I was reading editorial editorial for problem here.There was a problem link here and editorial for that here. I got what is written in editorial but don't know why that works.Can anybody comment on correctness of algorithm.thanks.
Firstly note that C mod X1 is less that 10^6. So now create 10^6 nodes starting from 0, 1 ... to 10^6 — 1. Now for every node add an edge for every bucket i.e for node numbered i adding an edge of bucket j means adding edge between i and (i + bucket[j]) % X1. So adding edges like this we get X1 * (number of buckets) number of edges. Now basically our problem is reaching from 0 to C mod X1. So apply djikstra's algorithm with 0 as root and find the shortest route to C mod X1. If the value of shortest path is less than C then clearly we have a solution as coefficient of X1 could be increased appropriately, otherwise there is no solution as the shortest coefficient of X1 would have to be negative which is not allowed
Firstly note that C mod X1 is less that 10^6. So now create 10^6 nodes starting from 0, 1 ... to 10^6 — 1. Now for every node add an edge for every bucket i.e for node numbered i adding an edge of bucket j means adding edge between i and (i + bucket[j]) % X1. So adding edges like this we get X1 * (number of buckets) number of edges. Now basically our problem is reaching from 0 to C mod X1. So apply djikstra's algorithm with 0 as root and find the shortest route to C mod X1. If the value of shortest path is less than C then clearly we have a solution as coefficient of X1 could be increased appropriately, otherwise there is no solution as the shortest coefficient of X1 would have to be negative which is not allowed