Given an integer represented as a string, we need to get the sum of all possible substrings of this string
Examples:
Input: num = “1234”
Output: 1670
Explanation: Sum = 1 + 2 + 3 + 4 + 12 + 23 +34 + 123 + 234 + 1234
= 1670Input: num = “421”
Output: 491
Explanation: Sum = 4 + 2 + 1 + 42 + 21 + 421 = 491
Sum of all substrings of a string representing a number using Dynamic-Programming:
To solve the problem follow the below idea:
We can solve this problem by using dynamic programming. We can write a summation of all substrings on basis of the digit at which they are ending in that case,
Sum of all substrings = sumofdigit[0] + sumofdigit[1] + sumofdigit[2] … + sumofdigit[n-1] where n is length of string.
Where sumofdigit[i] stores the sum of all substring ending at ith index digit, in the above example,Example: num = “1234”
sumofdigit[0] = 1 = 1
sumofdigit[1] = 2 + 12 = 14
sumofdigit[2] = 3 + 23 + 123 = 149
sumofdigit[3] = 4 + 34 + 234 + 1234 = 1506
Result = 1670Now we can get the relation between sumofdigit values and can solve the question iteratively. Each sumofdigit can be represented in terms of previous value as shown below, For above example,
sumofdigit[3] = 4 + 34 + 234 + 1234
= 4 + 30 + 4 + 230 + 4 + 1230 + 4
= 4*4 + 10*(3 + 23 +123)
= 4*4 + 10*(sumofdigit[2])In general, sumofdigit[i] = (i+1)*num[i] + 10*sumofdigit[i-1]
Follow the given steps to solve the problem:
- Declare an array of size n to store the sum of previous digits, processed so far, and a variable result
- Traverse over the string and for every character
- Set sumOfDigit[i] = (i + 1) * toDigit(num[i]) + 10 * sumOfDigit[i-1]
- Add the value of sumOfDigit[i] to result
- Return result
Below is the implementation of the above approach:
// C++ program to print sum of all substring of // a number represented as a string #include <bits/stdc++.h> using namespace std;
// Utility method to convert character digit to // integer digit int toDigit( char ch) { return (ch - '0' ); }
// Returns sum of all substring of num int sumOfSubstrings(string num)
{ int n = num.length();
// allocate memory equal to length of string
int sumofdigit[n];
// initialize first value with first digit
sumofdigit[0] = toDigit(num[0]);
int res = sumofdigit[0];
// loop over all digits of string
for ( int i = 1; i < n; i++) {
int numi = toDigit(num[i]);
// update each sumofdigit from previous value
sumofdigit[i]
= (i + 1) * numi + 10 * sumofdigit[i - 1];
// add current value to the result
res += sumofdigit[i];
}
return res;
} // Driver code int main()
{ string num = "1234" ;
// Function call
cout << sumOfSubstrings(num) << endl;
return 0;
} |
// Java program to print sum of all substring of // a number represented as a string import java.util.Arrays;
class GFG {
// Returns sum of all substring of num
public static int sumOfSubstrings(String num)
{
int n = num.length();
// allocate memory equal to length of string
int sumofdigit[] = new int [n];
// initialize first value with first digit
sumofdigit[ 0 ] = num.charAt( 0 ) - '0' ;
int res = sumofdigit[ 0 ];
// loop over all digits of string
for ( int i = 1 ; i < n; i++) {
int numi = num.charAt(i) - '0' ;
// update each sumofdigit from previous value
sumofdigit[i]
= (i + 1 ) * numi + 10 * sumofdigit[i - 1 ];
// add current value to the result
res += sumofdigit[i];
}
return res;
}
// Driver code
public static void main(String[] args)
{
String num = "1234" ;
// Function call
