Leetcode 315. Count of Smaller Numbers After Self

Posted 2020-10-28 Hwangzhiyoung

You are given an integer array nums and you have to return a new counts array. The counts array has the property where counts[i] is the number of smaller elements to the right of nums[i].

Example:

Given nums = [5, 2, 6, 1]

To the right of 5 there are 2 smaller elements (2 and 1).
To the right of 2 there is only 1 smaller element (1).
To the right of 6 there is 1 smaller element (1).
To the right of 1 there is 0 smaller element.

Return the array [2, 1, 1, 0].

题目意思：给出一个数组你需要返回后面的数比数组里各自的数小的个数，组成一个count数组 ，例子上面有。

解题思路：暴力解法就是来两个for循环，第二个循环从当前下标的下一个开始与其当前比较遍历，但是这样的话，时间复杂度是O(n²)，会超时不通过leetCode；另一种想法是这样：用vector去储存一对pair<int value,int postion>,pair里左边是数组中值，第二个是值对应的下标。采用分治->合并的方法去计算每次两两合并后当前合并后数组的position位置对应比较的count是多少，接着递归到下一个归并过程中。

 1 #include <stdio.h>
 2 
 3 #include <vector>
 4 class Solution {
 5 public:
 6     std::vector<int> countSmaller(std::vector<int>& nums) {
 7         std::vector<std::pair<int, int> > vec;
 8         std::vector<int> count;
 9         for (int i = 0; i < nums.size(); i++){
10             vec.push_back(std::make_pair(nums[i], i));
11             count.push_back(0);
12         }
13         merge_sort(vec, count);
14         return count;
15     }
16 private:
17     void merge_sort_two_vec(
18                 std::vector<std::pair<int, int> > &sub_vec1,
19                 std::vector<std::pair<int, int> > &sub_vec2,
20                 std::vector<std::pair<int, int> > &vec,
21                 std::vector<int> &count){
22         int i = 0;
23         int j = 0;
24         while(i < sub_vec1.size() && j < sub_vec2.size()){
25             if (sub_vec1[i].first <= sub_vec2[j].first){
26                 count[sub_vec1[i].second] += j;
27                 vec.push_back(sub_vec1[i]);
28                 i++;
29             }
30             else{
31                 vec.push_back(sub_vec2[j]);
32                 j++;
33             }
34         }
35         for (; i < sub_vec1.size(); i++){
36             count[sub_vec1[i].second] += j;
37             vec.push_back(sub_vec1[i]);
38         }
39         for (; j < sub_vec2.size(); j++){
40             vec.push_back(sub_vec2[j]);
41         }
42     }
43     void merge_sort(std::vector<std::pair<int, int> > &vec,
44                     std::vector<int> &count){
45         if (vec.size() < 2){
46             return;
47         }
48         int mid = vec.size() / 2;
49         std::vector<std::pair<int, int> > sub_vec1;
50         std::vector<std::pair<int, int> > sub_vec2;
51         for (int i = 0; i < mid; i++){
52             sub_vec1.push_back(vec[i]);
53         }
54         for (int i = mid; i < vec.size(); i++){
55             sub_vec2.push_back(vec[i]);
56         }
57         merge_sort(sub_vec1, count);
58         merge_sort(sub_vec2, count);
59         vec.clear();
60         merge_sort_two_vec(sub_vec1, sub_vec2, vec, count);
61     }
62 };
63 
64 int main(){
65     int test[] = {5, -7, 9, 1, 3, 5, -2, 1};
66     std::vector<int> nums;
67     for (int i = 0; i < 8; i++){
68         nums.push_back(test[i]);
69     }
70     Solution solve;
71     std::vector<int> result = solve.countSmaller(nums);
72     for (int i = 0; i < result.size(); i++){
73         printf("[%d]", result[i]);
74     }
75     printf("\\n");
76     return 0;
77 }

通过~

 方法二：

学习了二叉排序树的数据结构，觉得这个方法比较好想，记录一下。

 1 #include <stdio.h>
 2 
 3 #include <vector>
 4 struct BSTNode {
 5     int val;
 6     int count;
 7     BSTNode *left;
 8     BSTNode *right;
 9     BSTNode(int x) : val(x), left(NULL), right(NULL), count(0) {}
10 };
11 
12 void BST_insert(BSTNode *node, BSTNode *insert_node, int &count_small){
13     if (insert_node->val <= node->val){
14         node->count++;
15         if (node->left){
16             BST_insert(node->left, insert_node, count_small);
17         }
18         else{
19             node->left = insert_node;
20         }
21     }
22     else{
23         count_small += node->count + 1;
24         if (node->right){
25             BST_insert(node->right, insert_node, count_small);
26         }
27         else{
28             node->right = insert_node;
29         }
30     }
31 }
32 
33 class Solution {
34 public:
35     std::vector<int> countSmaller(std::vector<int>& nums) {
36         std::vector<int> result;
37         std::vector<BSTNode *> node_vec;
38         std::vector<int> count;
39         for (int i = nums.size() - 1; i >= 0; i--){
40             node_vec.push_back(new BSTNode(nums[i]));
41         }
42         count.push_back(0);
43         for (int i = 1; i < node_vec.size(); i++){
44             int count_small = 0;
45             BST_insert(node_vec[0], node_vec[i], count_small);
46             count.push_back(count_small);
47         }
48         for (int i = node_vec.size() - 1; i >= 0; i--){
49             delete node_vec[i];
50             result.push_back(count[i]);
51         }
52         return result;
53     }
54 };
55 
56 int main(){
57     int test[] = {5, -7, 9, 1, 3, 5, -2, 1};
58     std::vector<int> nums;
59     for (int i = 0; i < 8; i++){
60         nums.push_back(test[i]);
61     }
62     Solution solve;
63     std::vector<int> result = solve.countSmaller(nums);
64     for (int i = 0; i < result.size(); i++){
65         printf("[%d]", result[i]);
66     }
67     printf("\\n");
68     return 0;
69 }