updated icon and test my own note

_posts/Complexity (NP).md

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+---
+layout:       post
+title:        "Complexity (NP related)"
+author:       "Nancycy"
+header-style: text
+catalog:      true
+tags:
+    - Complexity
+---
+
+Reference:
+1. https://www.baeldung.com/cs/p-np-np-complete-np-hard
+2. https://blog.csdn.net/huang1024rui/article/details/49154507
+
+### Big-O notation for complexity
+
+- $O(1)$ - constant time
+- $O(log_2(n))$ - logarithmic time
+- $O(n)$ - linear time
+- $O(n^2)$ - quadratic time
+- $O(n^k)$ - polynomial time
+- $O(k^n)$ - exponential time
+- $O(n!)$ - factorial time
+
+## P problem
+
+P stands for "polynomial". The problem can be solved in polynomial time. Generally, the complexity can be written as 
+$$T(n)=O(C*n^k)$$
+where $C>0$ and $k>0$, $C$ and $k$ are constant, $n$ is input size.  Usually, $k$ is expected to be less than $n$.
+
+## NP problem
+
+NP stands for "non-deterministic polynomial". The problem cannot be solved in polynomial time, but can be verified / certified in polynomial time. The complexity is expected to be
+$$T(n)=O(C_{1}*k^{C_{2*n}})$$
+## NP-complete problem
+
+They all belong to NP problem, but they hold another characteristic: completeness. For any NP problem that is complete, there exists a polynomial-time algorithm that can transform it into other NP-complete problem. This transformation is called reduction.
+
+约化/归约 reduction:
+问题A可以约化为问题B，指可以用问题B的解法解决问题A。NPC问题难度>= NP问题。其他所有的NP问题都可以约化为NPC问题。比如一元一次方程可以约化为一元二次方程。
+
+NPC问题的条件
+1. 是一个NP问题
+2. 所有NP问题都可以约化到它
+
+证明一个问题是NPC问题
+1. 证明是一个NP问题
+2. 证明一个已知的NPC问题能约化到它（由约化的传递性）
+
+## NP-hard problem
+
+The solution cannot be verified in polynomial time. They are at least as hard as any other problem in NP.
+
+![[Pasted image 20240327223757.png|397]]

_posts/ML analysis.md

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+---
+layout:       post
+title:        "ML analysis"
+author:       "Nancycy"
+header-style: text
+catalog:      true
+tags:
+    - Machine Learning
+---
+
+## ablation study
+
+in a research context, it involves systematically removing or disabling parts of a system to study the impact of these changes.