1 Intersection of two sets. Given two arrays a[] and b[], each containing n distinct 2D points in the plane, design a subquadratic algorithm to count the number of points that are contained both in array a[] and array b[].
Hint: shellsort (or any other subquadratic sort).
2 Permutation. Given two integer arrays of size n, design a subquadratic algorithm to determine whether one is a permutation of the other. That is, do they contain exactly the same entries but, possibly, in a different order.
Hint: sort both arrays.
3 **Dutch national flag. Given an array of n buckets, each containing a red, white, or blue pebble, sort them by color. The allowed operations are:
swap(i,j): swap the pebble in bucket i with the pebble in bucket j.
color(i): determine the color of the pebble in bucket i.
The performance requirements are as follows:
At most n calls to color().
At most n calls to swap().
Constant extra space.**
Hint: 3-way partitioning.
https://yq.aliyun.com/articles/3604