Given a string representing a number, we need to get the sum of all possible sub strings of this string.
Examples :
Input : s = "6759"
Output : 8421
sum = 6 + 7 + 5 + 9 + 67 + 75 +
59 + 675 + 759 + 6759
= 8421
Input : s = "16"
Output : 23
sum = 1 + 6 + 16 = 23
We have discussed a solution in below post.
Sum of all substrings of a string representing a number | Set 1
The solution is based on a different approach which does not use any extra space.
This problem can be viewed as follows.
Let number be s = “6759”
1 10 100 1000
6 1 1 1 1
7 2 2 2
5 3 3
9 4
The above table indicates that, when all the substrings are converted further to the ones, tens, hundreds etc.. form, each index of the string will have some fixed occurrence. The 1st index will have 1 occurrence each of ones, tens etc..The 2nd will have 2, 3rd will have 3 and so on.
One more point is that the occurrence of the last element will only be restricted to ones. Last 2nd element will be restricted to ones and tens. last 3rd will be up to a hundred and so on.
From the above points lets find out the sum.
sum = 6*(1*1 + 1*10 + 1*100 + 1*1000) + 7*(2*1 + 2*10 + 2*100) +
5*(3*1 + 3*10) + 9*(4*1)
= 6*1*(1111) + 7*2*(111) + 5*3*(11) + 9*4*(1)
= 6666 + 1554 + 165 + 36
= 8421
Now, to handle the multiplication we will be having a multiplying factor which starts from 1. It’s clear from the example that the multiplying factor(in reverse) is 1, 11, 111, … and so on. So the multiplication will be based on three factors. number, its index, and a multiplying factor.
Implementation:
C++
// C++ program to print sum of all substring of// a number represented as a string#include <bits/stdc++.h>using namespace std;// Returns sum of all substring of numint sumOfSubstrings(string num){ long long int sum = 0; // Initialize result // Here traversing the array in reverse // order.Initializing loop from last // element. // mf is multiplying factor. long long int mf = 1; for (int i=num.size()-1; i>=0; i--) { // Each time sum is added to its previous // sum. Multiplying the three factors as // explained above. // s[i]-'0' is done to convert char to int. sum += (num[i]-'0')*(i+1)*mf; // Making new multiplying factor as // explained above. mf = mf*10 + 1; } return sum;}// Driver code to test above methodsint main(){ string num = "6759"; 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;public class GFG { // Returns sum of all substring of num public static long sumOfSubstrings(String num) { long sum = 0; // Initialize result // Here traversing the array in reverse // order.Initializing loop from last // element. // mf is multiplying factor. long mf = 1; for (int i = num.length() - 1; i >= 0; i --) { // Each time sum is added to its previous // sum. Multiplying the three factors as // explained above. // s[i]-'0' is done to convert char to int. sum += (num.charAt(i) - '0') * (i + 1) * mf; // Making new multiplying factor as // explained above. mf = mf * 10 + 1; } return sum; } // Driver code to test above methods public static void main(String[] args) { String num = "6759"; 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): sum = 0 # Initialize result # Here traversing the array in reverse # order.Initializing loop from last # element. # mf is multiplying factor. mf = 1 for i in range(len(num) - 1, -1, -1): # Each time sum is added to its previous # sum. Multiplying the three factors as # explained above. # int(s[i]) is done to convert char to int. sum = sum + (int(num[i])) * (i + 1) * mf # Making new multiplying factor as # explained above. mf = mf * 10 + 1 return sum# Driver code to test above methodsif __name__=='__main__': num = "6759" 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; public class GFG { // Returns sum of all substring of num public static long sumOfSubstrings(string num) { long sum = 0; // Initialize result // Here traversing the array in reverse // order.Initializing loop from last // element. // mf is multiplying factor. long mf = 1; for (int i = num.Length - 1; i >= 0; i --) { // Each time sum is added to its previous // sum. Multiplying the three factors as // explained above. // s[i]-'0' is done to convert char to int. sum += (num[i] - '0') * (i + 1) * mf; // Making new multiplying factor as // explained above. mf = mf * 10 + 1; } return sum; } // Driver code to test above methods public static void Main() { string num = "6759"; Console.WriteLine(sumOfSubstrings(num)); }}// This code is contributed by Sam007. |
PHP
<?php// PHP program to print sum of// all substring of a number // represented as a string// Returns sum of all // substring of numfunction sumOfSubstrings($num){ // Initialize result $sum = 0; // Here traversing the array // in reverse order.Initializing // loop from last element. // mf is multiplying factor. $mf = 1; for ($i = strlen($num) - 1; $i >= 0; $i--) { // Each time sum is added to // its previous sum. Multiplying // the three factors as explained above. // s[i]-'0' is done to convert char to int. $sum += ($num[$i] - '0') * ($i + 1) * $mf; // Making new multiplying // factor as explained above. $mf = $mf * 10 + 1; } return $sum;}// Driver Code$num = "6759";echo sumOfSubstrings($num), "\n";// This code is contributed by m_kit?> |
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 sum = 0; // Initialize result // Here traversing the array in reverse // order.Initializing loop from last // element. // mf is multiplying factor. let mf = 1; for (let i = num.length - 1; i >= 0; i --) { // Each time sum is added to its previous // sum. Multiplying the three factors as // explained above. // s[i]-'0' is done to convert char to int. sum += (num[i].charCodeAt() - '0'.charCodeAt()) * (i + 1) * mf; // Making new multiplying factor as // explained above. mf = mf * 10 + 1; } return sum; } let num = "6759"; document.write(sumOfSubstrings(num)); // This code is contributed by rameshtravel07.</script> |
8421
Time Complexity: O(n)
Auxiliary Space: O(1)
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