# Longest Increasing Subsequence Problem

## Description

LeetCode Problem 300.

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:

``````1
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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:

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

Example 3:

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

Constraints:

• 1 <= nums.length <= 2500
• -10^4 <= nums[i] <= 10^4

## Sample C++ Code

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class Solution {
public:
int lengthOfLIS(vector<int>& nums) {
int len = nums.size();
vector<int> dp(len, 0);

int ans = 0;
for (int i = 0; i < len; i ++) {
for (int j = 0; j < i; j ++) {
if (nums[j] < nums[i])
dp[i] = max(dp[i], dp[j] + 1);
}
ans = max(ans, dp[i]);
}

return ans;
}
};
``````