meet in the middle

divide search space into two parts, combine results at the end

sum to $x$

finding some numbers in list that sum to some $x$

• divide list in roughly half, creating two lists
• sum different subsets in each list
• choose single sum from each list and check if equals $x$

xor paths

codeforces

finding paths from $0,0$ to $n,m$ that have every value xor’d together equal $k$

• find all $x,y$ positions reachable after half the moves from $0,0$ and $n,m$
• split problem calculating xors from $0,0\to x,y$ and from $x,y\to n,m$
• for each $x,y$ then calculate $0,0\to x,y\oplus x,y\to n,m$ and increment answers if equals $k$