Create Daily 05-01-24 Another Approach.md

Author: 15-Ab

2024 January/Daily 05-01-24 Another Approach.md

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+## Today's 05-01-24 [Problem Link](https://leetcode.com/problems/longest-increasing-subsequence/description/?envType=daily-question&envId=2024-01-05)
+
+# Intuition
+<!-- Describe your first thoughts on how to solve this problem. -->
+- Dynamic Programming Array (gp):
+
+- - My code creates a dynamic programming array (gp) to store the length of the longest increasing subsequence ending at each index i of the array nums.
+- Initialization
+- - The array gp is initialized with all elements set to 1. This is because each element in nums singularly represents a subsequence of length 1.
+- Comparison and Update
+- - My code iterates through each element of nums, comparing it with previous elements and updating the gp array based on the increasing subsequence property.
+- Final Result
+- - The result is the maximum value present in the gp array, which represents the length of the longest increasing subsequence.
+
+
+# Approach
+<!-- Describe your approach to solving the problem. -->
+- Dynamic Programming Array (gp) :
+- - gp[i] represents the length of the longest increasing subsequence ending at index i.
+- - gp[i] will store the numbers form index '0' to 'i-1' which is smaller than nums[i] = that would be  the length of increasing sunsequence with nums[i] as largest of that sequence
+- Initialization of gp :
+- - Initially, all elements in gp are set to 1 because each element in nums forms a subsequence of length 1.
+- - filled with '1' as every element singularly represents a subsequence of length '1'
+- Iterative Comparison and Update :
+- - My code uses a nested loop to iterate through each pair of indices (i, j) where j is less than i.
+- - For each pair, if nums[i] > nums[j], it means that nums[i] can be included in the increasing subsequence ending at index i, and the length is updated accordingly
+- Maximum Length in gp :
+- - The final result is the maximum value present in the gp array, representing the length of the longest increasing subsequence.
+---
+Have a look at the code , still have any confusion then please let me know in the comments
+Keep Solving.:)
+# Complexity
+- Time complexity : $$O(l^2)$$
+<!-- Add your time complexity here, e.g. $$O(n)$$ -->
+
+- Space complexity : $$O(l)$$
+<!-- Add your space complexity here, e.g. $$O(n)$$ -->
+$$l$$ : length of array.
+# Code
+```
+class Solution {
+    public int lengthOfLIS(int[] nums) {
+        
+        int[] gp = new int[nums.length]; // gp[i] will store the numbers form index '0' to 'i-1' which is smaller than nums[i] = that would be  the length of increasing sunsequence with nums[i] as largest of that sequence
+       Arrays.fill(gp, 1); // fill with '1' as every element singularly represents a subsequence of length '1'
+       for( int i = 1; i < nums.length; i++){
+           for( int j = 0; j < i; j++){
+               if( nums[i] > nums[j]){
+                   gp[i] = Math.max( gp[i] , gp[j] + 1);
+               }
+           }
+       }
+        return Arrays.stream(gp).max().getAsInt(); // this will give the maximum value present in array 
+    }
+}
+```