### eleganc's blog

By eleganc, history, 12 months ago, Hi, I faced this question in a recent mock assessment. I cannot think of any approach to solve this. Ideas are welcomed. Problem: A new method has to be derived for decrypting secret codes. THere is a secret array arr of length n, along with a 2D array query with dimension m*2, where each row denotes a pair (L, R) which denotes the sum arr[L] + arr[L+1] + .... + arr[R]. The goal is to determine all the indices of arr whose value can be identified.

Eg. n = 4 query = [[1, 3], [1, 2], [4, 4]]

First query gives the value of arr + arr + arr. The second query gives the value of arr+ arr. Third query gives the value of arr directly.

Using the above only index 3 and 4 can be determined (1 based indexing). So ans = [3, 4].

Constraints: 1 <= n <= 1e5; 1 <= m <= 1e5; 1 <= l <= r <= n  Comments (2)
 » https://atcoder.jp/contests/abc238/tasks/abc238_eInspire from the above problem, my idea is for each $L-R$, connect the node $L-1$ and $R$. Then for each node $i$ we check if $i-1$ or $i+1$ lies in the same connected component maybe ?
 » My idea is to use UFDS.whenever you get a query in the form of l,r , merge r and l-1 if they don't lie in the same CC.after all query we just have to check if i and i+1 lie in the same component where 0<=i<=n-1, if yes ans+=1.I am not sure if this works though.