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functions.cpp
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functions.cpp
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#include "functions.h"
matrixVec
MatrixMultiplication(matrixVec A, matrixVec B) {
// if matrices are not compatible for multiplication, exit the program
if (A[0].size() != B.size()) {
cout << "MatrixMultiplication: matrices are not multiplicable. Exiting...\n";
exit(1);
}
// create a vector with rows = a rows, cols = b cols
matrixVec C(A[0].size(), vector<uint64_t>(B.size()));
// go through each row
for (size_t i = 0; i < A.size(); i++) {
// go through each column
for (size_t j = 0; j < B[0].size(); j++) {
uint64_t sum = 0;
// calculate products and sums for dot product
for (size_t k = 0; k < B.size(); k++) {
sum += A[i][k] * B[k][j];
C[i][j] = sum;
}
}
}
return C;
}
void printMatrix(matrixVec v) {
// debugging method for looping through and printing matrix
for (size_t i = 0; i < v.size(); i++) {
for (size_t j = 0; j < v[0].size(); j++) {
cout << v[i][j] << " ";
}
cout << "\n";
}
}
uint64_t FibMatrix(uint64_t x) {
if (x == 0) return 1;
// declare matrices
matrixVec squareMatrix(2, vector<uint64_t>(2, 1)),
f0f1(2, vector<uint64_t>(1, 1)), // base case matrix. f(0) = 1, f(1) = 1
resultMatrix;
squareMatrix[0][0] = 0; // [[0,1],[1,1]] for matrix powers
// dot product of squareMatrix^x and base case matrix
resultMatrix = MatrixMultiplication(MatrixPower(squareMatrix, x), f0f1);
return resultMatrix[0][0];
}
matrixVec MatrixPower(matrixVec matrix, int power) {
// if matrices are not compatible for multiplication, exit the program
if (matrix.size() != matrix[0].size()) {
cout << "MatrixPower: matrix is not square. Exiting...\n";
exit(1);
}
matrixVec ans;
while (power > 0) {
if (power & 1) {
// we could use the identity matrix if ans empty,
// but this is a bit easier
// set ans to matrix or multiply by matrix ans
ans = ans.empty() ? matrix : MatrixMultiplication(matrix, ans);
}
// get power from bit
power >>= 1;
// calculate matrix power
matrix = MatrixMultiplication(matrix, matrix);
}
return ans;
}
uint64_t FibLoop(size_t x) {
uint64_t a = 1, b = 1, c;
// iterate through from 2 to x, calculate fibonaccis
for (size_t i = 2; i <= x; i++) {
c = a + b;
a = b;
b = c;
}
return b;
}
uint64_t FibRecur(uint64_t x) {
// base case
if (x < 2) return 1;
//otherwise recursively find answer
return FibRecur(x - 1) + FibRecur(x - 2);
}
uint64_t FibRecurDP(size_t x) {
// vector cache
map<uint64_t, uint64_t> fibsCache{ {0, 1}, {1, 1} };
return FibRecurDPWorker(x, fibsCache);
}
uint64_t FibRecurDPWorker(size_t x, map<uint64_t, uint64_t>&fibsCache) {
// base case
if (x < 2) return 1;
uint64_t ans;
// return answer if in cache
if (fibsCache.find(x) != fibsCache.end()) {
return fibsCache[x];
}
// recursively find answer
ans = FibRecurDPWorker(x - 1, fibsCache) + FibRecurDPWorker(x - 2, fibsCache);
// store answer
fibsCache.emplace(x, ans);
return ans;
}
uint64_t FibRecurDPTail(uint64_t x) {
return FibRecurDPTailWorker(x);
}
uint64_t FibRecurDPTailWorker(uint64_t x, uint64_t a, uint64_t b) {
if (x == 0) {
return a;
}
return FibRecurDPTailWorker(x - 1, b, a + b);
}