代码面试最常用的10种类型算法

Love The Way You Lie 2022-07-19 01:29 108阅读 0赞

http://www.csdn.net/article/2014-04-10/2819237-Top-10-Algorithms-for-Coding-Interview

在程序员的职业生涯中，算法亦算是一门基础课程，尤其是在面试的时候，很多公司都会让程序员编写一些算法实例，例如快速排序、二叉树查找等等。

本文总结了程序员在代码面试中最常遇到的10大算法类型，想要真正了解这些算法的原理，还需程序员们花些功夫。

**1.String/Array/Matrix**

在Java中，String是一个包含char数组和其它字段、方法的类。如果没有IDE自动完成代码，下面这个方法大家应该记住：

toCharArray() //get char array of a String
    Arrays.sort()  //sort an array
    Arrays.toString(char[] a) //convert to string
    charAt(int x) //get a char at the specific index
    length() //string length
    length //array size 
    substring(int beginIndex) 
    substring(int beginIndex, int endIndex)
    Integer.valueOf()//string to integer
    String.valueOf()/integer to string

String/arrays很容易理解，但与它们有关的问题常常需要高级的算法去解决，例如动态编程、递归等。

下面列出一些需要高级算法才能解决的经典问题：

*  [Evaluate Reverse Polish Notation][][逆波兰表达式][Link 1]
 *      import java.io.IOException;
        import java.util.Stack;
        
        public class EvaluateTest {
        
         /**
          * @param args
          */
         public static void main(String[] args) throws IOException {
          String[] tokens = new String[] { "2", "1", "+", "3", "*" };
          System.out.println(evalRPN(tokens));
         }
        
         public static int evalRPN(String[] tokens) {
          int returnValue = 0;
          String operators = "+-*/";
        
          Stack<String> stack = new Stack<String>();
        
          for (String t : tokens) {
           if (!operators.contains(t)) {
            stack.push(t);
           } else {
            int a = Integer.valueOf(stack.pop());
            int b = Integer.valueOf(stack.pop());
            switch (t) {
            case "+":
             stack.push(String.valueOf(a + b));
             break;
            case "-":
             stack.push(String.valueOf(b - a));
             break;
            case "*":
             stack.push(String.valueOf(a * b));
             break;
            case "/":
             stack.push(String.valueOf(b / a));
             break;
            }
           }
          }
          returnValue = Integer.valueOf(stack.pop());
        
          return returnValue;
         }
        }
    
      
      
    
 *  [Longest Palindromic Substring][](最长回文子串)
 *  http://www.cnblogs.com/bitzhuwei/p/Longest-Palindromic-Substring-Par-I.html  
    
 *  http://www.cnblogs.com/bitzhuwei/p/Longest-Palindromic-Substring-Part-II.html  
    
 *  [单词分割][Link 2]
 *  [字梯][Link 3]
 *  [Median of Two Sorted Arrays][]
 *  [正则表达式匹配][Link 4]
 *  [合并间隔][Link 5]
 *  [插入间隔][Link 6]
 *  [Two Sum][]
 *  [3Sum][]
 *  [4Sum][]
 *  [3Sum Closest][]
 *  [String to Integer][]
 *  [合并排序数组][Link 7]
 *  [Valid Parentheses][]
 *  [实现strStr()][strStr]
 *  [Set Matrix Zeroes][]
 *  [搜索插入位置][Link 8]
 *  [Longest Consecutive Sequence][]
 *  [Valid Palindrome][]
 *  [螺旋矩阵][Link 9]
 *  [搜索一个二维矩阵][Link 10]
 *  [旋转图像][Link 11]
 *  [三角形][Link 12]
 *  [Distinct Subsequences Total][]
 *  [Maximum Subarray][]
 *  [删除重复的排序数组][Link 13]
 *  [删除重复的排序数组2][2]
 *  [查找没有重复的最长子串][Link 14]
 *  [包含两个独特字符的最长子串][Link 15]
 *  [Palindrome Partitioning][]

**2.链表**

在Java中实现链表是非常简单的，每个节点都有一个值，然后把它链接到下一个节点。

class Node {
    	int val;
    	Node next;
     
    	Node(int x) {
    		val = x;
    		next = null;
    	}
    }

比较流行的两个链表例子就是栈和队列。

栈（Stack）

class Stack{
    	Node top; 
     
    	public Node peek(){
    		if(top != null){
    			return top;
    		}
     
    		return null;
    	}
     
    	public Node pop(){
    		if(top == null){
    			return null;
    		}else{
    			Node temp = new Node(top.val);
    			top = top.next;
    			return temp;	
    		}
    	}
     
    	public void push(Node n){
    		if(n != null){
    			n.next = top;
    			top = n;
    		}
    	}
    }

