300. Longest Increasing Subsequence

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

A subsequence is a sequence that can be derived from an array by deleting some or no elements without changing the order of the remaining elements. For example, `[3,6,2,7]` is a subsequence of the array `[0,3,1,6,2,2,7]`.

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`

• Could you come up with the `O(n2)` solution?
• Could you improve it to `O(n log(n))` time complexity?

300. Longest Increasing Subsequence
``````struct Solution;

impl Solution {
fn length_of_lis(nums: Vec<i32>) -> i32 {
let mut dp: Vec<i32> = vec![];
for x in nums {
if let Err(i) = dp.binary_search(&x) {
if i == dp.len() {
dp.push(x)
} else {
dp[i] = x;
}
}
}
dp.len() as i32
}
}

#[test]
fn test() {
let nums = vec![10, 9, 2, 5, 3, 7, 101, 18];
let res = 4;
assert_eq!(Solution::length_of_lis(nums), res);
}
``````