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| /* | |
| * | 1 1 |n |Fn+1 Fn | | |
| * | 1 0 | = |Fn Fn-1 | | |
| * | |
| * Figure 1 | |
| */ | |
| public int FibonacciLogN(int n) | |
| { | |
| if(n <= 0) | |
| return 0; | |
| if(n == 1 || n == 2) | |
| return 1; | |
| // calculate n - 1 term (see above figure 1) | |
| return FibonacciMatrix(FIBONACCI_MATRIX, n - 1)[0][0]; | |
| } | |
| private int[][] FibonacciMatrix(int[][] m, int n) | |
| { | |
| if(n == 1) | |
| return FIBONACCI_MATRIX; | |
| if(n == 2) | |
| return multiply(FIBONACCI_MATRIX, FIBONACCI_MATRIX); | |
| int solution[][] = FibonacciMatrix(m, n/2); | |
| solution = multiply(solution, solution); | |
| if(n%2 != 0) | |
| solution = multiply(solution, FIBONACCI_MATRIX); | |
| return solution; | |
| } | |
| // for quick multiplication | |
| private int[][] multiply(int[][] m, int[][] n) | |
| { | |
| int[][] result = new int[2][2]; | |
| result[0][0] = m[0][0] * n[0][0] + m[0][1] * n[1][0]; | |
| result[0][1] = m[0][0] * n[0][1] + m[0][1] * n[1][1]; | |
| result[1][0] = m[1][0] * n[0][0] + m[1][1] * n[1][0]; | |
| result[1][1] = m[1][0] * n[0][1] + m[1][1] * n[1][1]; | |
| return result; | |
| } | |
| private int[][] FIBONACCI_MATRIX = new int[][] { {1,1}, {1,0} }; |
