Leetcode 解题报告

347. Top K Frequent Elements

Given a non-empty array of integers, return the k most frequent elements.

For example,
Given [1,1,1,2,2,3] and k = 2, return [1,2].

Note: 

• You may assume k is always valid, 1 ≤ k ≤ number of unique elements.
• Your algorithm's time complexity must be better than O(n log n), where n is the array's size.

思路：算法上没有什么新颖的地方，主要是数据结构和相应函数的使用。

　　　先用Map 来存储数值和数值出现的次数，再对map进行排序，排序的时候按照value的值排序，最后输出后k个值。

　　　需要注意的是排序的方法，这里用到了Collections.sort()函数的其中一种方式，就是自定义compare函数，来实现自己想要的函数。

    public List<Integer> topKFrequent(int[] nums, int k) {
        Map<Integer,Integer> m = new HashMap<Integer,Integer>();
        List<Integer> res = new ArrayList<Integer>();
        for (int i = 0; i < nums.length; i++) {
            if (m.containsKey(nums[i])) {
                m.put(nums[i], m.get(nums[i])+1);
            } else {
                m.put(nums[i], 1);
            }
        }
        List<Map.Entry<Integer, Integer>> l = new ArrayList<Map.Entry<Integer, Integer>>(m.entrySet());
        Collections.sort(l, new Comparator<Map.Entry<Integer,Integer>>() {
            public int compare(Map.Entry<Integer, Integer> me1, Map.Entry<Integer, Integer> me2) {
                return me1.getValue().compareTo(me2.getValue());
            }
        });
        int size = m.size();
        for (int i = 0; i < k; i++) {
            res.add(l.get(size - 1 - i).getKey());
        }
        return res;
    }

96. Unique Binary Search Trees

Given n, how many structurally unique BST's (binary search trees) that store values 1...n?

For example,
Given n = 3, there are a total of 5 unique BST's.

   1         3     3      2      1
           /     /      /       
     3     2     1      1   3      2
    /     /                        
   2     1         2                 3

思路：考虑根节点的可能性，有n种，对于每一个数字i（1<=i<=n）为根节点时，所对应的BST的数量是 左子树的数量*右子树的数量。

　　　左右子树的节点数量之和为i-1，并且分别是从0~i-1 和i-1~0对应变化。用dp[i]表示有i个节点的BST的数量，以j表示左子树节点数量，初始条件为dp[0] = 1,则有

　　　for j: 0~i-1

　　　　dp[i] += dp[j]*dp[i-1-j];

　　

    public int numTrees(int n) {
        int[] dp = new int[n+1];
        dp[0] = 1;
        for (int i = 1; i <= n; i++) {
            for (int j = 0;j <= i-1; j++) {
                dp[i] += dp[j] * dp[i - 1 - j];
            }
        }
        return dp[n];
    }

338. Counting Bits --20160518

 Given a non negative integer number num. For every numbers i in the range 0 ≤ i ≤ num calculate the number of 1's in their binary representation and return them as an array.

Example:
For num = 5 you should return [0,1,1,2,1,2].

Follow up:

• It is very easy to come up with a solution with run time O(n*sizeof(integer)). But can you do it in linear time O(n) /possibly in a single pass?
• Space complexity should be O(n).
• Can you do it like a boss? Do it without using any builtin function like __builtin_popcount in c++ or in any other language.

Hint:

1. You should make use of what you have produced already.
2. Divide the numbers in ranges like [2-3], [4-7], [8-15] and so on. And try to generate new range from previous.
3. Or does the odd/even status of the number help you in calculating the number of 1s?

思路：这是一个找规律的题，前后数字的1的个数是有增长的规律的。在稿纸上写出来就可以清晰地看到，这里就不赘述，直接上代码。

public class S338 {
    public int[] countBits(int num) {
        int[] count = new int[num+1];
        int k = 0;
        for (int i = 1; i <= num;) {
            int temp = (int)Math.pow(2, k);
            for (int j = 0; j < temp; j++) {
                count[i] = count[i - temp] + 1;
                i++;
                if(i > num) {
                    break;
                }
            }
            k++;
        }
        return count;
    }
}