Wiggle Subsequence

A sequence of numbers is called a wiggle sequence if the differences between successive numbers strictly alternate between positive and negative. The first difference (if one exists) may be either positive or negative. A sequence with fewer than two elements is trivially a wiggle sequence.

For example, [1,7,4,9,2,5] is a wiggle sequence because the differences (6,-3,5,-7,3) are alternately positive and negative. In contrast, [1,4,7,2,5] and [1,7,4,5,5] are not wiggle sequences, the first because its first two differences are positive and the second because its last difference is zero.

Given a sequence of integers, return the length of the longest subsequence that is a wiggle sequence. A subsequence is obtained by deleting some number of elements (eventually, also zero) from the original sequence, leaving the remaining elements in their original order.

Examples:

Input: [1,7,4,9,2,5] Output: 6 The entire sequence is a wiggle sequence.

Input: [1,17,5,10,13,15,10,5,16,8] Output: 7 There are several subsequences that achieve this length. One is [1,17,10,13,10,16,8].

Input: [1,2,3,4,5,6,7,8,9] Output: 2

Follow up: Can you do it in O(n) time?

Credits:Special thanks to @agave and @StefanPochmann for adding this problem and creating all test cases.

Solution

public class Solution {
      public int wiggleMaxLength(int[] nums) {
        if (nums == null || nums.length == 0) return 0;

        int size = nums.length;
        int[] f = new int[size]; // decreasing
        int[] g = new int[size]; // increasing
        f[0] = 1;
        g[0] = 1;

        for (int i = 1; i < size; i++) {
            int fTemp = Integer.MIN_VALUE;
            int gTemp = Integer.MIN_VALUE;
            for (int j = 0; j < i; j++) {
                if (nums[j] < nums[i]) {
                    gTemp = Math.max(gTemp, f[j] + 1);
                } else if (nums[j] > nums[i]) {
                    fTemp = Math.max(fTemp, g[j] + 1);
                }
            }

            f[i] = fTemp;
            g[i] = gTemp;
        }

        int result = Integer.MIN_VALUE;
        for(int i = 0; i < size; i ++) {
            result = Math.max(result, f[i]);
            result = Math.max(result, g[i]);
        }

        return result;
    }

}