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++
// 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 digitint toDigit(char ch) { return (ch - '0'); }// Returns sum of all substring of numint 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 codeint main(){ string num = "1234"; // Function call cout << sumOfSubstrings(num) << endl; return 0;} |
Java
// Java program to print sum of all substring of// a number represented as a stringimport 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
# Python3 program to print# sum of all substring of# a number represented as# a string# Returns sum of all# substring of numdef 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 codeif __name__ == '__main__': num = "1234" # Function call 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 stringusing 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// PHP program to print sum of all// substring of a number represented // as a string// Method to convert character// digit to integer digitfunction toDigit($ch){ return ($ch - '0');}// Returns sum of all// substring of numfunction 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.?> |
Javascript
<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> |
Output:
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++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 digitint toDigit(char ch) { return (ch - '0'); }// Returns sum of all substring of numint 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 codeint main(){ string num = "1234"; // Function call cout << sumOfSubstrings(num) << endl; return 0;} |
Java
// Java program to print// sum of all subString of// a number represented as a Stringimport 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
# Python3 program to print sum of all substring of# a number represented as a string# Returns sum of all substring of numdef 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 codeif __name__ == '__main__': num = "1234" # Function call print(sumOfSubstrings(num))# This code is contributed by divyeshrabadiya07 |
C#
// C# program to print sum of all substring of// a number represented as a stringusing 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 |
Javascript
<script>// JavaScript program to print // sum of all subString of// a number represented as a String// Utility method to // convert character // digit to integer digitfunction toDigit(ch){ return (ch - '0');}// Returns sum of all subString of numfunction 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> |
Output:
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)
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