Number of substrings of a string

Find total number of non-empty substrings of a string with N characters. Here we use the word proper because we do not consider string itself as part of output.

Input : str = “abc”
Output : 6
Proper substrings are “a”, “b”, “c”, “ab”, “bc”, “abc”

Input : str = “abcd”
Output : 10
Proper substrings are “a”, “b”, “c”, “d”, “ab”, “bc”, “cd”, “abc”, “bcd” and “abcd”



Count of non-empty substrings is n*(n+1)/2

If we include empty string also as substring, the count becomes n*(n+1)/2 + 1

How does above formula work?

  1. Number of substrings of length one is n (We can choose any of the n characters)
  2. Number of substrings of length two is n-1 (We can choose any of the n-1 pairs formed by adjacent)
  3. Number of substrings of length three is n-2
    (We can choose any of the n-2 triplets formed by adjacent)
  4. In general, mumber of substrings of length k is n-k+1 where 1 <= k <= n

Total number of substrings of all lengths from 1 to n =
n + (n-1) + (n-2) + (n-3) + … 2 + 1
= n * (n + 1)/2

C++

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// CPP program to count number of substrings
// of a string
#include <bits/stdc++.h>
using namespace std;
  
int countNonEmptySubstr(string str)
{
   int n = str.length();
   return n*(n+1)/2;
}
  
// driver code
int main()
{
    string s = "abcde";
    cout << countNonEmptySubstr(s);
    return 0;
}

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Java

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// Java program to count number of substrings
// of a string
import java.io.*;
  
public class GFG {
      
    static int countNonEmptySubstr(String str)
    {
        int n = str.length();
        return n * (n + 1) / 2;
    }
      
    // Driver code
    public static void main(String args[])
    {
        String s = "abcde";
        System.out.println(
                  countNonEmptySubstr(s));
    }
}
  
// This code is contributed 
// by Manish Shaw (manishshaw1)

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Python3

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# Python3 program to count number
# of substrings of a string
  
def countNonEmptySubstr(str):
    n = len(str);
    return int(n * (n + 1) / 2);
  
# driver code
s = "abcde";
print (countNonEmptySubstr(s));
  
# This code is contributed by
# Manish Shaw (manishshaw1)

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C#

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// C# program to count number 
// of substrings of a string
using System;
class GFG {
      
    static int countNonEmptySubstr(string str)
    {
        int n = str.Length;
        return n * (n + 1) / 2;
    }
      
    // Driver Code
    public static void Main()
    {
        string s = "abcde";
        Console.Write(countNonEmptySubstr(s));
    }
}
  
// This code is contributed 
// by Manish Shaw (manishshaw1)

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PHP

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<?php
// PHP program to count number
// of substrings of a string
  
function countNonEmptySubstr($str)
{
    $n = strlen($str);
    return $n * ($n + 1) / 2;
}
  
// Driver Code
$s = "abcde";
echo countNonEmptySubstr($s);
      
// This code is contributed by Anuj_67
?>

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Output:

15


My Personal Notes arrow_drop_up

Maths is the language of nature

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Improved By : manishshaw1, vt_m



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