Collection of some unexpected things I came across on my journey of Competitive Programming so far.

• DP through recursion (top down) often takes more time than bottom up.
  • In DP through recusrsion, keep unvisited states in array initialsed to something which never occurs in answer set (and not simply to 0).
• Only a 1 D array can be initialized with 0 like this (int a[n] = {0}) in CPP, it doesn't works with 2 D.
  • This is because = {0} means a[0][0] = 0.
• Adding ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); in your main function sometimes helps in avoiding unnecessary TLE verdict by online judges.
  • This makes cin and cout as fast as printf and scanf which reduces time.
• (a - b + m) % m = ((a%m) - (b%m) + m) % m
• We can use memset() to set all values of integer array to 0 or -1 only. Doesnot work with other values like 1, 5, 132 etc..
  • Because memset works byte by byte.
• vector v[N] -> an array of N different vector objects, can be used as a 2D array.
  • For weighted graph implementation as Adjacency list, we use vector<pair<int, int> > adj[V];, where V is the Maximum possible vertex.
• When you are given expressions in CP problems, try to simplify it by rearranging before jumping into the problem.
• If you want the priority_queue in decreasing order, that is first element largest then smaller and smaller, in custom comparator function use return a < b which is in contrast to what we do in vectors.
• For P and N, P % N must be a multiple of their common factor.
• stringstream ss(s) is used in cpp for easy tokenization of string s, just like python.
• While giving custom_sort() function for sort(), the function has to be decisive otherwise it may end up in an infinite loop giving RE. That is for any element i, if custom_sort(a[i] , b[i]) is true custom_sort(b[i] , a[i]) must be false and vice versa.
  • Beacuse std::sort() is not stable sort.
• Use vector instead of array, when size is too large. Memory allocation to array is limited.