# Sub-string Divisibility by 11 Queries

Given a large number, n (having number digits up to 10^6) and various queries of the below form :

Query(l, r) : find if the sub-string between the indices l and r (Both inclusive) are divisible by 11.

Examples:

Input: n = 122164154695 Queries: l = 0 r = 3, l = 1 r = 2, l = 5 r = 9, l = 0 r = 11 Output: True False False True Explanation: In the first query, 1221 is divisible by 11 In the second query, 22 is divisible by 11 and so on.

We know that any number is divisible by 11 if the difference between sum of odd indexed digits and the sum of even indexed digits is divisible by 11, i.e.,

*
Sum(digits at odd places) – Sum(digits at even places) should be divisible by 11*.

Hence the idea is to pre-process an auxiliary array that would store sum of digits at odd and even places.

To evaluate a query we can use the auxiliary array to answer it in O(1).

`// C++ program to check divisibility by 11 in ` `// substrings of a number string ` `#include <iostream> ` `using` `namespace` `std; ` ` ` `const` `int` `MAX = 1000005; ` ` ` `// To store sums of even and odd digits ` `struct` `OddEvenSums ` `{ ` ` ` `// Sum of even placed digits ` ` ` `int` `e_sum; ` ` ` ` ` `// Sum of odd placed digits ` ` ` `int` `o_sum; ` `}; ` ` ` `// Auxiliary array ` `OddEvenSums sum[MAX]; ` ` ` `// Utility function to evaluate a character's ` `// integer value ` `int` `toInt(` `char` `x) ` `{ ` ` ` `return` `int` `(x) - 48; ` `} ` ` ` `// This function receives the string representation ` `// of the number and precomputes the sum array ` `void` `preCompute(string x) ` `{ ` ` ` `// Initialize everb ` ` ` `sum[0].e_sum = sum[0].o_sum = 0; ` ` ` ` ` `// Add the respective digits depending on whether ` ` ` `// they're even indexed or odd indexed ` ` ` `for` `(` `int` `i=0; i<x.length(); i++) ` ` ` `{ ` ` ` `if` `(i%2==0) ` ` ` `{ ` ` ` `sum[i+1].e_sum = sum[i].e_sum+toInt(x[i]); ` ` ` `sum[i+1].o_sum = sum[i].o_sum; ` ` ` `} ` ` ` `else` ` ` `{ ` ` ` `sum[i+1].o_sum = sum[i].o_sum+toInt(x[i]); ` ` ` `sum[i+1].e_sum = sum[i].e_sum; ` ` ` `} ` ` ` `} ` `} ` ` ` `// This function receives l and r representing ` `// the indices and prints the required output ` `bool` `query(` `int` `l,` `int` `r) ` `{ ` ` ` `int` `diff = (sum[r+1].e_sum - sum[r+1].o_sum) - ` ` ` `(sum[l].e_sum - sum[l].o_sum); ` ` ` ` ` `return` `(diff%11==0); ` `} ` ` ` `//driver function to check the program ` `int` `main() ` `{ ` ` ` `string s = ` `"122164154695"` `; ` ` ` ` ` `preCompute(s); ` ` ` ` ` `cout << query(0, 3) << endl; ` ` ` `cout << query(1, 2) << endl; ` ` ` `cout << query(5, 9) << endl; ` ` ` `cout << query(0, 11) << endl; ` ` ` ` ` `return` `0; ` `} ` |

*chevron_right*

*filter_none*

Output:

1 1 0 1

This article is contributed by **Ashutosh Kumar**. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

## Recommended Posts:

- Sub-string Divisibility by 3 Queries
- Check divisibility by 7
- Repeated Unit Divisibility
- Divisibility by 12 for a large number
- Check if a large number is divisibility by 15
- Check divisibility in a binary stream
- To check divisibility of any large number by 999
- Divisibility by 64 with removal of bits allowed
- Maximize profit when divisibility by two numbers have associated profits
- Divisibility by 3 where each digit is the sum of all prefix digits modulo 10
- Maximum path sum for each position with jumps under divisibility condition
- XOR of a submatrix queries
- Queries for bitwise OR in the given matrix
- Sum of even values and update queries on an array
- Queries to print all divisors of number