检查两个向量是否是子集

Question

我正在尝试检查 {1,...,M} 中是否存在整数 i 使得 a_i = 1 和 b_i = 0 以及 {1,...,M} 中是否存在整数 j 使得 b_j = 1 和 a_j = 0。如果成立，则输出 1（无法比较）；否则，输出 0（它们具有可比性）。

我试过这个：

a<-c(1,0,1,0)
b<-c(1,0,0,1)
M<-length(a)
incomparable<-function(M, a, b)
{
  for(i in 1:M){
    for(j in 1:M){
    if(a[i]!=b[i] && b[j]!=a[j]) {
      print (1)
    }
    else {
      print(0)
      }
    }
  }
}
incomparable(M,a,b)

> incomparable(M,a,b)
[1] 0
[1] 0
[1] 0
[1] 0
[1] 0
[1] 0
[1] 0
[1] 0
[1] 0
[1] 0
[1] 1
[1] 1
[1] 0
[1] 0
[1] 1
[1] 1

我需要的只是 0 或 1 作为我的输出。如何修复我的代码？

Answer 1

我相信这适用于您描述的条件。

incomparable <- function(a,b){
cond1 <- sum(a>b) > 0 # Returns true is if there is at least one case such that a_i is 1 and b_i is 0
cond2 <- sum(b>a) > 0 # True if at least one case such that one case with b_i is 1 and a_i is 0
  cond1*cond2
}

##### Check a case where they are incomparable vectors

a<-c(1,0,0,1,0,0,1,0)
b<-c(1,0,0,1,1,0,0,0)

incomparable(a,b)
[1] 1

##### Check case where a = b
a<-c(1,0,0,1)
b<-c(1,0,0,1)
incomparable(a,b)
[1] 0

#### Case where a \subset b
a<-c(1,0,0,0,1,0,1)
b<-c(1,0,0,1,1,0,1)

incomparable(a,b)
[1] 0

### Case where b \subset a
a<-c(1,1,1,0,1,0)
b<-c(1,1,0,0,1,0)

incomparable(a,b)
[1] 0