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What is the best way to populate an upper triangular (or alternatively: lower triangular or symmetric) matrix from a vector of elements?

This example input:

{1, 2, 3, 4, 5, 6}

should give

{{0, 1, 2, 3},
 {0, 0, 4, 5},
 {0, 0, 0, 6},
 {0, 0, 0, 0}}

or alternatively

{{0, 1, 2, 3}, 
 {1, 0, 4, 5}, 
 {2, 4, 0, 6}, 
 {3, 5, 6, 0}}

This problem has many solutions of course. I'm looking for the best (criteria: most elegant/readable, shortest, fastest) ones.

The input has length $\binom{n}{2} = \frac{n(n-1)}{2}$. Consider $n$ known. Feel free to use any version 10 functionality.

What is the best way to populate an upper triangular (or alternatively: lower triangular or symmetric) matrix from a vector of elements?

This example input:

{1, 2, 3, 4, 5, 6}

should give

{{0, 1, 2, 3},
 {0, 0, 4, 5},
 {0, 0, 0, 6},
 {0, 0, 0, 0}}

or alternatively

{{0, 1, 2, 3}, 
 {1, 0, 4, 5}, 
 {2, 4, 0, 6}, 
 {3, 5, 6, 0}}

or even

{{0, 0, 0, 0},
 {1, 0, 0, 0},
 {2, 3, 0, 0},
 {4, 5, 6, 0}}

This problem has many solutions of course. I'm looking for the best (criteria: most elegant/readable, shortest, fastest) ones.

The input has length $\binom{n}{2} = \frac{n(n-1)}{2}$. Consider $n$ known. Feel free to use any version 10 functionality.

What is the best way to populate an upper triangular (or alternatively: symmetric) matrix from a vector of elements?

This example input:

{1, 2, 3, 4, 5, 6}

should give

{{0, 1, 2, 3},
 {0, 0, 4, 5},
 {0, 0, 0, 6},
 {0, 0, 0, 0}}

or alternatively

{{0, 1, 2, 3}, 
 {1, 0, 4, 5}, 
 {2, 4, 0, 6}, 
 {3, 5, 6, 0}}

This problem has many solutions of course. I'm looking for the best (criteria: most elegant/readable, shortest, fastest) ones.

The input has length $\binom{n}{2} = \frac{n(n-1)}{2}$. Consider $n$ known. Feel free to use any version 10 functionality.

What is the best way to populate an upper triangular (or alternatively: lower triangular or symmetric) matrix from a vector of elements?

This example input:

{1, 2, 3, 4, 5, 6}

should give

{{0, 1, 2, 3},
 {0, 0, 4, 5},
 {0, 0, 0, 6},
 {0, 0, 0, 0}}

or alternatively

{{0, 1, 2, 3}, 
 {1, 0, 4, 5}, 
 {2, 4, 0, 6}, 
 {3, 5, 6, 0}}

This problem has many solutions of course. I'm looking for the best (criteria: most elegant/readable, shortest, fastest) ones.

The input has length $\binom{n}{2} = \frac{n(n-1)}{2}$. Consider $n$ known. Feel free to use any version 10 functionality.