You are given a positive integer N. Find the number of triples (X,Y,Z) such that:
0 < X,Y,Z < N,
X + Y + Z = N,
X ∣∣ Y ∣∣ Z = N, where ∣∣ represents the bitwise OR operation.
Since the number of triples can be huge, print them modulo 10^9+7.
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You are given a positive integer N. Find the number of triples (X,Y,Z) such that:
0 < X,Y,Z < N,
X + Y + Z = N,
X ∣∣ Y ∣∣ Z = N, where ∣∣ represents the bitwise OR operation.
Since the number of triples can be huge, print them modulo 10^9+7.
You are given an integer n. A game is played on a square field consisting of n × n cells. Initially all cells are empty. On each turn a player chooses and paint an empty cell that has no common sides with previously painted cells. Adjacent corner of painted cells is allowed. On the next turn another player does the same, then the first one and so on. The player with no cells to paint on his turn loses. Output the player who wins
You are given a chess board of size (2n)(2n), some of the color of the board is flipped and the board is broken down in 4 square piece each with size nn. You can join the 4 pieces in any order without rotating or flipping. As the some of the colors were flipped, so to get a valid chessboard there must need to be some recoloring. Output the minimum number of recoloring such that the 4 pieces can be joined to get a valid chessboard.
You have a string of N decimal digits.
Now you are given M queries, each of whom is of following two types.
- Type 1: 1 X Y: Replace A[X] by Y.
- Type 2: 2 C D: Print the number of sub-strings divisible by 3 of the string denoted by A[C],A[C+1] ... A[D].
Formally, you have to print the number of pairs (i,j) such that the string A[i],A[i+1]...A[j]
, (C ≤ i ≤ j ≤ D)
, when considered as a decimal number, is divisible by 3
There is a robot in a 4*4 matrix. The robot is initilly in cell (a,b) and wants to go to another cell (c,d). However, the robot doesn't know the exact route and will move to any of its adjacent cell at equal probability. What is the probability that the robot will go from initial cell (a,b) to final cell (c,d) in exactly 4 moves.
There is a robot in a undirected tree. The robot will move from a node to any of its adjacent node with equal probability. What is the expected number of moves required for the robot to go from node a to node b.
You are given an array of integers. You want to make the array non increasing. To do that you can cut out a subsegment of the array to discard and concat the remaining segment(s). What is the minimum length of the cut segment to make the remaining parts nondecreasing.
Example: [9,7,4,3,6,6,2] : we can remove the subsegment containing [4,3] to make the array [9,7,6,6,2] or remove the segment [6,6] to make the array [9,7,4,3,2]. Both of them are non increasing.