队列（Queue）

class Queue{
    	Node first, last;
     
    	public void enqueue(Node n){
    		if(first == null){
    			first = n;
    			last = first;
    		}else{
    			last.next = n;
    			last = n;
    		}
    	}
     
    	public Node dequeue(){
    		if(first == null){
    			return null;
    		}else{
    			Node temp = new Node(first.val);
    			first = first.next;
    			return temp;
    		}	
    	}
    }

值得一提的是，Java标准库中已经包含一个叫做Stack的类，链表也可以作为一个队列使用（add()和remove()）。（链表实现队列接口）如果你在面试过程中，需要用到栈或队列解决问题时，你可以直接使用它们。

在实际中，需要用到链表的算法有：

*  [插入两个数字][Link 16]
 *  [重新排序列表][Link 17]
 *  [链表周期][Link 18]
 *  [Copy List with Random Pointer][]
 *  [合并两个有序列表][Link 19]
 *  [合并多个排序列表][Link 20]
 *  [从排序列表中删除重复的][Link 21]
 *  [分区列表][Link 22]
 *  [LRU缓存][LRU]

**3.树&堆**

这里的树通常是指二叉树。

class TreeNode{
    	int value;
    	TreeNode left;
    	TreeNode right;
    }

下面是一些与二叉树有关的概念：

*  二叉树搜索：对于所有节点，顺序是：left children <= current node <= right children；
 *  平衡vs.非平衡：它是一 棵空树或它的左右两个子树的高度差的绝对值不超过1，并且左右两个子树都是一棵平衡二叉树；
 *  满二叉树：除最后一层无任何子节点外，每一层上的所有结点都有两个子结点；
 *  完美二叉树（Perfect Binary Tree）：一个满二叉树，所有叶子都在同一个深度或同一级，并且每个父节点都有两个子节点；
 *  完全二叉树：若设二叉树的深度为h，除第 h 层外，其它各层 (1～h-1) 的结点数都达到最大个数，第 h 层所有的结点都连续集中在最左边，这就是完全二叉树。

堆（Heap）是一个基于树的数据结构，也可以称为优先队列（ [PriorityQueue][]），在队列中，调度程序反复提取队列中第一个作业并运行，因而实际情况中某些时间较短的任务将等待很长时间才能结束，或者某些不短小，但具有重要性的作业，同样应当具有优先权。堆即为解决此类问题设计的一种数据结构。

下面列出一些基于二叉树和堆的算法：

*  [二叉树前序遍历][Link 23]
 *  [二叉树中序遍历][Link 24]
 *  [二叉树后序遍历][Link 25]
 *  [字梯][Link 3]
 *  [验证二叉查找树][Link 26]
 *  [把二叉树变平放到链表里][Link 27]
 *  [二叉树路径和][Link 28]
 *  [从前序和后序构建二叉树][Link 29]
 *  [把有序数组转换为二叉查找树][Link 30]
 *  [把有序列表转为二叉查找树][Link 31]
 *  [最小深度二叉树][Link 32]
 *  [二叉树最大路径和][Link 33]
 *  [平衡二叉树][Link 34]

**4.Graph**

与Graph相关的问题主要集中在深度优先搜索和宽度优先搜索。深度优先搜索非常简单，你可以从根节点开始循环整个邻居节点。下面是一个非常简单的宽度优先搜索例子，核心是用队列去存储节点。

[![534655cfcf7a0.jpg][] ][534655cfcf7a0.jpg]

第一步，定义一个GraphNode

class GraphNode{ 
    	int val;
    	GraphNode next;
    	GraphNode[] neighbors;
    	boolean visited;
     
    	GraphNode(int x) {
    		val = x;
    	}
     
    	GraphNode(int x, GraphNode[] n){
    		val = x;
    		neighbors = n;
    	}
     
    	public String toString(){
    		return "value: "+ this.val; 
    	}
    }

第二步，定义一个队列

class Queue{
    	GraphNode first, last;
     
    	public void enqueue(GraphNode n){
    		if(first == null){
    			first = n;
    			last = first;
    		}else{
    			last.next = n;
    			last = n;
    		}
    	}
     
    	public GraphNode dequeue(){
    		if(first == null){
    			return null;
    		}else{
    			GraphNode temp = new GraphNode(first.val, first.neighbors);
    			first = first.next;
    			return temp;
    		}	
    	}
    }

