Number of substrings of a string

Find total number of non-empty substrings of a string with N characters. 

Input : str = "abc" 
Output : 6 
Every substring of the given string : "a", "b", "c", "ab", "bc", "abc"

Input : str = "abcd" 
Output : 10 
Every substring of the given string : "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, number 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

Implementation:

// 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;
}

#include <stdio.h>
#include <string.h>

int countNonEmptySubstr(const char* str)
{
    int n = strlen(str);
    return n * (n + 1) / 2;
}

// driver code
int main()
{
    const char* s = "abcde";
    printf("%d\n", countNonEmptySubstr(s));
    return 0;
}

// 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)

# 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)

// 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)

<?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
?>

<script>

// JavaScript program to count number of substrings
// of a string
function countNonEmptySubstr(str)
    {
        let n = str.length;
        return n * (n + 1) / 2;
    }
    
    // Driver code
        let s = "abcde";
        document.write(countNonEmptySubstr(s));


// This code is contributed shivanisinghss2110

</script>

15

Complexity Analysis:

• Time Complexity: O(1).
• Auxiliary Space: O(1).