lintcode(603)Largest Divisible Subset

Description:

Given a set of distinct positive integers, find the largest subset such that every pair (Si, Sj) of elements in this subset satisfies: Si % Sj = 0 or Sj % Si = 0.

 注意事项

If there are multiple solutions, return any subset is fine.

Explanation:

Given nums = [1,2,3], return [1,2] or [1,3]

Given nums = [1,2,4,8], return [1,2,4,8]

Solution:

Dynamic programming. Set up two arrays, one records the path, the other records the number. 

public class Solution {
    /**
     * @param nums a set of distinct positive integers
     * @return the largest subset 
     */
    public List<Integer> largestDivisibleSubset(int[] nums) {
        // Write your code here
        ArrayList<Integer> result = new ArrayList<Integer>();
        if(nums == null || nums.length == 0){
            return result;
        }
        
        Arrays.sort(nums);
        
        int len = nums.length;
        int[] count = new int[len];
        Arrays.fill(count , 1);
        int[] path = new int[len];
        Arrays.fill(path , -1);
        int max = 0;
        
        for(int i = 0;i<len;i++){
            for(int j = 0;j<i;j++){
                if(nums[i]%nums[j] == 0 && count[j]+1 > count[i]){
                    count[i] = count[j] + 1;
                    path[i] = j;
                }
            }
            if(count[i] > count[max]){
                max = i;
            }
        }
        
        for(int i = max;i >= 0;i = path[i]){
            result.add(nums[i]);
        }
        
        return result;
    }
}