在给定字符串具有最大频率的长度为 K 的子字符串

给定一个字符串str ，任务是找到出现次数最多的长度为K的子字符串。如果超过一个字符串出现最大次数，则打印字典序最小的子字符串。

例子：

Input: str = “bbbbbaaaaabbabababa”, K = 5
Output: ababa
Explanation:
The substrings of length 5 from the above strings are {bbbbb, bbbba, bbbaa, bbaaa, baaaa, aaaaa, aaaab, aaabb, aabba, abbab, bbaba, babab, ababa, babab, ababa}.
Among all of them, substrings {ababa, babab} ocuurs the maximum number of times(= 2).
The lexicographically smallest string from {ababa, babab} is ababa.
Therefore, “ababa” is the required answer.

Input:  str = “heisagoodboy”, K = 5
Output: agood
Explanation: 
The substrings of length 5 from the above string are {heisa, eisag, isago, sagoo, agood, goodb, oodbo, odboy}.
All of them occur only once. But the lexicographically smallest string among them is “agood”.
Therefore, “agood” is the required answer.

朴素方法：解决问题的最简单方法是从给定的字符串生成所有大小为K的子字符串，并将每个子字符串的频率存储在 Map 中。然后，遍历Map并找到出现次数最多的字典序最小的子串并打印出来。

时间复杂度： O(N*( K + log K))
辅助空间： O(N * K)

高效的方法：为了优化上述方法，想法是使用滑动窗口技术。考虑一个大小的窗口
K生成长度为K 的所有子串，并计算 Map 中生成的子串的频率。遍历地图，找到出现次数最多的子串并打印出来。如果存在多个，则打印字典序最小的子串。

下面是上述方法的实现。

C++

// C++ program for the above approach
  
#include 
using ll = long long int;
using namespace std;
  
// Function that generates substring
// of length K that occurs maximum times
void maximumOccurringString(string s, ll K)
{
    // Store the frequency of substrings
    map, ll> M;
  
    ll i;
  
    // Deque to maintain substrings
    // window size K
    deque D;
  
    for (i = 0; i < K; i++) {
        D.push_back(s[i]);
    }
  
    // Update the frequency of the
    // first substring in the Map
    M[D]++;
  
    // Remove the first character of
    // the previous K length substring
    D.pop_front();
  
    // Traverse the string
    for (ll j = i; j < s.size(); j++) {
  
        // Insert the current character
        // as last character of
        // current substring
        D.push_back(s[j]);
  
        M[D]++;
  
        // Pop the first character of
        // previous K length substring
        D.pop_front();
    }
  
    ll maxi = INT_MIN;
  
    deque ans;
  
    // Find the substring that occurs
    // maximum number of times
    for (auto it : M) {
        if (it.second > maxi) {
            maxi = it.second;
            ans = it.first;
        }
    }
  
    // Print the substring
    for (ll i = 0; i < ans.size(); i++) {
        cout << ans[i];
    }
}
  
// Driver Code
int main()
{
    // Given string
    string s = "bbbbbaaaaabbabababa";
  
    // Given K size of substring
    ll K = 5;
  
    // Function Call
    maximumOccurringString(s, K);
  
    return 0;
}

Python3

# Python3 program for the above approach
from collections import deque, Counter, defaultdict
import sys
  
# Function that generates substring
# of length K that occurs maximum times
def maximumOccurringString(s, K):
      
    # Store the frequency of substrings
    M = {}
  
    # Deque to maintain substrings
    # window size K
    D = deque()
  
    for i in range(K):
        D.append(s[i])
  
    # Update the frequency of the
    # first subin the Map
    # E="".join(list(D
    M[str("".join(list(D)))] = M.get(
        str("".join(list(D))), 0) + 1
  
    # Remove the first character of
    # the previous K length substring
    D.popleft()
  
    # Traverse the string
    for j in range(i, len(s)):
  
        # Insert the current character
        # as last character of
        # current substring
        D.append(s[j])
  
        M[str("".join(list(D)))] = M.get(
            str("".join(list(D))), 0) + 1
  
        # Pop the first character of
        # previous K length substring
        D.popleft()
  
    maxi = -sys.maxsize - 1
  
    ans = deque()
  
    # Find the subthat occurs
    # maximum number of times
    # print(M)
    for it in M:
          
        # print(it[0])
        if (M[it] >= maxi):
            maxi = M[it]
              
            # print(maxi)
            ans = it
  
    # Print the substring
    for i in range(len(ans)):
        print(ans[i], end = "")
  
# Driver Code
if __name__ == '__main__':
      
    # Given string
    s = "bbbbbaaaaabbabababa"
  
    # Given K size of substring
    K = 5
  
    # Function call
    maximumOccurringString(s, K)
  
# This code is contributed by mohit kumar 29

输出：

ababa

时间复杂度： O((N – K)*log(N – K))
辅助空间： O(N – K)

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