problem 202,263、232、21、231

【263】Ugly Number

Write a program to check whether a given number is an ugly number.

Ugly numbers are positive numbers whose prime factors only include 2, 3, 5. For example, 6, 8 are ugly while 14 is not ugly since it includes another prime factor 7.

Note that 1 is typically treated as an ugly number.

思路：prime factors：素数，就是这个数只能被1和自身整除。所以检验这个数分别循环除以2、3、5的，如果最后只剩下1，则这个数就是由素数组成。

public class Solution {
    public boolean isUgly(int num) {
        if(num==0)return false;
       
       //way 1:
        for(int i =2; i<6;i++){
            while(num%i==0){
                num/=i;
            }
        }
        
        /*way 2:
        while(num%2==0){
           num/=2; 
        }
        while(num%3==0){
           num/=3; 
        }
        while(num%5==0){
           num/=5; 
        }*/
        return num==1;
    }
}

 【202】Happy Number

Write an algorithm to determine if a number is "happy".

A happy number is a number defined by the following process: Starting with any positive integer, replace the number by the sum of the squares of its digits, and repeat the process until the number equals 1 (where it will stay), or it loops endlessly in a cycle which does not include 1. Those numbers for which this process ends in 1 are happy numbers.

Example: 19 is a happy number

• 12 + 92 = 82
• 82 + 22 = 68
• 62 + 82 = 100
• 12 + 02 + 02 = 1

思路：循环取出一个数各个位，然后平方和，问题的关键在于这个循环什么时候结束，题干中说的很清楚，当平方和是1或者存在环路（平方和经过循环计算又是计算过的平方和）陷入死循环的时候，不再迭代。

有两种方法，一种是通过类似快慢指针的方式检测环路，这种要快很多，另一种是通过Java的set结构，每计算一个数，则添加进set，如果循环出添加过的数字，则set添加失败，所以存在环路

public class Solution {
    public boolean isHappy(int n) {
        //way 2 to use two pointers:fast and slow pointers t detect of there is a loop
        int slow ,fast ;
        slow = fast = n;
        do{
         slow = computeSum(slow);
         fast = computeSum(fast);
         fast = computeSum(fast);  
        }while(slow!=fast);
        
        if(slow==1)return true;
        else return false;
        /*way1:use the hashset to detect if there is a loop
        
        HashSet<Integer> sumSet = new HashSet<Integer>();
        while(sumSet.add(n)){
            int sum = 0;
            while(n>0){
                int m = n%10;
                sum+=m*m;
                n/=10;
                
            }
            if(sum==1)return true;
            else n = sum;;
        }
        return false;*/
    }
    
    int computeSum(int n){
       int sum = 0;
       while(n>0){
            int temp = n%10;
            sum+= temp*temp;
            n/=10;
       }
       return sum;
    }
}

【232】 Implement Queue using Stacks

Implement the following operations of a queue using stacks.

• push(x) -- Push element x to the back of queue.
• pop() -- Removes the element from in front of queue.
• peek() -- Get the front element.
• empty() -- Return whether the queue is empty.

Notes:

• You must use only standard operations of a stack -- which means only push to top, peek/pop from top, size, and is empty operations are valid.
• Depending on your language, stack may not be supported natively. You may simulate a stack by using a list or deque (double-ended queue), as long as you use only standard operations of a stack.
• You may assume that all operations are valid (for example, no pop or peek operations will be called on an empty queue).

思路： 使用栈来模拟队列的基本操作，肯定是需要两个栈，一个用来push，一个用来pop，pop的时候，要把push栈里的元素一个一个弹出来push进pop栈里

class MyQueue {
    private Stack<Integer> stackForPush = new Stack<Integer>();
    private Stack<Integer> stackForPop = new Stack<Integer>();
    // Push element x to the back of queue.
    public void push(int x) {
        stackForPush.push(new Integer(x));
    }

    // Removes the element from in front of queue.
    public void pop() {
       peek();//the subprocess is the same to peek,so call peek() for short.
       stackForPop.pop(); 
    }

    // Get the front element.
    public int peek() {
        if(stackForPop.isEmpty()){
            while(!stackForPush.isEmpty()){
                stackForPop.push(stackForPush.pop());
            }
            //return stackForPop.peek();
        }
        return stackForPop.peek();
    }

    // Return whether the queue is empty.
    public boolean empty() {
          return stackForPop.isEmpty()&&stackForPush.isEmpty();
    }
}

 【21】Merge Two Sorted Lists

Merge two sorted linked lists and return it as a new list. The new list should be made by splicing together the nodes of the first two lists.

 

思路:把两个有序的链表合并，并保持有序。这里运用迭代思想更简单，以此对比两个链表的节点

 

/**
 * Definition for singly-linked list.
 * public class ListNode {
 *     int val;
 *     ListNode next;
 *     ListNode(int x) { val = x; }
 * }
 */
public class Solution {
    public ListNode mergeTwoLists(ListNode l1, ListNode l2) {
        if(l1==null)return l2;
        if(l2==null)return l1;
        ListNode newHead = null;
        if(l1.val<l2.val){
            newHead = l1;
            newHead.next = mergeTwoLists(l1.next,l2);
        }else{
            newHead = l2;
            newHead.next = mergeTwoLists(l2.next,l1);
        }
        return newHead;
    }
}

 【231】Power of Two

Given an integer, write a function to determine if it is a power of two.

思路：判断一个数是不是2的幂，其实也就是判断这个数的二进制位数只能有一位，可以用Integer.bitCount()==1，也可以用n&n-1==0

 

public class Solution {
    public boolean isPowerOfTwo(int n) {
      return (n>0&&(n&(n-1))==0);
        
    }
}