Solving a relation
Practice
0 (0 votes)
Dynamic programming
Hard
Recurrence relation
Recurrence relations
Algorithms
Dp
Matrix exponentiation
Advanced
Problem
75% Success 16 Attempts 50 Points 5s Time Limit 256MB Memory 1024 KB Max Code
You are required to determine the \(n^{th}\) terms of the following relation:
\(f(0)=p\)
\(f(1)=q\)
\(f(2)= r\)
\(for n>2\)
\(f(n)= a*f(n-1) + b*f(n-2) + c*f(n-3) +g(n)\)
\(where\ g(n)=n*n*(n+1)\)
Since the \(n^{th}\) term can be too large, therefore you are required to print \(f(n)\ modulo\ (1000000007)\).
Input format
- First line: \(t\) denoting the number of test cases
- Each of the \(t\) line: Seven integers \(p,\ q,\ r,\ a,\ b,\ c,\ n\)
Output format
For each test case, print \(f(n) modulo(1000000007)\) that represents the \(n^{th}\) term of the sequence in a new line.
Constraints
\(1 \leq t \leq 50\)
\(1 \leq p,q,r,a,b,c,n \leq 10^{18}\)
Explanation
In Test case 4:
For the given values of p,q,r,a,b,c
f[0]= 1
f[1]= 2
f[2]= 3
f[3]= 1*f[2] + 1*f[1] + 1*f[0] + 3*3*(3+1)
f[3]= 1 + 2 + 3 + 36
f[3]= 42
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