memoization for recursive Longest Increasing subsequence

问题

I came up with simple following recursive solution for Longest increasing sub-sequence. But, Can you help to include memoization into this recursive solution.

public int findLIS(int a[], int maxSoFar, int item, int count) {

        if(item == a.length) {
            return count;
        }
        int length1 = findLIS(a,maxSoFar, item+1, count);
        int length2 = 0;
        if(a[item] > maxSoFar) {

            length2 = findLIS(a, a[item], item+1, count + 1);
        }
        return Math.max(length1, length2);
}

PS: This not a homework question, it is more of my interest.

回答1:

Use a Map<Pair<Integer,Integer>,Integer>, and at the beginning of the method add:

Integer cache = map.get(new Pair<Integer,Integer>(maxSoFar,item));
if (cache != null) return cache;

Each time you return anything - make sure to write (maxSoFar,item)=returnValue to the map.

The idea is to map between the pair that represent where you are in the calculation - to the maximal value found for this state, to avoid recalculating it.

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It seems java, so you can use apache commons Pair as your Pair interface.

来源：https://stackoverflow.com/questions/13781979/memoization-for-recursive-longest-increasing-subsequence