[go/method record] Combination problems in mathematics

Problem Description

• It mainly solves the combination problem in permutation and combination in mathematics, namely:
  $$C_n^r=\frac{A_n^r}{r!}$$

solve

• see this
• principle
  • Calculate ${\sum }_{r=0}^n{C}_n^r$, that is, the binomial theorem, a total of $2^n$ kinds of combinations can be represented by n bits.
    For example$n=3$ o'clock:
    000, 001, 010,
  • Take out the combination that satisfies: the number of bit 1 is r, that is, the result
    For example, $n=3,r=2$ o'clock:
    011, 101, 110
• the code

  // 其他数组类型均可使用
  func Combinations(set []string, n int) (subsets [][]string) {
        
        
  	length := uint(len(set))
  
  	if n <= 0 {
        
        
  		return
  	}
  
  	if n > len(set) {
        
        
  		n = len(set)
  	}
  
  	// 从1遍历到2^length
  	for subsetBits := 1; subsetBits < (1 << length); subsetBits++ {
        
        
  		// 如果subsetBits中bit 1的数量不为n，跳过
  		if n > 0 && bits.OnesCount(uint(subsetBits)) != n {
        
        
  			continue
  		}
  
  		var subset []string
  
  		// 将对应bit 1的位置(index)对应的set[index]取出来
  		for object := uint(0); object < length; object++ {
        
        
  			if (subsetBits>>object)&1 == 1 {
        
        
  				subset = append(subset, set[object])
  			}
  		}
  		// 添加到返回值
  		subsets = append(subsets, subset)
  	}
  	return subsets
  }