# Program to find total sum of all substrings of a number given as string in Python

PythonServer Side ProgrammingProgramming

Suppose we have a number in string format, and we have to find the sum of all substrings of s. The answer may be very large, so return result modulo 10^9+7.

So, if the input is like s = "268", then the output will be 378 as the substrings are "2", "6", "8", "26", "68" and "268" total sum is 378.

To solve this, we will follow these steps −

• M := 10^9 + 7
• sum_val := 0
• B := 1
• res := 0
• for i in range size of s - 1 down to 0, decrease by 1, do
• res :=(res + digit value of s[i] * B *(i + 1)) mod M
• sum_val := sum_val - digit value of s[i]
• B := (B * 10 + 1) mod M
• return res

## Example

Let us see the following implementation to get better understanding −

def solve(s):
M = 10 ** 9 + 7
sum_val = 0
B = 1
res = 0
for i in range(len(s) - 1, -1, -1):
res = (res + int(s[i]) * B * (i + 1)) % M
sum_val -= int(s[i])
B = (B * 10 + 1) % M
return res

s = "268"
print(solve(s))

## Input

"268"


## Output

378
Published on 07-Oct-2021 12:36:02