R根据条件填充矩阵

Question

有一个矩阵5x5，其中行和和列总和给出

mat1<-matrix(0,ncol = 5, nrow = 5)
colnames(mat1) <- c("A","B","C","D","E")
rownames(mat1) <- c(1:5)
mat1<-rbind(mat1, Sum = 2)
mat1<-cbind(mat1, Sum = c(1,3,2,3,1,""))
View(mat1)

行和列的总和意味着，不能超过总和的单元格可以填充1。 必须填充矩阵，以尽可能满足条件（每个矩阵元素的行和和列总和）。
但是每行的单元格必须在定义区间内填充：

mat2[1,]<-c(1,1,0,0,0)
mat2[2,]<-c(1,1,1,1,0)
mat2[3,]<-c(0,1,1,0,0)
mat2[4,]<-c(0,1,1,1,1)
mat2[5,]<-c(0,0,0,1,1)
mat2<-rbind(mat2, Sum = 2)
mat2<-cbind(mat2, Sum = c(1,3,2,3,1,"")) 
View(mat2)

因此，我希望收到以下矩阵：

否则，矩阵只能在间隔内填充，在下面的矩阵中是红色的：

提前谢谢你！

Answer 1

您的问题有多种解决方案。查看使用Patefield's algorithm的代码（每次运行时，您都有不同的解决方案，这里我给出3个不同的示例）：

mat1 <- r2dtable(n=1, r=c(1,3,2,3,1), c=rep(2,5))[[1]]

colnames(mat1) <- c("A","B","C","D","E")
rownames(mat1) <- c(1:5)
mat1 <- rbind(mat1, Sum = 2)
mat1 <- cbind(mat1, Sum = c(1,3,2,3,1,""))

mat1

     A   B   C   D   E   Sum
1   "0" "1" "0" "0" "0" "1"
2   "1" "0" "0" "1" "1" "3"
3   "0" "0" "1" "1" "0" "2"
4   "0" "1" "1" "0" "1" "3"
5   "1" "0" "0" "0" "0" "1"
Sum "2" "2" "2" "2" "2" ""

     A   B   C   D   E   Sum
1   "0" "0" "0" "0" "1" "1"
2   "2" "0" "1" "0" "0" "3"
3   "0" "0" "1" "1" "0" "2"
4   "0" "1" "0" "1" "1" "3"
5   "0" "1" "0" "0" "0" "1"
Sum "2" "2" "2" "2" "2" ""

     A   B   C   D   E   Sum
1   "0" "0" "0" "1" "0" "1"
2   "0" "1" "1" "0" "1" "3"
3   "0" "1" "0" "0" "1" "2"
4   "1" "0" "1" "1" "0" "3"
5   "1" "0" "0" "0" "0" "1"
Sum "2" "2" "2" "2" "2" ""