LeetCode #300 — MEDIUM

Longest Increasing Subsequence

Move from brute-force thinking to an efficient approach using array strategy.

The Problem

Problem Statement

Given an integer array nums, return the length of the longest strictly increasing subsequence.

Example 1:

Input: nums = [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.

Example 2:

Input: nums = [0,1,0,3,2,3]
Output: 4

Example 3:

Input: nums = [7,7,7,7,7,7,7]
Output: 1

Constraints:

1 <= nums.length <= 2500
-10⁴ <= nums[i] <= 10⁴

Follow up: Can you come up with an algorithm that runs in O(n log(n)) time complexity?

Step 01

Brute Force Baseline

Problem summary: Given an integer array nums, return the length of the longest strictly increasing subsequence.

Baseline thinking

Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.

Pattern signal: Array · Binary Search · Dynamic Programming

Example 1

[10,9,2,5,3,7,101,18]

Example 2

[0,1,0,3,2,3]

Example 3

[7,7,7,7,7,7,7]

Core Insight

What unlocks the optimal approach

No official hints in dataset. Start from constraints and look for a monotonic or reusable state.

Interview move: turn each hint into an invariant you can check after every iteration/recursion step.

Step 03

Algorithm Walkthrough

Iteration Checklist

Define state (indices, window, stack, map, DP cell, or recursion frame).
Apply one transition step and update the invariant.
Record answer candidate when condition is met.
Continue until all input is consumed.

Use the first example testcase as your mental trace to verify each transition.

Step 04

Edge Cases

Minimum Input

Single element / shortest valid input

Validate boundary behavior before entering the main loop or recursion.

Duplicates & Repeats

Repeated values / repeated states

Decide whether duplicates should be merged, skipped, or counted explicitly.

Extreme Constraints

Upper-end input sizes

Re-check complexity target against constraints to avoid time-limit issues.

Invalid / Corner Shape

Empty collections, zeros, or disconnected structures

Handle special-case structure before the core algorithm path.

Step 05

Full Annotated Code

Source-backed implementations are provided below for direct study and interview prep.

// Accepted solution for LeetCode #300: Longest Increasing Subsequence
class Solution {
    public int lengthOfLIS(int[] nums) {
        int n = nums.length;
        int[] f = new int[n];
        Arrays.fill(f, 1);
        int ans = 1;
        for (int i = 1; i < n; ++i) {
            for (int j = 0; j < i; ++j) {
                if (nums[j] < nums[i]) {
                    f[i] = Math.max(f[i], f[j] + 1);
                }
            }
            ans = Math.max(ans, f[i]);
        }
        return ans;
    }
}

// Accepted solution for LeetCode #300: Longest Increasing Subsequence
func lengthOfLIS(nums []int) int {
	n := len(nums)
	f := make([]int, n)
	for i := range f {
		f[i] = 1
	}
	ans := 1
	for i := 1; i < n; i++ {
		for j := 0; j < i; j++ {
			if nums[j] < nums[i] {
				f[i] = max(f[i], f[j]+1)
				ans = max(ans, f[i])
			}
		}
	}
	return ans
}

# Accepted solution for LeetCode #300: Longest Increasing Subsequence
class Solution:
    def lengthOfLIS(self, nums: List[int]) -> int:
        n = len(nums)
        f = [1] * n
        for i in range(1, n):
            for j in range(i):
                if nums[j] < nums[i]:
                    f[i] = max(f[i], f[j] + 1)
        return max(f)

// Accepted solution for LeetCode #300: Longest Increasing Subsequence
impl Solution {
    pub fn length_of_lis(nums: Vec<i32>) -> i32 {
        let n = nums.len();
        let mut f = vec![1; n];
        for i in 1..n {
            for j in 0..i {
                if nums[j] < nums[i] {
                    f[i] = f[i].max(f[j] + 1);
                }
            }
        }
        *f.iter().max().unwrap()
    }
}

// Accepted solution for LeetCode #300: Longest Increasing Subsequence
function lengthOfLIS(nums: number[]): number {
    const n = nums.length;
    const f: number[] = new Array(n).fill(1);
    for (let i = 1; i < n; ++i) {
        for (let j = 0; j < i; ++j) {
            if (nums[j] < nums[i]) {
                f[i] = Math.max(f[i], f[j] + 1);
            }
        }
    }
    return Math.max(...f);
}

Step 06

Interactive Study Demo

Use this to step through a reusable interview workflow for this problem.

Custom checkpoints (one per line)

Press Step or Run All to begin.

Step 07

Complexity Analysis

Time

O(log n)

Space

O(1)

Approach Breakdown

LINEAR SCAN

O(n) time

O(1) space

Check every element from left to right until we find the target or exhaust the array. Each comparison is O(1), and we may visit all n elements, giving O(n). No extra space needed.

BINARY SEARCH

O(log n) time

O(1) space

Each comparison eliminates half the remaining search space. After k comparisons, the space is n/2ᵏ. We stop when the space is 1, so k = log₂ n. No extra memory needed — just two pointers (lo, hi).

Shortcut: Halving the input each step → O(log n). Works on any monotonic condition, not just sorted arrays.

Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Off-by-one on range boundaries

Wrong move: Loop endpoints miss first/last candidate.

Usually fails on: Fails on minimal arrays and exact-boundary answers.

Fix: Re-derive loops from inclusive/exclusive ranges before coding.

Boundary update without `+1` / `-1`

Wrong move: Setting `lo = mid` or `hi = mid` can stall and create an infinite loop.

Usually fails on: Two-element ranges never converge.

Fix: Use `lo = mid + 1` or `hi = mid - 1` where appropriate.

State misses one required dimension

Wrong move: An incomplete state merges distinct subproblems and caches incorrect answers.

Usually fails on: Correctness breaks on cases that differ only in hidden state.

Fix: Define state so each unique subproblem maps to one DP cell.