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