Score : $700$ points
We have a directed weighted graph with $N$ vertices. Each vertex has two integers written on it, and the integers written on Vertex $i$ are $A_i$ and $B_i$.
In this graph, there is an edge from Vertex $x$ to Vertex $y$ for all pairs $1 \leq x,y \leq N$, and its weight is ${\rm min}(A_x,B_y)$.
We will consider a directed cycle in this graph that visits every vertex exactly once. Find the minimum total weight of the edges in such a cycle.
Input is given from Standard Input in the following format:
$N$ $A_1$ $B_1$ $A_2$ $B_2$ $:$ $A_N$ $B_N$
Print the minimum total weight of the edges in such a cycle.
3 1 5 4 2 6 3
7
Consider the cycle $1→3→2→1$. The weights of those edges are ${\rm min}(A_1,B_3)=1$, ${\rm min}(A_3,B_2)=2$ and ${\rm min}(A_2,B_1)=4$, for a total of $7$. As there is no cycle with a total weight of less than $7$, the answer is $7$.
4 1 5 2 6 3 7 4 8
10
6 19 92 64 64 78 48 57 33 73 6 95 73
227