Drawing Edge

A network has n distinct nodes. Every pair of different nodes can either have one undirected edge or remain disconnected; self-edges are not allowed.
Return the number of distinct network configurations modulo 10^9 + 7.

Function
drawingEdge(n: int) → int

Examples
Example 1
n = 3
return = 8
For three nodes A, B, and C, the possible edges are AB, AC, and BC. The eight configurations are:
no edges
only AB
only AC
only BC
AB and AC
AB and BC
AC and BC
all three edges
Each of the three edges has two independent states, so there are 2^3 = 8 configurations.

The trick is counting, not graph search. There are n(n-1)/2 possible pairs of distinct nodes, and each pair is independently either an edge or not. So the answer is 2^(n(n-1)/2) mod 10^9 + 7. Example 1 checks out: n = 3 gives 3 pairs, 2^3 = 8. The common pitfall is computing the exponent n(n-1)/2 and then looping or using a naive power, which overflows or times out. Use fast modular exponentiation (square and multiply), and compute the exponent in a wide integer type first. Also watch the n = 0 or n = 1 edge cases, where the exponent is 0 and the answer is 1. Don't reduce the exponent mod 10^9 + 7. If you want to reduce it, use Fermat and mod by 10^9 + 6, since the modulus is prime. StealthCoder is the hedge if the modular power slips your mind live.

Memorize the pattern. If you can't, run StealthCoder. The proctor sees the IDE. They don't see what's behind it.