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?
- Number of substrings of length one is n (We can choose any of the n characters)
- Number of substrings of length two is n-1 (We can choose any of the n-1 pairs formed by adjacent)
- Number of substrings of length three is n-2
(We can choose any of the n-2 triplets formed by adjacent) - 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++
// 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; } |
Java
// 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
# 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#
// 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 // 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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