构建字符串的最小成本

给定一个字符串s（仅包含小写字母），我们必须找到构造给定字符串的最小成本。可以使用以下操作确定成本：
1. 附加单个字符成本为 1 个单位
2. 新字符串的子字符串（中间字符串）可以不加任何费用追加
注意* 中间字符串是到目前为止形成的字符串。
例子：

Input : "geks"
Output : cost: 4
Explanation:
appending 'g' cost 1, string "g"
appending 'e' cost 1, string "ge"
appending 'k' cost 1, string "gek"
appending 's' cost 1, string "geks"
Hence, Total cost to construct "geks" is 4

Input :  "abab"
Output : cost: 2
Explanation: 
Appending 'a' cost 1, string "a"
Appending 'b' cost 1, string "ab"
Appending  "ab" cost nothing as it 
is substring of intermediate.
Hence, Total cost to construct "abab" is 2

朴素的方法：检查要构造的剩余字符串是否有子字符串，该子字符串也是中间字符串的子字符串，如果有则免费追加，如果没有则以1个单位为代价追加每个字符。
在上面的例子中，当中间字符串是“ab”并且我们需要构造“abab”时，剩下的字符串是“ab”。因此，剩余字符串中有一个子字符串，它也是中间字符串（即“ab”）的子字符串，因此我们不需要任何费用。
更好的方法：我们将使用散列技术，以保持我们是否看到了一个字符。如果我们已经看到了字符，那么附加这个字符就没有任何成本，如果没有，那么它会花费我们 1 个单位。
现在在这种方法中，我们一次取一个字符，而不是一个字符串。这是因为如果“ab”是“abab”的子串，那么 ‘a’ 和 ‘b’ 也是如此，因此没有区别。
这也使我们得出结论，如果字符串包含所有字母 (az)，则构造字符串的成本永远不会超过 26。

C++

// C++ Program to find minimum cost to
// construct a string
#include 
using namespace std;
 
int minCost(string& s)
{
    // Initially all characters are un-seen
    bool alphabets[26] = { false };
 
    // Marking seen characters
    for (int i = 0; i < s.size(); i++)
        alphabets[s[i] - 97] = true;
 
    // Count total seen character, and that
    // is the cost
    int count = 0;
    for (int i = 0; i < 26; i++)
        if (alphabets[i])
            count++;
 
    return count;
}
 
int main()
{
    // s is the string that needs to be constructed
    string s = "geeksforgeeks";
 
    cout << "Total cost to construct "
         << s << " is " << minCost;
 
    return 0;
}

Java

// Java Program to find minimum cost to
// construct a string
 
class GFG
{
 
    static int minCost(char[] s)
    {
         
        // Initially all characters are un-seen
        boolean alphabets[] = new boolean[26];
 
        // Marking seen characters
        for (int i = 0; i < s.length; i++)
        {
            alphabets[(int) s[i] - 97] = true;
        }
 
        // Count total seen character,
        // and that is the cost
        int count = 0;
        for (int i = 0; i < 26; i++)
        {
            if (alphabets[i])
            {
                count++;
            }
        }
 
        return count;
    }
 
    // Driver code
    public static void main(String[] args)
    {
        // s is the string that needs to be constructed
        String s = "geeksforgeeks";
        System.out.println("Total cost to construct " +
                s + " is " + minCost(s.toCharArray()));
    }
}
 
// This code is contributed by 29AjayKumar

Python3

# Python 3 Program to find minimum cost to
# construct a string
 
def minCost(s):
     
    # Initially all characters are un-seen
    alphabets = [False for i in range(26)]
 
    # Marking seen characters
    for i in range(len(s)):
        alphabets[ord(s[i]) - 97] = True
 
    # Count total seen character, and that
    # is the cost
    count = 0
    for i in range(26):
        if (alphabets[i]):
            count += 1
 
    return count
 
# Driver Code
if __name__ == '__main__':
     
    # s is the string that needs to
    # be constructed
    s = "geeksforgeeks"
 
    print("Total cost to construct", s,
                      "is", minCost(s))
     
# This code is contributed by
# Surendra_Gangwar

C#

// C# Program to find minimum cost to
// construct a string
using System;
 
class GFG
{
 
    static int minCost(char[] s)
    {
         
        // Initially all characters are un-seen
        bool []alphabets = new bool[26];
 
        // Marking seen characters
        for (int i = 0; i < s.Length; i++)
        {
            alphabets[(int) s[i] - 97] = true;
        }
 
        // Count total seen character,
        // and that is the cost
        int count = 0;
        for (int i = 0; i < 26; i++)
        {
            if (alphabets[i])
            {
                count++;
            }
        }
 
        return count;
    }
 
    // Driver code
    public static void Main(String[] args)
    {
        // s is the string that
        // needs to be constructed
        String s = "geeksforgeeks";
        Console.WriteLine("Total cost to construct " +
                s + " is " + minCost(s.ToCharArray()));
    }
}
 
// This code is contributed by Rajput-Ji

Javascript

      // JavaScript Program to find minimum cost to
      // construct a string
      function minCost(s)
      {
       
        // Initially all characters are un-seen
        var alphabets = new Array(26).fill(0);
 
        // Marking seen characters
        for (var i = 0; i < s.length; i++) {
          alphabets[s[i].charCodeAt(0) - 97] = true;
        }
 
        // Count total seen character,
        // and that is the cost
        var count = 0;
        for (var i = 0; i < 26; i++) {
          if (alphabets[i]) {
            count++;
          }
        }
 
        return count;
      }
 
      // Driver code
      // s is the string that
      // needs to be constructed
      var s = "geeksforgeeks";
      document.write(
        "Total cost to construct " + s + " is " + minCost(s.split(""))
      );
       
      // This code is contributed by rdtank.
    

输出：

Total cost to construct geeksforgeeks is 7

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