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Initial data commit

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Ingy döt Net 2023-07-01 11:58:00 -04:00
parent 72d218235f
commit f23f22d71c
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37
Task/Pascal-matrix-generation/R/pascal-matrix-generation-1.r Normal file
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lower.pascal <- function(n) {
a <- matrix(0, n, n)
a[, 1] <- 1
if (n > 1) {
for (i in 2:n) {
j <- 2:i
a[i, j] <- a[i - 1, j - 1] + a[i - 1, j]
}
}
a
}
# Alternate version
lower.pascal.alt <- function(n) {
a <- matrix(0, n, n)
a[, 1] <- 1
if (n > 1) {
for (j in 2:n) {
i <- j:n
a[i, j] <- cumsum(a[i - 1, j - 1])
}
}
a
}
# While it's possible to modify lower.pascal to get the upper matrix,
# here we simply transpose the lower one.
upper.pascal <- function(n) t(lower.pascal(n))
symm.pascal <- function(n) {
a <- matrix(0, n, n)
a[, 1] <- 1
for (i in 2:n) {
a[, i] <- cumsum(a[, i - 1])
}
a
}

28
Task/Pascal-matrix-generation/R/pascal-matrix-generation-2.r Normal file
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> lower.pascal(5)
[,1] [,2] [,3] [,4] [,5]
[1,] 1 0 0 0 0
[2,] 1 1 0 0 0
[3,] 1 2 1 0 0
[4,] 1 3 3 1 0
[5,] 1 4 6 4 1
> lower.pascal.alt(5)
[,1] [,2] [,3] [,4] [,5]
[1,] 1 0 0 0 0
[2,] 1 1 0 0 0
[3,] 1 2 1 0 0
[4,] 1 3 3 1 0
[5,] 1 4 6 4 1
> upper.pascal(5)
[,1] [,2] [,3] [,4] [,5]
[1,] 1 1 1 1 1
[2,] 0 1 2 3 4
[3,] 0 0 1 3 6
[4,] 0 0 0 1 4
[5,] 0 0 0 0 1
> symm.pascal(5)
[,1] [,2] [,3] [,4] [,5]
[1,] 1 1 1 1 1
[2,] 1 2 3 4 5
[3,] 1 3 6 10 15
[4,] 1 4 10 20 35
[5,] 1 5 15 35 70