20251024 baekjoon

code_study/Baekjoon/c/11444.c

@@ -0,0 +1,71 @@
+#include <stdio.h>
+// Fn      | 1 1 | ^n-1 F1(1)
+// Fn-1    | 1 0 |      F0(0)
+
+#define MOD 1000000007
+
+typedef long long matrix[2][2];
+
+void multyply_matrix(matrix A, matrix B, matrix result);
+void power_matrix(matrix A, long long exp, matrix result);
+
+int main() {
+    long long n;
+    scanf("%lld", &n);
+
+    if (n <= 1) {
+        printf("%lld\n", n);
+        return 0;
+    }
+
+    matrix A = {{1, 1}, {1, 0}};
+    matrix result_matrix;
+
+    power_matrix(A, n - 1, result_matrix);
+
+    printf("%lld\n", result_matrix[0][0]);
+
+    return 0;
+}
+
+void multyply_matrix(matrix A, matrix B, matrix result) {
+    matrix temp;
+    temp[0][0] = (A[0][0] * B[0][0] + A[0][1] * B[1][0]) % MOD;
+    temp[0][1] = (A[0][0] * B[0][1] + A[0][1] * B[1][1]) % MOD;
+    temp[1][0] = (A[1][0] * B[0][0] + A[1][1] * B[1][0]) % MOD;
+    temp[1][1] = (A[1][0] * B[0][1] + A[1][1] * B[1][1]) % MOD;
+    
+    result[0][0] = temp[0][0];
+    result[0][1] = temp[0][1];
+    result[1][0] = temp[1][0];
+    result[1][1] = temp[1][1];
+}
+
+void power_matrix(matrix A, long long exp, matrix result) {
+    if (exp == 0) {
+        result[0][0] = 1; result[0][1] = 0;
+        result[1][0] = 0; result[1][1] = 1;
+        return;
+    }
+
+    if (exp == 1) {
+        result[0][0] = A[0][0]; result[0][1] = A[0][1];
+        result[1][0] = A[1][0]; result[1][1] = A[1][1];
+        return;
+    }
+
+    matrix half;
+    power_matrix(A, exp / 2, half);
+
+    matrix temp;
+    multyply_matrix(half, half, temp);
+
+    if (exp % 2 == 1) {
+        multyply_matrix(temp, A, result);
+    } else {
+        result[0][0] = temp[0][0];
+        result[0][1] = temp[0][1];
+        result[1][0] = temp[1][0];
+        result[1][1] = temp[1][1];
+    }
+}