System.out.println(sumOfSubstrings(num));
}
} // This code is contributed by Arnav Kr. Mandal. |
# Python3 program to print # sum of all substring of # a number represented as # a string # Returns sum of all # substring of num def sumOfSubstrings(num):
n = len (num)
# allocate memory equal
# to length of string
sumofdigit = []
# initialize first value
# with first digit
sumofdigit.append( int (num[ 0 ]))
res = sumofdigit[ 0 ]
# loop over all
# digits of string
for i in range ( 1 , n):
numi = int (num[i])
# update each sumofdigit
# from previous value
sumofdigit.append((i + 1 ) *
numi + 10 * sumofdigit[i - 1 ])
# add current value
# to the result
res + = sumofdigit[i]
return res
# Driver code if __name__ = = '__main__' :
num = "1234"
# Function call
print (sumOfSubstrings(num))
# This code is contributed # by Sanjit_Prasad |
// C# program to print sum of // all substring of a number // represented as a string using System;
class GFG {
// Returns sum of all
// substring of num
public static int sumOfSubstrings(String num)
{
int n = num.Length;
// allocate memory equal to
// length of string
int [] sumofdigit = new int [n];
// initialize first value
// with first digit
sumofdigit[0] = num[0] - '0' ;
int res = sumofdigit[0];
// loop over all digits
// of string
for ( int i = 1; i < n; i++) {
int numi = num[i] - '0' ;
// update each sumofdigit
// from previous value
sumofdigit[i]
= (i + 1) * numi + 10 * sumofdigit[i - 1];
// add current value
// to the result
res += sumofdigit[i];
}
return res;
}
// Driver code
public static void Main()
{
String num = "1234" ;
// Function call
Console.Write(sumOfSubstrings(num));
}
} // This code is contributed by Nitin Mittal. |
<?php // PHP program to print sum of all // substring of a number represented // as a string // Method to convert character // digit to integer digit function toDigit( $ch )
{ return ( $ch - '0' );
} // Returns sum of all // substring of num function sumOfSubstrings( $num )
{ $n = strlen ( $num );
// allocate memory equal to
// length of string
$sumofdigit [ $n ] = 0;
// initialize first value
// with first digit
$sumofdigit [0] = toDigit( $num [0]);
$res = $sumofdigit [0];
// loop over all digits of string
for ( $i = 1; $i < $n ; $i ++)
{
$numi = toDigit( $num [ $i ]);
// update each sumofdigit
// from previous value
$sumofdigit [ $i ] = ( $i + 1) * $numi + 10 *
$sumofdigit [ $i - 1];
// add current value to the result
$res += $sumofdigit [ $i ];
}
return $res ;
} // Driver Code
$num = "1234" ;
// Function call
echo sumOfSubstrings( $num ) ;
// This code is contributed by nitin mittal. ?> |
<script> // Javascript program to print sum of
// all substring of a number
// represented as a string
// Returns sum of all
// substring of num
function sumOfSubstrings(num)
{
let n = num.length;
// allocate memory equal to
// length of string
let sumofdigit = new Array(n);
// initialize first value
// with first digit
sumofdigit[0] = num[0].charCodeAt() - '0' .charCodeAt();
let res = sumofdigit[0];
// loop over all digits
// of string
for (let i = 1; i < n; i++) {
let numi = num[i].charCodeAt() - '0' .charCodeAt();
// update each sumofdigit
// from previous value
sumofdigit[i] = (i + 1) * numi + 10 * sumofdigit[i - 1];
// add current value
// to the result
res += sumofdigit[i];
}
return res;
}
let num = "1234" ;
document.write(sumOfSubstrings(num));
</script> |
1670
Time Complexity: O(N) where N is the length of the input string.