第三步，使用队列进行宽度优先搜索

public class GraphTest {
     
    	public static void main(String[] args) {
    		GraphNode n1 = new GraphNode(1); 
    		GraphNode n2 = new GraphNode(2); 
    		GraphNode n3 = new GraphNode(3); 
    		GraphNode n4 = new GraphNode(4); 
    		GraphNode n5 = new GraphNode(5); 
     
    		n1.neighbors = new GraphNode[]{n2,n3,n5};
    		n2.neighbors = new GraphNode[]{n1,n4};
    		n3.neighbors = new GraphNode[]{n1,n4,n5};
    		n4.neighbors = new GraphNode[]{n2,n3,n5};
    		n5.neighbors = new GraphNode[]{n1,n3,n4};
     
    		breathFirstSearch(n1, 5);
    	}
     
    	public static void breathFirstSearch(GraphNode root, int x){
    		if(root.val == x)
    			System.out.println("find in root");
     
    		Queue queue = new Queue();
    		root.visited = true;
    		queue.enqueue(root);
     
    		while(queue.first != null){
    			GraphNode c = (GraphNode) queue.dequeue();
    			for(GraphNode n: c.neighbors){
     
    				if(!n.visited){
    					System.out.print(n + " ");
    					n.visited = true;
    					if(n.val == x)
    						System.out.println("Find "+n);
    					queue.enqueue(n);
    				}
    			}
    		}
    	}
    }

输出结果：

> value: 2 value: 3 value: 5 Find value: 5  
> value: 4

实际中，基于Graph需要经常用到的算法：

*  [克隆Graph][Graph]

**5.排序**

不同排序算法的时间复杂度，大家可以到wiki上查看它们的基本思想。

[![53465710a87e6.jpg][] ][53465710a87e6.jpg]

BinSort、Radix Sort和CountSort使用了不同的假设，所有，它们不是一般的排序方法。

下面是这些算法的具体实例，另外，你还可以阅读： [Java开发者在实际操作中是如何排序的][Java]。

*  [归并排序][Link 35]
 *  [快速排序][Link 36]
 *  [插入排序][Link 37]

**6.递归和迭代**

下面通过一个例子来说明什么是递归。

问题：

> 这里有n个台阶，每次能爬1或2节，请问有多少种爬法？

步骤1：查找n和n-1之间的关系

为了获得n，这里有两种方法：一个是从第一节台阶到n-1或者从2到n-2。如果f(n)种爬法刚好是爬到n节，那么f(n)=f(n-1)+f(n-2)。

步骤2：确保开始条件是正确的

f(0) = 0;  
f(1) = 1;

public static int f(int n){
    	if(n <= 2) return n;
    	int x = f(n-1) + f(n-2);
    	return x;
    }

递归方法的时间复杂度指数为n，这里会有很多冗余计算。

f(5)
    f(4) + f(3)
    f(3) + f(2) + f(2) + f(1)
    f(2) + f(1) + f(2) + f(2) + f(1)

该递归可以很简单地转换为迭代。

public static int f(int n) {
     
    	if (n <= 2){
    		return n;
    	}
     
    	int first = 1, second = 2;
    	int third = 0;
     
    	for (int i = 3; i <= n; i++) {
    		third = first + second;
    		first = second;
    		second = third;
    	}
     
    	return third;
    }

在这个例子中，迭代花费的时间要少些。关于迭代和递归，你可以去 [这里][Link 38]看看。

**7.动态规划**

动态规划主要用来解决如下技术问题：

*  通过较小的子例来解决一个实例；
 *  对于一个较小的实例，可能需要许多个解决方案；
 *  把较小实例的解决方案存储在一个表中，一旦遇上，就很容易解决；
 *  附加空间用来节省时间。

上面所列的爬台阶问题完全符合这四个属性，因此，可以使用动态规划来解决：

public static int[] A = new int[100];
     
    public static int f3(int n) {
    	if (n <= 2)
    		A[n]= n;
     
    	if(A[n] > 0)
    		return A[n];
    	else
    		A[n] = f3(n-1) + f3(n-2);//store results so only calculate once!
    	return A[n];
    }

一些基于动态规划的算法：

*  [编辑距离][Link 39]
 *  [最长回文子串][Longest Palindromic Substring]
 *  [单词分割][Link 2]
 *  [最大的子数组][Maximum Subarray]

**8.位操作**

位操作符：

[![53465e7bc51e0.jpg][]][53465e7bc51e0.jpg]

