Fibonacci Number
The Fibonacci numbers, commonly denoted F(n)
form a sequence, called the Fibonacci sequence, such that each number is the sum of the two preceding ones, starting from 0
and 1
. That is,
F(0) = 0, F(1) = 1
F(N) = F(N - 1) + F(N - 2), for N > 1.
Given N
, calculate F(N)
.
Example 1:
Input: 2
Output: 1
Explanation: F(2) = F(1) + F(0) = 1 + 0 = 1.
Example 2:
Input: 3
Output: 2
Explanation: F(3) = F(2) + F(1) = 1 + 1 = 2.
Example 3:
Input: 4
Output: 3
Explanation: F(4) = F(3) + F(2) = 2 + 1 = 3.
Note:
0 ≤ N
≤ 30.
class Solution {
public int fib(int N) {
if (N == 0)
return 0;
int[][] x = { { 1, 1 }, { 1, 0 } };
// Identity matrix
int[][] ans = { { 1, 0 }, { 0, 1 } };
while (N > 0) {
if (N % 2 != 0)
ans = multiply(ans, x);
N = N / 2;
x = multiply(x, x);
}
return ans[0][1];
}
public int[][] multiply(int[][] x, int[][] y) {
int[][] res = new int[2][2];
res[0][0] = x[0][0] * y[0][0] + x[0][1] * y[1][0];
res[0][1] = x[0][0] * y[0][1] + x[0][1] * y[1][1];
res[1][0] = x[1][0] * y[0][0] + x[1][1] * y[1][0];
res[1][1] = x[1][0] * y[0][1] + x[1][1] * y[1][1];
return res;
}
}
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