右侧按字典顺序排列的较小字符的计数

给定一个仅由小写英文字母组成的字符串。任务是计算每个索引处字符右侧按字母顺序排列的较小字符的总数。

例子：

Input: str = “edcba” 
Output: 4 3 2 1 0 
Explanation: 
The number of characters on the right side of index 0 which is smaller than 
e are dcba = 4 
The number of characters on the right side of index 1 which is smaller than 
d are cba = 3 
The number of characters on the right side of index 2 which is smaller than 
c are ba = 2 
The number of characters on the right side of index 3 which is smaller than 
b are a = 1 
The number of characters on the right side of index 4 which is smaller than 
a are ‘\0’ = 0 

Input: str = “eaaa” 
Output: 3 0 0 0  

天真的方法：
这个想法是一个一个地遍历字符串每个索引右侧的所有字符，并打印按字母顺序排列较小的字符数。

C++

#include 
using namespace std;
 
// function to count the smaller
// characters at the right of index i
void countSmaller(string str)
{
 
    // store the length of string
    int n = str.length();
    for (int i = 0; i < n; i++) {
 
        // for each index initialize
        // count as zero
        int cnt = 0;
        for (int j = i + 1; j < n; j++) {
 
            // increment the count if
            // characters are smaller
            // than at ith index
            if (str[j] < str[i]) {
                cnt += 1;
            }
        }
 
        // print the count of characters
        // smaller than the index i
        cout << cnt << " ";
    }
}
 
// Driver code
int main()
{
    // input string
    string str = "edcba";
    countSmaller(str);
}

Java

class GFG
{
 
// function to count the smaller
// characters at the right of index i
static void countSmaller(String str)
{
 
    // store the length of String
    int n = str.length();
    for (int i = 0; i < n; i++)
    {
 
        // for each index initialize
        // count as zero
        int cnt = 0;
        for (int j = i + 1; j < n; j++)
        {
 
            // increment the count if
            // characters are smaller
            // than at ith index
            if (str.charAt(j) < str.charAt(i))
            {
                cnt += 1;
            }
        }
 
        // print the count of characters
        // smaller than the index i
        System.out.print(cnt+ " ");
    }
}
 
// Driver code
public static void main(String[] args)
{
    // input String
    String str = "edcba";
    countSmaller(str);
}
}
 
// This code is contributed by 29AjayKumar

Python3

# function to count the smaller
# characters at the right of index i
def countSmaller(str):
 
    # store the length of String
    n = len(str);
    for i in range(n):
 
        # for each index initialize
        # count as zero
        cnt = 0;
        for j in range(i + 1, n):
 
            # increment the count if
            # characters are smaller
            # than at ith index
            if (str[j] < str[i]):
                cnt += 1;
             
        # print the count of characters
        # smaller than the index i
        print(cnt, end =" ");
     
# Driver code
if __name__ == '__main__':
 
    # input String
    str = "edcba";
    countSmaller(str);
 
# This code is contributed by PrinciRaj1992

C#

using System;
 
class GFG
{
 
// function to count the smaller
// characters at the right of index i
static void countSmaller(String str)
{
 
    // store the length of String
    int n = str.Length;
    for (int i = 0; i < n; i++)
    {
 
        // for each index initialize
        // count as zero
        int cnt = 0;
        for (int j = i + 1; j < n; j++)
        {
 
            // increment the count if
            // characters are smaller
            // than at ith index
            if (str[j] < str[i])
            {
                cnt += 1;
            }
        }
 
        // print the count of characters
        // smaller than the index i
        Console.Write(cnt+ " ");
    }
}
 
// Driver code
public static void Main(String[] args)
{
    // input String
    String str = "edcba";
    countSmaller(str);
}
}
 
// This code is contributed by 29AjayKumar

Javascript

 
 
// function to count the smaller
// characters at the right of index i
function countSmaller(str)
{
 
    // store the length of string
    var n = str.length;
    for (var i = 0; i < n; i++) {
 
        // for each index initialize
        // count as zero
        var cnt = 0;
        for (var j = i + 1; j < n; j++) {
 
            // increment the count if
            // characters are smaller
            // than at ith index
            if (str[j] < str[i]) {
                cnt += 1;
            }
        }
 
        // print the count of characters
        // smaller than the index i
        document.write( cnt + " ");
    }
}
 
// Driver code
// input string
var str = "edcba";
countSmaller(str);
 
 
 

输出：

4 3 2 1 0

时间复杂度： O( N ² )，其中 N =字符串长度
辅助空间： O(1)

更好的方法：这个想法是使用自平衡 BST。
自平衡二叉搜索树(AVL、Red Black、.. 等)可用于获得 O(N log N) 时间复杂度的解决方案。我们可以扩充这些树，以便每个节点 N 都包含以 N 为根的子树的大小。我们在以下实现中使用了 AVL 树。
我们从右到左遍历字符串，将所有元素一一插入到一棵 AVL 树中。在 AVL 树中插入新密钥时，我们首先将密钥与根进行比较。如果键大于根，则它大于根左子树中的所有节点。因此，我们将左子树的大小添加到要插入的键的较小元素的计数中。我们对根下的所有节点递归地遵循相同的方法。
上述方法的实现请参考这篇文章。
时间复杂度： O( N*log N )
辅助空间： O( N )

有效的方法：
这个想法是使用散列技术，因为字符串仅由小写字母组成。所以这里我们可以使用一个大小为26的数组，用于存储该索引右侧的较小字符的计数。
从右侧遍历数组并不断更新哈希数组中的字符数。现在，为了找到右边较小字符的数量，我们可以简单地每次遍历大小为 26 的哈希数组来计算到目前为止遇到的较小字符的数量。

