Sum of all substrings of a string representing a number

Sum of all substrings of a string representing a number | Set 1

Difficulty Level : Medium
Last Updated : 18 Dec, 2020

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
Sum = 1 + 2 + 3 + 4 + 12 + 23 +
       34 + 123 + 234 + 1234 
    = 1670

Input  : num = “421”
Output : 491
Sum = 4 + 2 + 1 + 42 + 21 + 421 = 491

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 = 1670

Now 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]

Using the above relation we can solve the problem in linear time. In the below code a complete array is taken to store sumofdigit, as each sumofdigit value requires just the previous value, we can solve this problem without allocating the complete array also.

C++

// 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 to test above methods
int main()
{
    string num = "1234";
    cout << sumOfSubstrings(num) << endl;
    return 0;
}

Java

// 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 to test above methods
    public static void main(String[] args)
    {
        String num = "1234";
 
        System.out.println(sumOfSubstrings(num));
    }
}
// This code is contributed by Arnav Kr. Mandal.

Python3

# Python 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 
num = "1234"
print(sumOfSubstrings(num))
 
# This code is contributed 
# by Sanjit_Prasad

C#

// 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";
 
        Console.Write(sumOfSubstrings(num));
    }
}
 
// This code is contributed by Nitin Mittal.

PHP

<?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
    $num = "1234";
    echo sumOfSubstrings($num) ;
     
// This code is contributed by nitin mittal.
?>

Output:

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 | Set 2 (Constant Extra Space)
This article is contributed by Utkarsh Trivedi. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
O(1) space approach
The approach is the same as described above. What we have observed that at the current index we are dependent on the current sum + previous index sum so instead of storing in a dp array we can store it in two variables current and prev.

C++14

// 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 to test above methods
int main()
{
    string num = "1234";
    cout << sumOfSubstrings(num) << endl;
    return 0;
}

Java

// 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 to test above methods
public static void main(String[] args)
{
  String num = "1234";
  System.out.print(sumOfSubStrings(num) + "\n");
}
}
 
// This code is contributed by gauravrajput1

Python3

# 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
     
num = "1234"
print(sumOfSubstrings(num))
 
# This code is contributed by divyeshrabadiya07

C#

// 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;
    }
 
  static void Main() {
    string num = "1234";
    Console.WriteLine(sumOfSubStrings(num));
  }
}
 
// This code is contributed by divyesh072019

Output:

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