LeetCode: 300. Longest Increasing Subsequence

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300. Longest Increasing Subsequence

LeetCode - Longest Increasing Subsequence

动态规划+二分查找的算法还需要再仔细研究一下。还是有些懵逼！

Given an unsorted array of integers, find the length of longest increasing subsequence.

Example:

Input: [10,9,2,5,3,7,101,18]
Output: 4
Explanation: The longest increasing subsequence is [2,3,7,101], therefore the length is 4.

*Note: *

There may be more than one LIS combination, it is only necessary for you to return the length.
Your algorithm should run in O(n²) complexity.

Follow up: Could you improve it to O(n log n) time complexity?

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/**
 * Runtime: 2 ms, faster than 76.15% of Java online submissions for Longest Increasing Subsequence.
 *
 * Memory Usage: 42.1 MB, less than 5.00% of Java online submissions for Longest Increasing Subsequence.
 *
 * Copy from: https://leetcode-cn.com/problems/longest-increasing-subsequence/solution/zui-chang-shang-sheng-zi-xu-lie-dong-tai-gui-hua-2/[最长上升子序列（动态规划 + 二分查找，清晰图解） - 最长上升子序列 - 力扣（LeetCode）]
 */
public int lengthOfLIS(int[] nums) {
    if (Objects.isNull(nums) || nums.length == 0) {
        return 0;
    }
    int[] tails = new int[nums.length];
    int result = 0;
    for (int num : nums) {
        int i = 0, j = result;
        while (i < j) {
            int m = (i + j) / 2;
            if (tails[m] < num) {
                i = m + 1;
            } else {
                j = m;
            }
        }
        tails[i] = num;
        if (result == j) {
            result++;
        }
    }
    return result;
}

/**
 * Runtime: 2 ms, faster than 76.15% of Java online submissions for Longest Increasing Subsequence.
 *
 * Memory Usage: 42.1 MB, less than 5.00% of Java online submissions for Longest Increasing Subsequence.
 *
 * Copy from: https://leetcode.com/problems/longest-increasing-subsequence/solution/[Longest Increasing Subsequence solution - LeetCode]
 */
public int lengthOfLISDPBS(int[] nums) {
    if (Objects.isNull(nums) || nums.length == 0) {
        return 0;
    }
    int[] dp = new int[nums.length];
    int len = 0;
    for (int num : nums) {
        int i = Arrays.binarySearch(dp, 0, len, num);
        if (i < 0) {
            i = -(i + 1);
        }
        dp[i] = num;
        if (i == len) {
            len++;
        }
    }
    return len;
}

/**
 * Runtime: 56 ms, faster than 5.76% of Java online submissions for Longest Increasing Subsequence.
 *
 * Memory Usage: 43.2 MB, less than 5.00% of Java online submissions for Longest Increasing Subsequence.
 *
 * Copy from: https://leetcode.com/problems/longest-increasing-subsequence/solution/[Longest Increasing Subsequence solution - LeetCode]
 */
public int lengthOfLISDP(int[] nums) {
    if (Objects.isNull(nums) || nums.length == 0) {
        return 0;
    }
    int[] dp = new int[nums.length];
    dp[0] = 1;
    int result = 1;
    for (int i = 1; i < nums.length; i++) {
        int maxval = 0;
        for (int j = 0; j < i; j++) {
            if (nums[i] > nums[j]) {
                maxval = Math.max(maxval, dp[j]);
            }
        }
        dp[i] = maxval + 1;
        result = Math.max(result, dp[i]);
    }

    return result;
}