C++

#include 
using namespace std;
 
// Function to count the smaller
// characters on the right of index i
void countSmaller(string str)
{
    // store the length of string
    int n = str.length();
 
    // initialize each elements of
    // arr to zero
    int arr[26] = { 0 };
 
    // array to store count of smaller characters on
    // the right side of that index
    int ans[n];
 
    for (int i = n - 1; i >= 0; i--) {
 
        arr[str[i] - 'a']++;
 
        // initialize the variable to store
        // the count of characters smaller
        // than that at index i
        int ct = 0;
 
        // adding the count of characters
        // smaller than index i
        for (int j = 0; j < str[i] - 'a'; j++) {
            ct += arr[j];
        }
        ans[i] = ct;
    }
 
    // print the count of characters smaller
    // than index i stored in ans array
    for (int i = 0; i < n; i++) {
        cout << ans[i] << " ";
    }
}
 
// Driver Code
int main()
{
    string str = "edcbaa";
    countSmaller(str);
 
    return 0;
}

Java

class GFG
{
 
// Function to count the smaller
// characters on the right of index i
static void countSmaller(String str)
{
    // store the length of String
    int n = str.length();
 
    // initialize each elements of
    // arr to zero
    int arr[] = new int[26];
 
    // array to store count of smaller characters on
    // the right side of that index
    int ans[] = new int[n];
 
    for (int i = n - 1; i >= 0; i--)
    {
 
        arr[str.charAt(i) - 'a']++;
 
        // initialize the variable to store
        // the count of characters smaller
        // than that at index i
        int ct = 0;
 
        // adding the count of characters
        // smaller than index i
        for (int j = 0; j < str.charAt(i) - 'a'; j++)
        {
            ct += arr[j];
        }
        ans[i] = ct;
    }
 
    // print the count of characters smaller
    // than index i stored in ans array
    for (int i = 0; i < n; i++)
    {
        System.out.print(ans[i] + " ");
    }
}
 
// Driver Code
public static void main(String[] args)
{
    String str = "edcbaa";
    countSmaller(str);
}
}
 
// This code is contributed by 29AjayKumar

蟒蛇3

# Function to count the smaller
# characters on the right of index i
def countSmaller(str):
 
    # store the length of String
    n = len(str);
 
    # initialize each elements of
    # arr to zero
    arr = [0]*26;
 
    # array to store count of smaller characters on
    # the right side of that index
    ans = [0]*n;
 
    for i in range(n - 1, -1, -1):
 
        arr[ord(str[i] ) - ord('a')] += 1;
 
        # initialize the variable to store
        # the count of characters smaller
        # than that at index i
        ct = 0;
 
        # adding the count of characters
        # smaller than index i
        for j in range(ord(str[i] ) - ord('a')):
            ct += arr[j];
         
        ans[i] = ct;
     
    # print the count of characters smaller
    # than index i stored in ans array
    for i in range(n):
        print(ans[i], end = " ");
     
# Driver Code
if __name__ == '__main__':
    str = "edcbaa";
    countSmaller(str);
     
# This code is contributed by Rajput-Ji

C＃

using System;
 
class GFG
{
 
// Function to count the smaller
// characters on the right of index i
static void countSmaller(String str)
{
    // store the length of String
    int n = str.Length;
 
    // initialize each elements of
    // arr to zero
    int []arr = new int[26];
 
    // array to store count of smaller characters on
    // the right side of that index
    int []ans = new int[n];
 
    for (int i = n - 1; i >= 0; i--)
    {
 
        arr[str[i] - 'a']++;
 
        // initialize the variable to store
        // the count of characters smaller
        // than that at index i
        int ct = 0;
 
        // adding the count of characters
        // smaller than index i
        for (int j = 0; j < str[i] - 'a'; j++)
        {
            ct += arr[j];
        }
        ans[i] = ct;
    }
 
    // print the count of characters smaller
    // than index i stored in ans array
    for (int i = 0; i < n; i++)
    {
        Console.Write(ans[i] + " ");
    }
}
 
// Driver Code
public static void Main(String[] args)
{
    String str = "edcbaa";
    countSmaller(str);
}
}
 
// This code is contributed by 29AjayKumar

Javascript

 
 
// Function to count the smaller
// characters on the right of index i
function countSmaller(str)
{
    // store the length of string
    var n = str.length;
 
    // initialize each elements of
    // arr to zero
    var arr = Array(26).fill(0);
 
    // array to store count of smaller characters on
    // the right side of that index
    var ans = Array(n);
 
    for (var i = n - 1; i >= 0; i--) {
 
        arr[str[i].charCodeAt(0) - 'a'.charCodeAt(0)]++;
 
        // initialize the variable to store
        // the count of characters smaller
        // than that at index i
        var ct = 0;
 
        // adding the count of characters
        // smaller than index i
        for (var j = 0; j < str[i].charCodeAt(0) - 'a'.charCodeAt(0); j++) {
            ct += arr[j];
        }
        ans[i] = ct;
    }
 
    // print the count of characters smaller
    // than index i stored in ans array
    for (var i = 0; i < n; i++) {
        document.write( ans[i] + " ");
    }
}
 
// Driver Code
var str = "edcbaa";
countSmaller(str);
 

输出：

5 4 3 2 0 0

时间复杂度： O(N*26)
辅助空间： O(N+26)

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