CSES Subtree Queries

You are given a rooted tree consisting of n nodes. The nodes are numbered 1,2,…,n, and node 1 is the root. Each node has a value.

Your task is to process following types of queries:

1. change the value of node s to x

2. calculate the sum of values in the subtree of node s

Constraints

$1\le n, q \le 2 \cdot 10^5$
$1≤a,b,s≤n$

$1≤v_i,x≤10^9$

CSES Exponentiation II

Problem : Find the value of $(a^{b^c})mod(10^9+7)$ where $1\le n\le 10^5$ and $1\le a,b,c \le 10^9$

In order to solve this problem, we need to understand the Fermat's little theorem:

$(a^p\equiv a) mod(p)$ Where p is a prime number.

CSES Tree Matching

Tree Matching solved with dynamic programming

Let's define :

$dp(P,0)$ : The max matching number that DOES NOT INCLUDE node P.

$dp(P,1)$ : The max matching number that INCLUDES node P.

Naive Bayes Classifier VS Logistic Regression

Both classification models are linear functions of features

Joint Distribution VS Conditional Distribution

Naive Bayes models the joint distribution:  $P(X,Y) = P(Y)P(X|Y)$

Logistic Regression models the conditional distribution: $P(Y|X)$

Correlated VS Independent features