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. ?> |
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 | Set 2 (Constant Extra Space)
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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 |
1670
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