we match first half with second half to make a big gap between kangaroos and select more of them. assume this example :2 2 3 5 5 10 we can select 10 with 5 and 5 with 2 but we cant select 3 with 2 because we reduce big differnecs but we can select them using two half algorithm .

hope it will__

I think key observation is, that if there is a perfect match with maximum possible number of pairs, then it is exactly the one where the upper half puts one of the lower half into its pocket.