GH-202: Big-O in Java (#203)

Author: rain1024

concepts/general/big-o.md

@@ -1,6 +1,6 @@
 # Big O
 
-*See implementation in* [C++](../cpp/big-o.md), Java, [Python](../python/big-o.md), [Typescript](../typescript/big-o.md)
+*See implementation in* [C++](../cpp/big-o.md), [Java](../java/big-o/README.md), [Python](../python/big-o.md), [Typescript](../typescript/big-o.md)
 
 > In computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by the algorithm, supposing that each elementary operation takes a fixed amount of time to perform.
 
@@ -11,26 +11,18 @@
 $O(1)$: Constant time, the time complexity of the algorithm is independent of the size of the input. Examples include accessing an element in an array by its index or performing a single operation on a single value.
 
 ```cpp
-#include <iostream>
-
-using namespace std;
-
-void doRandomStuff(){
-    bool foo = true;    // 1 operation
-    int bar = 8 * 3;    // 1 operation
-    if(bar < 20){
-        cout << "bar is small" << endl;    // 1 opeartion
-    }
-    for(int i=0; i<bar; i++){
-        // 24 operations 
-        cout << i << endl;
-    }
-}
-int main() {
-    doRandomStuff();    // O(1)
-    doRandomStuff();    // O(1)
-    doRandomStuff();    // O(1)
-}
+def do_random_stuff():
+    foo = True  # 1 operation
+    bar = 8 * 3  # 1 operation
+    if bar < 20:  # 1 operation
+        print("bar is small")  # 1 operation
+    for i in range(0, bar):  # 24 operations
+        print(i)  # 1 operation
+
+
+do_random_stuff()  # O(1)
+do_random_stuff()  # O(1)
+do_random_stuff()  # O(1)
 ```
 
 Run time for `doRandomStuff` is $O(1)$

concepts/java/big-o/README.md

@@ -0,0 +1,197 @@
+# Big-O in Java
+
+## Constant Run Time
+
+$O(1)$: Constant time, the time complexity of the algorithm is independent of the size of the input. Examples include accessing an array element by index or pushing/popping from a stack.
+
+
+```Java
+void doRandomStuff(){
+  boolean foo = true;  // 1 operation
+  int bar = 8 * 3;
+  
+  if(bar < 20){
+    System.out.println("bar is small");
+  }
+
+  for(int i=0; i<bar; i++){
+    System.out.println(i);
+  }
+}
+
+doRandomStuff() // O(1)
+```
+
+    0
+    1
+    2
+    3
+    4
+    5
+    6
+    7
+    8
+    9
+    10
+    11
+    12
+    13
+    14
+    15
+    16
+    17
+    18
+    19
+    20
+    21
+    22
+    23
+
+
+## Linear Run Time 
+
+$O(n)$: Linear time, the time complexity of the algorithm increases linearly with the size of the input. Examples include linear search, traversing a list, or calculating the sum of an array.
+
+
+```Java
+boolean isContains(int target, int[] arr){
+  for(int i=0; i<arr.length; i++){
+    if(arr[i] == target){
+      return true;
+    }
+  }
+  return false;
+}
+```
+
+
+
+
+    true
+
+
+
+
+```Java
+int[] arr;
+
+arr = new int[]{1, 2, 3, 4, 5, 8, 10}; 
+System.out.println(isContains(8, arr)); // O(n)
+
+arr = new int[]{1, 2, 3, 4, 5, 6, 7, 9, 10}; 
+System.out.println(isContains(8, arr)); // O(n)
+
+arr = new int[]{1, 2, 100, 200, 300, 500}; 
+System.out.println(isContains(8, arr)); // O(n)
+
+```
+
+    true
+    false
+    false
+
+
+Run time for `isContains` function is $O(n)$
+
+## Quadaric Run Time
+
+$O(n^2)$: Quadratic time, the time complexity of the algorithm increases as the square of the size of the input. Examples include bubble sort and selection sort.
+
+
+```Java
+void printPairs(int n){
+  for(int i=1; i<=n; i++){
+    for(int j=i+1; j<=n; j++){
+      System.out.print("(" + i + ", " + j + ") ");
+    }
+    System.out.println();
+  }
+}
+
+printPairs(4)
+```
+
+    (1, 2) (1, 3) (1, 4) 
+    (2, 3) (2, 4) 
+    (3, 4) 
+    
+
+
+$f(n) = n * (n-1) * 1$
+
+$O(f(n)) = O(n^2)$
+
+Run time for `printPairs` is $O(n^2)$
+
+## Logarithm Run Time
+
+$O(log n)$: Logirthm time describes an algorithm that performs a logarithmic number of operations, where the log is typically base 2. Examples include binary search and finding the height of a balanced binary tree.
+
+
+```Java
+boolean isContains(int target, int[] numbers){
+  /* arr is sorted array */
+  int lo = 0;
+  int hi = numbers.length - 1;
+  int mid;
+  while(lo <= hi){
+    mid = (lo + hi) / 2;
+    if(numbers[mid] == target){
+      return true;
+    } else if(numbers[mid] < target){
+      lo = mid + 1;
+    } else {
+      hi = mid - 1;
+    }
+  }
+  return false;
+}
+
+int[] numbers;
+
+numbers = new int[]{1, 2, 3, 4, 5, 8, 10};
+System.out.println(isContains(8, numbers)); // O(log n)
+
+numbers = new int[]{1, 2, 3, 4, 5, 9, 10};
+System.out.println(isContains(8, numbers)); // O(log n)
+
+numbers = new int[]{8, 9, 10, 11, 12};
+System.out.println(isContains(8, numbers));  // O(log n)
+```
+
+    true
+    false
+    true
+
+
+$f(n) = 1 + 1 + 1 + 3log(n)= 3 + 3log(n)$
+
+$O(f(n)) = O(log(n))$
+
+Run time for `isContains` (with numbers is sorted array) is $O(log(n))$
+
+## Combined Run Time
+
+```java
+void combine = (int[] nums) => {
+    foo(nums);  // O(1)
+    fuu(nums);  // O(log(n))
+    bar(nums);  // O(n)
+    baz(nums);  // O(n^2)
+}
+
+combine({1, 2, 3, 4, 5, 6}); // O(n^2)
+```
+
+$f(n) = 1 + log(n) + n + n^2$
+
+$O(f(n)) = O(n^2)$
+
+Runtime for `combine()` is $O(n^2)$
+
+## 🔗 Further Reading
+
+* [Time complexity](https://en.wikipedia.org/wiki/Time_complexity), wikipedia
+* [Space complexity](https://en.wikipedia.org/wiki/Space_complexity), wikipedia
+* ▶️ [Asymptotic Notation](https://www.youtube.com/watch?v=iOq5kSKqeR4&ab_channel=CS50), CS50
+* ▶️ 2020, [Data Structures in Typescript #3 - Big-O Algorithm Analysis](https://www.youtube.com/watch?v=F2wwpDgoSoc&ab_channel=JeffZhang), Jeff Zhang