She is like a magnet, closely intertwined with wealth, prosperity, well-being.
Beginning with 2004 and to 2024 of the year, the Chinese calendar speaks of the increased influence of the "eight", became a lucky star for planet Earth.
9
In feng shui, this figure is considered very successful., denoting the complete unity of heaven and earth.
The masters of this Eastern teaching call it no less positive, чем наполненная счастьем «восьмёрка». Besides, "Nine" certainly brings physical and spiritual health, which means, and longevity.
Opinions are divided. Some draw parallels with emptiness, and consider "zero" a bad number. But most associate it with balance and stability..
