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Q1 Help Your Master
Problem Description
GOAT-master got arrested in a police chase. He is trying to escape the high-tech prison he is held captive in. He needs a pass-code P for disabling all the cameras in order to escape. Passcode is the solution of matrix problem given below. Help him finding the pass-code.
You are given a matrix of order N×N. Each cell in a matrix has a value A : (o<=i,<N), which is either positive or equal to -1 (representing blocked cell)
Cells which are not blocked have distinct values. You can traverse from a cell in any direction (up, down, left or right), if there is no blockage.
For any cell Aj,j, sed-value S;,; is defined as sum of values of cells Ax, y which are multiple of Aj,j, but not reachable from A;,. For blocked cells, sed-value is -1.
Pass-code P is sum of sed-values of all the cells, modulo 1000000007.
Problem Constraints
1<=N<=1e3
1<=A[il [il<=1e6
A[il [j]=-1 for blocked cells only
Input Format
First argument is a 2-D array of integers denoting the above matrix.
Output Format
Return the sum of sed-values of all the cells, modulo 1000000007.
Example Input
Input 1:
[1, 3 ,-1, 5],
[-1,-1, -1 ,-1],
[2, 6 ,-1, 10],
[8, 7 ,- 1 ,11]]
Output 1:
68
Q2 XOR subsequences
Problem Description
You are given an array A, you have to create an array B which is a subsequence of A.
An array B is called valid if it satisfies both the conditions
- B[i] < B[i+1] where 1 <= i<|B|.
- bit_count( B[1] ^. ^ B[i-1] ^ B[i]) <= bit_count(B[i+1]) where 1 <= i < |B|.
.........
Let X be the Bitwise XOR of all the elements in valid array B.
You need to find the number of different values of X that can be formed.
Note: bit_count(t) is the number of set bits present in the binary representation of t
Problem Constraints
1 <= IAl <= 10^5
1 <= A[i] <= 100
Input Format
The first argument is an integer array A
Output Format
Return an integer denoting the number of different values of X that can be formed
Q3 Read Books nCdKd
Problem Description
There are N chapters in the library. The i-th chapter gives you A[i] knowledge. The i-th chapter can only be read after reading the (i-1)thchapter. You start reading from the first chapter. After reading the last chapter, you can again start from the first chapter.
You have to find out how many chapters you have to read in order to gain B[i] knowledge for every index i in B. If it is impossible to gain B[i] amount of knowledge, return -1.
Problem Constraints
1 <= N <= 105
IBI = N
-109 <=A[i] <= 109
1 <= B[i] <= 109
Input Format
The first argument contains the array A.
The second argument contains the array B.
Output Format
Return an array denoting the number of chapters required to read to gain B[i] amount of knowledge.
Example Input
Input 1:- A = [1, 2, 1]
Output Format
Return an array denoting the number of chapters required to read to gain B[i] amount of knowledge.
Example Input
Input 1:-
A = [1, 2, 1]
B = [10, 1, 2]
Input 2-
A = [1]
B=[100]
Example Output
Output 1:- [8, 1, 2]
Output 2:- [100]
Explanation
Explanation 1:- You read the whole book twice so 6 chapters and then again the first 2 chapters, so 8 chapters in total. Similarly 1 and 2 chapter for the rest two queries.
Explanation 2:- You read the first chapter 100 times to gain a knowledge of 100.
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