MEDIAN - Editorial

editorial
may12
median
medium

#1

PROBLEM LINKS

Practice
Contest

DIFFICULTY

MEDIUM

EXPLANATION

Any state of the array can be represented as a binary mask with each bit 1 means that corresponding number is equal to the max and 0 otherwise. You can run DP with state R[mask] and O(n) transits. You can proof (or just believe) that the number of statest will be not big, of course if you run good DP. The state of our DP will be the mask of numbers that are equal to max. Of course, it makes sense to use operation only for such subarray [l; r] that number of 1-bits is at least as much as number of 0-bits in submask [l; r], because otherwise nothing will change. Also you should notice that if the left bound of your operation is l it is good to make operation only with the maximal possible r (this gives number of transits equal to O(n)). It was also useful for C++ coders to use map structure to represent all states.

SETTER’S SOLUTION

Can be found here.

TESTER’S SOLUTION

Can be found here.