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

Given a 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 using dynamic programming. We can write summation of all substrings on basis of 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 sum of all substring ending at ith index digit, in 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 above relation we can solve the problem in linear time. In below code a complete array is taken to store sumofdigit, as each sumofdigit value requires just previous value, we can solve this problem without allocating complete array also.

C++

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// 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;
}

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Java














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// 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. 



















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Python3














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# 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 



















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C#














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// 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. 



















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PHP














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<?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. 


?> 



















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Output:


1670





Time Complexity : O(n) where n is length of 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 

Approach is same as described above. What we have observed that at current index we are dependent on current sum +  previous index sum so instead of storing in a dp array we can store it in two variables current and prev.











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// 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; 


} 



















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Output:


1670





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