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Problem_1137_tribonacci.cc
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Problem_1137_tribonacci.cc
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#include <vector>
using namespace std;
class Solution
{
public:
int tribonacci(int n)
{
if (n == 0)
{
return 0;
}
if (n == 1)
{
return 1;
}
if (n == 2)
{
return 1;
}
vector<vector<long>> start = {{1, 1, 0}};
vector<vector<long>> base = {{1, 1, 0}, {1, 0, 1}, {1, 0, 0}};
vector<vector<long>> ans = multiply(start, power(base, n - 2));
return ans[0][0];
}
// 矩阵相乘
// a的列数一定要等于b的行数
vector<vector<long>> multiply(vector<vector<long>>& a, vector<vector<long>> b)
{
int n = a.size();
int m = b[0].size();
int k = a[0].size();
vector<vector<long>> ans(n, vector<long>(m));
for (int i = 0; i < n; i++)
{
for (int j = 0; j < m; j++)
{
for (int c = 0; c < k; c++)
{
ans[i][j] += a[i][c] * b[c][j];
}
}
}
return ans;
}
// 矩阵快速幂
vector<vector<long>> power(vector<vector<long>>& m, int p)
{
int n = m.size();
vector<vector<long>> ans(n, vector<long>(n));
for (int i = 0; i < n; i++)
{
ans[i][i] = 1;
}
for (; p != 0; p >>= 1)
{
if ((p & 1) != 0)
{
ans = multiply(ans, m);
}
m = multiply(m, m);
}
return ans;
}
};