Leetcode 136 137 260 SingleNumber I II III

Leetccode 136 SingleNumber I

Given an array of integers, every element appears twice except for one. Find that single one.

Note:
Your algorithm should have a linear runtime complexity. Could you implement it without using extra memory?

1.自己想到了先排序，再遍历数组找，复杂度较高

2.参考其他想法，最好的是利用异或，详见代码

import java.util.Arrays;

public class S136 {
    
    public int singleNumber(int[] nums) {
        //AC but not good
/*        Arrays.sort(nums);
        int i = 0;
        for(;i<nums.length-1;i+=2){
            if(nums[i]!=nums[i+1]){
                return nums[i];
            }
        }
        return nums[i];*/
        //best one 异或运算的神奇之处 1.a^b == b^a  2.0^a == a
        if(nums.length<1)
            return 0;
        int ret = nums[0];
        for(int i = 0;i<nums.length;i++){
            ret = ret^nums[i];
        }
        return ret;
    }
}

Leetccode 137 SingleNumber II

Given an array of integers, every element appears three times except for one. Find that single one.

Note:
Your algorithm should have a linear runtime complexity. Could you implement it without using extra memory?

1.利用排序和遍历同样可以AC

2.利用异或，详见代码

public class S137 {
    public int singleNumber(int[] nums) {
        //AC but not good
/*        Arrays.sort(nums);
        int i = 0;
        for(;i<nums.length-1;i+=3){
            if(nums[i]!=nums[i+1]){
                return nums[i];
            }
        }
        return nums[i];*/
        //a general algorithm
        int a[] = new int[32];
        int ret = 0;
        for(int i = 0;i<32;i++){
            for(int j = 0;j<nums.length;j++){
                a[i] += (nums[j]>>i)&1;
                
            }
            ret |= (a[i]%3)<<i;
        }
        return ret;
    }
}

Leetccode 260 SingleNumber III

Given an array of numbers nums, in which exactly two elements appear only once and all the other elements appear exactly twice. Find the two elements that appear only once.

For example:

Given nums = [1, 2, 1, 3, 2, 5], return [3, 5].

Note:

1. The order of the result is not important. So in the above example, [5, 3] is also correct.
2. Your algorithm should run in linear runtime complexity. Could you implement it using only constant space complexity?

思路：先将所有元素异或得到的结果ret肯定不为零，再移位寻找第一个不为零的二进制位，记录位置pos。再遍历数组，将所有pos位置为零的数异或得到num1，所有pos位置为一的数异或得到num2，num1和num2即answer。因为ret中不为零的二进制位所对应位肯定是num1和num2对应位异或，必定是num1和num2此位不同，将数组分为两组分别异或其实就是第一种情况的解法了。详见代码

public class S260 {
    public int[] singleNumber(int[] nums) {
        int num1= 0,num2 = 0;
        int ret = 0;
        for(int i = 0;i<nums.length;i++){
            ret ^= nums[i]; 
        }
        int pos = 0;
        for(;pos<32;pos++){
            if((ret>>pos&1) == 1){
                break;
            }
        }
        for(int i = 0;i<nums.length;i++){
            if((nums[i]>>pos&1)==1){
                num1 ^= nums[i];
            }else{
                num2 ^= nums[i];
            }
        }
        int rets[] = {num1,num2};
        return rets;
    }
}