从一个给定的数n中找位i（i从0开始，然后向右开始）

public static boolean getBit(int num, int i){
    	int result = num & (1<<i);
     
    	if(result == 0){
    		return false;
    	}else{
    		return true;
    	}
    }

例如，获取10的第二位：

i=1, n=10
    1<<1= 10
    1010&10=10
    10 is not 0, so return true;

典型的位算法：

*  [Find Single Number][]
 *  [Maximum Binary Gap][]

**9.概率**

通常要解决概率相关问题，都需要很好地格式化问题，下面提供一个简单的例子：

> 有50个人在一个房间，那么有两个人是同一天生日的可能性有多大？（忽略闰年，即一年有365天）

算法：

public static double caculateProbability(int n){
    	double x = 1; 
     
    	for(int i=0; i<n; i++){
    		x *=  (365.0-i)/365.0;
    	}
     
    	double pro = Math.round((1-x) * 100);
    	return pro/100;
    }

结果：

> calculateProbability(50) = 0.97

**10.组合和排列**

组合和排列的主要差别在于顺序是否重要。

例1：

> 1、2、3、4、5这5个数字，输出不同的顺序，其中4不可以排在第三位，3和5不能相邻，请问有多少种组合？

例2：

> 有5个香蕉、4个梨、3个苹果，假设每种水果都是一样的，请问有多少种不同的组合？

基于它们的一些常见算法

*  [排列][Link 40]
 *  [排列2][2 1]
 *  [排列顺序][Link 41]

来自：[ProgramCreek][]

本文为CSDN编译整理，未经允许不得转载，如需转载请联系market\#csdn.net(\#换成@)

