300. Longest Increasing Subsequence

DP

class Solution {
    public int lengthOfLIS(int[] nums) {
        int maxLength = 1;

        // 定义 dp[i] 为以 nums[i] 结尾的最长严格递增子序列的长度
        int[] dp = new int[nums.length];
        Arrays.fill(dp, 1);

        for (int i = 1; i < nums.length; i++) {
            for (int j = 0; j < i; j++) {
                if (nums[j] < nums[i]) {
                    // 可能形成更长的递增子序列
                    dp[i] = Math.max(dp[i], dp[j] + 1);
                }

                maxLength = Math.max(maxLength, dp[i]);
            }
        }

        return maxLength;
    }
}

DP + Binary Search

class Solution {
    public int lengthOfLIS(int[] nums) {
        // 定义 tails 数组，tails[i] 为长度为 i + 1 的严格递增子序列且 tails[i] 尽可能小
        int[] tails = new int[nums.length];
        int nextIndex = 0;
        for (int num : nums) {
            int insertIndex = findInsertIndex(tails, 0, nextIndex - 1, num);
            tails[insertIndex] = num;
            if (insertIndex == nextIndex) {
                nextIndex++;
            }
        }

        return nextIndex;
    }

    private int findInsertIndex(int[] tails, int left, int right, int target) {
        while (left <= right) {
            int mid = (left + right) >>> 1;
            if (tails[mid] < target) {
                left = mid + 1;
            } else if (tails[mid] > target) {
                right = mid - 1;
            } else {
                right = mid - 1;
            }
        }

        // now: right, left
        return left;
    }
}

Reference

300. Longest Increasing Subsequence