Can this problem be solved using Binary Search

Link: https://codeforces.com/problemset/problem/1606/C

why he made this condition in his code in this problem : https://codeforces.com/contest/1512/problem/E if(s — i >= 1LL * (len — 1) * len / 2 && len > 0) i am talking about s-i =>(len-1)*(len)/2 code : https://ideone.com/sPISxq

Hi , i want to learn algorithms Is Algorithm specialization course for Tim Roughgarden  good or there are better than it ?