UVA 11885 - Number of Battlefields(斐波那契)
2017-07-31 16:00
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11885 - Number of Battlefields
题意:给周长。求能围成的战场数目。不包含矩形。
思路:详细的递推没递推出来,可是看了网上一个规律,假设包含矩形的答案应该是斐波那契数列(可是奇数情况为0),然后减去矩形数目就是答案,矩形数目为n / 2 - 1,用矩阵高速幂就能求了。
详细的递推过程哪位大神能指点下。
。。
代码:
#include <stdio.h> #include <string.h> const long long MOD = 987654321; int p; struct mat { long long v[2][2]; mat() {memset(v, 0, sizeof(v));} mat operator *(mat c) { mat ans; for (int i = 0; i < 2; i++) { for (int j = 0; j < 2; j++) { for (int k = 0; k < 2; k++) { ans.v[i][j] = (ans.v[i][j] + v[i][k] * c.v[k][j] % MOD) % MOD; } } } return ans; } mat operator^(int k) { mat x = *this, ans; ans.v[0][0] = ans.v[1][1] = 1; while (k) { if (k&1) ans = ans * x; x = x * x; k >>= 1; } return ans; } }; int main() { while (~scanf("%d", &p) && p) { if(p % 2) {printf("0\n"); continue;} mat pri; pri.v[0][0] = pri.v[0][1] = pri.v[1][0] = 1; pri = pri^(p - 4); printf("%lld\n",(pri.v[0][0] - ((long long)p / 2 - 1) + MOD) % MOD); } return 0; }
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