[Evaluate Reverse Polish Notation]: http://www.programcreek.com/2012/12/leetcode-evaluate-reverse-polish-notation/
[Link 1]: http://blog.csdn.net/soszou/article/details/37054503
[Longest Palindromic Substring]: http://www.programcreek.com/2013/12/leetcode-solution-of-longest-palindromic-substring-java/
[Link 2]: http://www.programcreek.com/2012/12/leetcode-solution-word-break/
[Link 3]: http://www.programcreek.com/2012/12/leetcode-word-ladder/
[Median of Two Sorted Arrays]: http://www.programcreek.com/2012/12/leetcode-median-of-two-sorted-arrays-java/
[Link 4]: http://www.programcreek.com/2012/12/leetcode-regular-expression-matching-in-java/
[Link 5]: http://merge%20intervals/
[Link 6]: http://www.programcreek.com/2012/12/leetcode-insert-interval/
[Two Sum]: http://www.programcreek.com/2012/12/leetcode-solution-of-two-sum-in-java/
[3Sum]: http://www.programcreek.com/2012/12/leetcode-3sum/
[4Sum]: http://www.programcreek.com/2013/02/leetcode-4sum-java/
[3Sum Closest]: http://www.programcreek.com/2013/02/leetcode-3sum-closest-java/
[String to Integer]: http://www.programcreek.com/2012/12/leetcode-string-to-integer-atoi/
[Link 7]: http://www.programcreek.com/2012/12/leetcode-merge-sorted-array-java/
[Valid Parentheses]: http://www.programcreek.com/2012/12/leetcode-valid-parentheses-java/
[strStr]: http://www.programcreek.com/2012/12/leetcode-implement-strstr-java/
[Set Matrix Zeroes]: http://www.programcreek.com/2012/12/leetcode-set-matrix-zeroes-java/
[Link 8]: http://www.programcreek.com/2013/01/leetcode-search-insert-position/
[Longest Consecutive Sequence]: http://www.programcreek.com/2013/01/leetcode-longest-consecutive-sequence-java/
[Valid Palindrome]: http://www.programcreek.com/2013/01/leetcode-valid-palindrome-java/
[Link 9]: http://www.programcreek.com/2013/01/leetcode-spiral-matrix-java/
[Link 10]: http://www.programcreek.com/2013/01/leetcode-search-a-2d-matrix-java/
[Link 11]: http://www.programcreek.com/2013/01/leetcode-rotate-image-java/
[Link 12]: http://www.programcreek.com/2013/01/leetcode-triangle-java/
[Distinct Subsequences Total]: http://www.programcreek.com/2013/01/leetcode-distinct-subsequences-total-java/
[Maximum Subarray]: http://www.programcreek.com/2013/02/leetcode-maximum-subarray-java/
[Link 13]: http://www.programcreek.com/2013/01/leetcode-remove-duplicates-from-sorted-array-java/
[2]: http://www.programcreek.com/2013/01/leetcode-remove-duplicates-from-sorted-array-ii-java/
[Link 14]: http://www.programcreek.com/2013/02/leetcode-longest-substring-without-repeating-characters-java/
[Link 15]: http://www.programcreek.com/2013/02/longest-substring-which-contains-2-unique-characters/
[Palindrome Partitioning]: http://www.programcreek.com/2013/03/leetcode-palindrome-partitioning-java/
[Link 16]: http://www.programcreek.com/2012/12/add-two-numbers/
[Link 17]: http://www.programcreek.com/2013/12/in-place-reorder-a-singly-linked-list-in-java/
[Link 18]: http://www.programcreek.com/2012/12/leetcode-linked-list-cycle/
[Copy List with Random Pointer]: http://www.programcreek.com/2012/12/leetcode-copy-list-with-random-pointer/
[Link 19]: http://www.programcreek.com/2012/12/leetcode-merge-two-sorted-lists-java/
[Link 20]: http://www.programcreek.com/2013/02/leetcode-merge-k-sorted-lists-java/
[Link 21]: http://www.programcreek.com/2013/01/leetcode-remove-duplicates-from-sorted-list/
[Link 22]: http://www.programcreek.com/2013/02/leetcode-partition-list-java/
[LRU]: http://www.programcreek.com/2013/03/leetcode-lru-cache-java/
[PriorityQueue]: http://www.programcreek.com/2009/02/using-the-priorityqueue-class-example/
[Link 23]: http://www.programcreek.com/2012/12/leetcode-solution-for-binary-tree-preorder-traversal-in-java/
[Link 24]: http://www.programcreek.com/2012/12/leetcode-solution-of-binary-tree-inorder-traversal-in-java/
[Link 25]: http://www.programcreek.com/2012/12/leetcode-solution-of-iterative-binary-tree-postorder-traversal-in-java/
[Link 26]: http://www.programcreek.com/2012/12/leetcode-validate-binary-search-tree-java/
[Link 27]: http://www.programcreek.com/2013/01/leetcode-flatten-binary-tree-to-linked-list/
[Link 28]: http://www.programcreek.com/2013/01/leetcode-path-sum/
[Link 29]: http://www.programcreek.com/2013/01/construct-binary-tree-from-inorder-and-postorder-traversal/
[Link 30]: http://www.programcreek.com/2013/01/leetcode-convert-sorted-array-to-binary-search-tree-java/
[Link 31]: http://www.programcreek.com/2013/01/leetcode-convert-sorted-list-to-binary-search-tree-java/
[Link 32]: http://www.programcreek.com/2013/02/leetcode-minimum-depth-of-binary-tree-java/
[Link 33]: http://www.programcreek.com/2013/02/leetcode-binary-tree-maximum-path-sum-java/
[Link 34]: http://www.programcreek.com/2013/02/leetcode-balanced-binary-tree-java/
[534655cfcf7a0.jpg]: http://cms.csdnimg.cn/article/201404/10/534655cfcf7a0.jpg
[Graph]: http://www.programcreek.com/2012/12/leetcode-clone-graph-java/
[53465710a87e6.jpg]: http://cms.csdnimg.cn/article/201404/10/53465710a87e6.jpg
[Java]: http://www.programcreek.com/2014/03/how-developers-sort-in-java/
[Link 35]: http://www.programcreek.com/2012/11/leetcode-solution-merge-sort-linkedlist-in-java/
[Link 36]: http://www.programcreek.com/2012/11/quicksort-array-in-java/
[Link 37]: http://www.programcreek.com/2012/11/leetcode-solution-sort-a-linked-list-using-insertion-sort-in-java/
[Link 38]: http://www.programcreek.com/2012/10/iteration-vs-recursion-in-java/
[Link 39]: http://www.programcreek.com/2013/12/edit-distance-in-java/
[53465e7bc51e0.jpg]: http://cms.csdnimg.cn/article/201404/10/53465e7bc51e0.jpg
[Find Single Number]: http://www.programcreek.com/2012/12/leetcode-solution-of-single-number-in-java/
[Maximum Binary Gap]: http://www.programcreek.com/2013/02/twitter-codility-problem-max-binary-gap/
[Link 40]: http://www.programcreek.com/2013/02/leetcode-permutations-java/
[2 1]: http://www.programcreek.com/2013/02/leetcode-permutations-ii-java/
[Link 41]: http://www.programcreek.com/2013/02/leetcode-permutation-sequence-java/
[ProgramCreek]: http://www.programcreek.com/2012/11/top-10-algorithms-for-coding-interview/