Sub-string Divisibility by 11 Queries - GeeksforGeeks
Given a large number, n (having number digits up to 10^6) and various queries of the below form :
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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.
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.
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).
To evaluate a query we can use the auxiliary array to answer it in O(1).
const int MAX = 1000005;// To store sums of even and odd digitsstruct OddEvenSums{ // Sum of even placed digits int e_sum; // Sum of odd placed digits int o_sum;};// Auxiliary arrayOddEvenSums sum[MAX];// Utility function to evaluate a character's// integer valueint toInt(char x){ return int(x) - 48;}// This function receives the string representation// of the number and precomputes the sum arrayvoid 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 outputbool 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);}