1. TIL (Today I learned)

Symmetry of Combinations

Unlike permutations & variations, picking more elements can lead to having fewer combinations.

Ex.
Going on a picnic and have six pieces of fruit you want to take with you. However, your basket only has a room for 4 of them. Using combinations formula:

	C₆ ₄ = 15 possible choices
    

You go and buy a bigger basket, but only fits 5

	C₆ ₅ = 6 possible choices
    

even bigger basket, fits 6

	C₆ ₆  1 possible choice
    

picking more elements leads to having fewer combinations

Instead of picking which pieces of fruit to take, we can choose the pieces to leave behind.
** Picking 4 fruits out of 6, is the same as choosing 2 fruits that will be left out

	C₆ ₂ = 6! / 2! * 4! = 15
    

** Picking 5 fruits out of 6, is the same as choosing 1 furit that will be left out

	C₆ ₁ = 6! / 1! 5! = 6
 

We can pick p-many elements in as many ways as we can pick n minus p many elements.

	Cₙ ₚ = Cₙ ₙ₋ₚ
    // symmetric with respect to no over 2
    

Recall
Select 3 out of 10 employees to represent the company

	C₁₀ ₃ = 120
    

What if instead of choosing 3 we had to pick 7 people?

	C₁₀ ₇ = 10! / 7! * 3! = 8 * 9 * 10 / 1 * 2 * 3 = 720 / 6
    

Thus we would also have 120 different ways of picking the 7 employees
** Picking 7 out of 10 employees to take to the conference is the same with choosing 3 out 10 to leave behind.

When

	p > n / 2 > n - p
    
   // Apply symmetry to avoid calculating factorials of large numbers
   // We use symmetry to simplify calculations.
   

Higher-Order Function

Achievement Goals

1. Explain the 3 characteristics of first-class citizen.
2. Explain what higher-order function is.
3. Be able to write a higher-order function using Javascript.

First Class Citizen

First class passengers in a airline receives a different service compared to that of other passengers.
Just like that, there is a first-class citizen in Javascript which is the function.

3 Characteristics

1. You can assign a function into a variable.
2. You can use a function as a parameter in another function.
3. You can return a function as a return value of another function.
   ** You can use a function as a data just like (string, number, boolean, area, object) .. Primitive or Reference Data types.

a. Assigning a function into a variable

	const square = function(num) {
    return num * num;
    };
    output square(7);
    console.log(output); // --> 49
    
  // Unlike function declaration, function expression does not encounter hoisting.
  "hoisting" allows the function to work wherever the declaration is made.
  // Relying on function declaration and hoisting is not good for a good maintenace of codes.
  

A callback function is a function used as a argument in another function(caller function).
Callback function is named that way because it is invoked when a task is done.

A caller fucntion can invoke a callback function multiple times or choose to not invoke at all.
A curry function is a function that returns a function.
If a curry function is used we say that a higher-order function is a function that uses another function as an argument in a caller function.
But, a curry function is also a part of higher-order function.

b. Using a callback fucntion in a caller function.

function double(num) {
    return num * 2;
    }
    function dobuleNum(func,num) {
    return func(num);
    }
    /* 
    ** The function doubleNum is a higher-order function that received another function as a parameter/argument.
    ** If the func parameter in the doubleNum is a function, func is a callback function of doubleNum.
    ** In the example below, double is a callback function of doubleNum.
    
    let output = doubleNum(double, 4);
    console.log(output); // --> 8;
    

c. Returning a function

function adder(added) {
    return function(num) {
    return num + added;
    };
   }
   
   //*
   ** The adder function is a higher-order function that returns another function.
   ** The adder function receives one parameter and returns a unknown function.
   ** The returned unknown function receives one parameter and adds it with added.
   ** adder(5) is a function therefore you can use the retrieve equation of a function '()'
   
   let output = adder(5)(3); // --> 8
   console.log(output); // --> 8
   
   //*
   ** You can assign a variable to the function adder is returning.
   ** This is because function is a first-class citizen in Javascript.
   
   const add3 = adder(3);
   output = add3(2);
   console.log(output); // --> 5
   

d. Receiving a function as a parameter and returning a function.

function double(num) {
    return num * 2;
    }
    function doubleAdder(added,func) {
    const doubled = func(added);
    return function(num) {
    return num + doubled;
    };
  }
  
  /*
  ** doubleAdder function is a higher-order function
  ** The parameter func in doubleAdder is a callback function.
  ** The double function is sent to doubleAdder's callback function.
  
  ** doubleAdder(5, double) is a function therefore we w=can use the function retrieve equation '()'
  
  doubleAdder(5, double)(3); // --> 13
  
  ** doubleAdder returned function can be assigned as a variable.
  
  const addTwice3 = doubleAdder(3, double);
  addTwice3(2); // --> 8
  

2. 3 Things to be Thankful for

• Thank God I had a good day on finishing my daily plans.
• Thank God for allowing me to have a good time with my colleagues.
• Thank God for being with Iris and my family and keeping them safe and happy, let them Thank God always.

3. Ideas or Things to think about

• If possible when you hear about people not in the conversation, try not to support or talk about it and forget it right away.
• Thank God always on everything you do, do not be over confident and break your faith.