LeetCode in Java

Introduction

Complexity Analysis

1. 时间复杂度 - 核心考察点
2. 空间复杂度 - 次要考察点
3. 编程复杂度 - 能看得懂
4. 思维复杂度 - 能想得出

• Time Complexcity

  • Polynomial(P probelm): O(n), O(n^2), O(n^3) O(n + m), O(√n), O(1) O(logn), O(nlogn)
  • Nondeterministic Polynomial(NP probelm): O(2^n), O(n^n), O(n!)

• 只考虑最高项

  • O(2^N+N^2) = O(2^N)
  • O(N^3+1000N^2) = O(N^3)

• 不考虑常数项和系数

  • O(100N+1000) = O(N)
  • O(logN) = O(log(N^2)) = O(log4(N))

Big O Complexity

Big O notation is used to describe the complexity of an algorithm when measuring its efficiency, which in this case means how well the algorithm scales with the size of the dataset.

• Other notations:
  • Big Omega: lower bound
  • Big Theta: tight bound
  • Big O: upper bound

T(n) = O(f(n))

• O(1) - Constant Complexity

  int x = 0;
  int y = 1;
  int temp = x;
  x = y;
  y = temp;
  

  No loop or recursive calculation.

• O(n) - Linear Complexity

  for (int i = 1; i <= n; i++) {
      x++;
  }
  

  • int i = 1 takes 1 time unit
  • i <= n, i++, x++ each takes n time unit
  • total T(1+3n) ≈T(n)

• O(logN) - Logarithmic Complexity

  int i = 1;
  while(i < n) {
      i = i * 2;
  }
  

• O(nlogN) - Linearithmic Complexity

  for(int i = 0; i <= n: i++) {
      int x = 1;
      while(x < n) {
          x = x * 2;
      }
  }
  

  • It loops n times T(logN), so total is T(nlogN)

• O(n²) - Quadratic Complexity

for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) {
        x++;
    }
}

• O(n3) - Cubic Complexity: Similar to O(n2), but consider that example with an added nested loop.

• O(2n) - Exponential Complexity: The algorithm takes twice as long for every new element added, so even small increases in n dramatically

• increase the running time.

Space Complexity

Space complexity represents the amount of memory one program uses in order to achieve its execution.

• O(1): space cost won't change when variables x, y vary

  int x = 0;
  int y = 0;
  x++;
  y++;
  

• O(n): space cost will increase along with variable n

  int[] newArray = new int[n];
  for (int i = 0; i < n; i++) {
      newArray[i] = i;
  }
  

• O(n²): 2D array

Sorting Algorithms

Algorithm	Best	Worst	Average
Selection Sort	Ω(n^2)	θ(n^2)	O(n^2)
Bubble Sort	Ω(n)	θ(n^2)	O(n^2)
Insertion Sort	Ω(n)	θ(n^2)	O(n^2)
Heap Sort	Ω(nlog(n))	θ(n log(n))	O(n log(n))
Quick Sort	Ω(nlog(n))	θ(n log(n))	O(n^2)
Merge Sort	Ω(nlog(n))	θ(n log(n))	O(n log(n))
Bucket Sort	Ω(n+k)	θ(n+k)	O(n^2)
Radix Sort	Ω(nk)	θ(nk)	O(nk)
Count Sort	Ω(n+k)	θ(n+k)	O(n+k)

常见算法 Big O

O(N)	O(NlogN)	O(logN)	O(N^2), O(N^3)	O(2^N)	O(N!)
双指针算法 (high frequency)	merge sort	binary search	Dynamic Programming (DP)	combination	permutation
打擂台算法 (high frequency)	quick sort
单调栈算法
单调队列算法

Problems Frequency

算法/数据结构	大公司考察频率	其他公司考察频率	难度	建议刷题数	性价比
字符串 / 模拟法	高	高	低	20~50	中
排序算法	中	高	中	2~5	高
二分法	高	高	中	10~20	高
二叉树/链表	高	高	低	30~50	高
递归 / DFS	高	高	高	20~40	中
BFS / 拓扑排序	高	高	中	5-10	超高
堆(优先队列)	低	低	中	5~10	中
哈希表	高	高	中	10~30	高
双指针	高	高	中	10~20	高
动态规划	中	低	高	40~60	低
字典树 / 并查集	中	低	低	2~5	高

Most Useful Methods

• int[]
  • size: arr.length
• String:
  • size: str.length()
  • char: str.charAt(i)
  • substring: str.substring(i, j) // does not include index j
  • char[]: str.toCharArray()

Map / HashMap	Java
create	Map<key, value> map = new HashMap<>()
add / update O(1)	map.put(key, value)
get (or check key) O(1)	map.get(key) -> return value or null
getOrDefault O(1)	map.getOrDefault(key, defaultValue) -> value
delete O(1)	map.remove(key)
keySets	map.keySet() -> set
values	map.values()
containsKey O(1)	map.containsKey()
containsValue O(n) /O(log(n))	map.containsValue()
iterate O(n)	for(Map.Entry<key, value> entry: map.entrySet()) for(Object key: map.keyset()) for(Object value : map.values())

• Set
  • No duplicates
  • un ordered

Set / HashSet	Java
create	Set set = new HashSet<>()
add O(1)	set.add(1)
delete O(1)	set.remove(2)
seach O(1)	set.contains(1)
size O(1)	set.size()
interate O(n)	for (Obj val : set)

Stack	Java
add	stack.push(o)
get and remove	stack.pop() // get and remove the top object from the stack
get	stack.peek() // look at the top object of the stack
isEmpty()	stack.isEmpty()

Queue	Java
add	quque.offer(object) // return false if fails to insert into the queue
remove head	quque.poll() // retrieve and removes the head of the queue
remove head	quque.remove() // retrieve and removes the head of the queue
read head	quque.peek() // retrieve the head value
check empty	queue.isEmpty()
container object	queue.contains(o)