Auxiliary Space: O(N)
Sum of all substrings of a string representing a number using constant Space:
To solve the problem follow the below idea:
The approach is the same as described above. What we have observed is that at the current index we are dependent on the current sum + previous index sum so instead of storing it in an array we can store it in two variables current and prev
Below is the implementation of the above approach:
// C++ program to print sum of all substring of // a number represented as a string #include <bits/stdc++.h> using namespace std;
// Utility method to convert character digit to // integer digit int toDigit( char ch) { return (ch - '0' ); }
// Returns sum of all substring of num int sumOfSubstrings(string num)
{ int n = num.length();
// storing prev value
int prev = toDigit(num[0]);
int res = prev; // ans
int current = 0;
// substrings sum upto current index
// loop over all digits of string
for ( int i = 1; i < n; i++) {
int numi = toDigit(num[i]);
// update each sumofdigit from previous value
current = (i + 1) * numi + 10 * prev;
// add current value to the result
res += current;
prev = current; // update previous
}
return res;
} // Driver code int main()
{ string num = "1234" ;
// Function call
cout << sumOfSubstrings(num) << endl;
return 0;
} |
// Java program to print // sum of all subString of // a number represented as a String import java.util.*;
class GFG {
// Utility method to
// convert character
// digit to integer digit
static int toDigit( char ch) { return (ch - '0' ); }
// Returns sum of all subString of num
static int sumOfSubStrings(String num)
{
int n = num.length();
// Storing prev value
int prev = toDigit(num.charAt( 0 ));
int res = prev;
int current = 0 ;
// SubStrings sum upto current index
// loop over all digits of String
for ( int i = 1 ; i < n; i++) {
int numi = toDigit(num.charAt(i));
// Update each sumofdigit
// from previous value
current = (i + 1 ) * numi + 10 * prev;
// Add current value to the result
res += current;
// Update previous
prev = current;
}
return res;
}
// Driver code
public static void main(String[] args)
{
String num = "1234" ;
// Function call
System.out.print(sumOfSubStrings(num) + "\n" );
}
} // This code is contributed by gauravrajput1 |
# Python3 program to print sum of all substring of # a number represented as a string # Returns sum of all substring of num def sumOfSubstrings(num):
n = len (num)
# storing prev value
prev = int (num[ 0 ])
res = prev # ans
current = 0
# substrings sum upto current index
# loop over all digits of string
for i in range ( 1 , n):
numi = int (num[i])
# update each sumofdigit from previous value
current = (i + 1 ) * numi + 10 * prev
# add current value to the result
res + = current
prev = current # update previous
return res
# Driver code if __name__ = = '__main__' :
num = "1234"
# Function call
print (sumOfSubstrings(num))
# This code is contributed by divyeshrabadiya07 |
// C# program to print sum of all substring of // a number represented as a string using System;
class GFG {
// Utility method to
// convert character
// digit to integer digit
static int toDigit( char ch) { return (ch - '0' ); }
// Returns sum of all subString of num
static int sumOfSubStrings( string num)
{
int n = num.Length;
// Storing prev value
int prev = toDigit(num[0]);
int res = prev;
int current = 0;
// SubStrings sum upto current index
// loop over all digits of String
for ( int i = 1; i < n; i++) {
int numi = toDigit(num[i]);
// Update each sumofdigit
// from previous value
current = (i + 1) * numi + 10 * prev;
// Add current value to the result
res += current;
// Update previous
prev = current;
}
return res;
}
// Driver code
static void Main()
{
string num = "1234" ;
// Function call
Console.WriteLine(sumOfSubStrings(num));
}
} // This code is contributed by divyesh072019 |
<script> // JavaScript program to print // sum of all subString of // a number represented as a String // Utility method to // convert character // digit to integer digit function toDigit(ch)
{ return (ch - '0' );
} // Returns sum of all subString of num function sumOfSubStrings(num)
{ let n = num.length;
// Storing prev value
let prev = toDigit(num[0]);
let res = prev;
let current = 0;
// SubStrings sum upto current index
// loop over all digits of String
for (let i = 1; i < n; i++)
{
let numi = toDigit(num[i]);
// Update each sumofdigit
// from previous value
current = (i + 1) * numi + 10 * prev;
// Add current value to the result
res += current;
// Update previous
prev = current;
}
return res;
} // Driver Code let num = "1234" ;
document.write(sumOfSubStrings(num) + "\n" );
</script> |
1670
Time complexity: O(N)
Auxiliary Space: O(1)
Related Article: Sum of all substrings of a string representing a number | Set 2 (Constant Extra Space)