The information of the problem is present in the screenshot attached below. The solution to the code is this in python def solve(a, b, c, i): MOD = 1000000007 if i == 0: return a % MOD if i == 1: return b % MOD if i == 2: return c % MOD def matrix_mult(A, B): C = [[0, 0, 0], [0, 0, 0], [0, 0, 0]] for i in range(3): for j in range(3): for k in range(3): C[i][j] = (C[i][j] + A[i][k] * B[k][j]) % MOD return C def matrix_pow(A, n): if n == 1: return A if n % 2 == 0: B = matrix_pow(A, n // 2) return matrix_mult(B, B) else: B = matrix_pow(A, (n - 1) // 2) return matrix_mult(matrix_mult(B, B), A) T = [[1, 1, 1], [1, 0, 0], [0, 1, 0]] res = matrix_pow(T, i-2) return (res[0][0] * c + res[0][1] * b + res[0][2] * a) % MOD a, b, c, i = list(map(int, input().rstrip().split(" "))) print(solve(a, b, c, i)) I need an explanation of why the bold highlighted part of the code, more specifically the reason behind the values of the T matrices when initialized and the whole segment of code succeeding it

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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The information of the problem is present in the screenshot attached below.

The solution to the code is this in python

def solve(a, b, c, i):
MOD = 1000000007
if i == 0:
return a % MOD
if i == 1:
return b % MOD
if i == 2:
return c % MOD

def matrix_mult(A, B):
C = [[0, 0, 0], [0, 0, 0], [0, 0, 0]]
for i in range(3):
for j in range(3):
for k in range(3):
C[i][j] = (C[i][j] + A[i][k] * B[k][j]) % MOD
return C

def matrix_pow(A, n):
if n == 1:
return A
if n % 2 == 0:
B = matrix_pow(A, n // 2)
return matrix_mult(B, B)
else:
B = matrix_pow(A, (n - 1) // 2)
return matrix_mult(matrix_mult(B, B), A)

  T = [[1, 1, 1], [1, 0, 0], [0, 1, 0]]
res = matrix_pow(T, i-2)
return (res[0][0] * c + res[0][1] * b + res[0][2] * a) % MOD

a, b, c, i = list(map(int, input().rstrip().split(" ")))
print(solve(a, b, c, i))

I need an explanation of why the bold highlighted part of the code, more specifically the reason behind the values of the T matrices when initialized and the whole segment of code succeeding it.

Let us define the custom tribonacci sequence as follows.
To = A
T₁ = B
T₂ = C
Ti = Ti-3 + Ti-2 + Ti-1 for i ≥ 3
Given A, B, C, and i, output T mod 10⁹ +7
Input Format
Input consists of one line containing four space-separated integers A, B, C, and i as described in
the problem statement.
Constraints
0 ≤ A, B, C, i < 260
Output Format
Output one line containing T mod 10⁹ +7
Sample Input 0
0 0 1 3
Sample Output 0
1

Constraints
0 ≤ A, B, C, i < 260
Output Format
Output one line containing T mod 10⁹ +7
Sample Input 0
0 0 1 3
Sample Output 0
1
Sample Input 1
4224
Sample Output 1
12
Sample Input 2
2 1 16
Sample Output 2
21

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