题目描述
Farmer John has purchased a lush new rectangular pasture composed of M by N (1 ≤ M ≤ 12; 1 ≤ N ≤ 12) square parcels. He wants to grow some yummy corn for the cows on a number of squares. Regrettably, some of the squares are infertile and can‘t be planted. Canny FJ knows that the cows dislike eating close to each other, so when choosing which squares to plant, he avoids choosing squares that are adjacent; no two chosen squares share an edge. He has not yet made the final choice as to which squares to plant.
Being a very open-minded man, Farmer John wants to consider all possible options for how to choose the squares for planting. He is so open-minded that he considers choosing no squares as a valid option! Please help Farmer John determine the number of ways he can choose the squares to plant.
农场主John新买了一块长方形的新牧场,这块牧场被划分成M行N列(1 ≤ M ≤ 12; 1 ≤ N ≤ 12),每一格都是一块正方形的土地。John打算在牧场上的某几格里种上美味的草,供他的奶牛们享用。
遗憾的是,有些土地相当贫瘠,不能用来种草。并且,奶牛们喜欢独占一块草地的感觉,于是John不会选择两块相邻的土地,也就是说,没有哪两块草地有公共边。
John想知道,如果不考虑草地的总块数,那么,一共有多少种种植方案可供他选择?(当然,把新牧场完全荒废也是一种方案)
输入输出格式
输入格式:
第一行:两个整数M和N,用空格隔开。
第2到第M+1行:每行包含N个用空格隔开的整数,描述了每块土地的状态。第i+1行描述了第i行的土地,所有整数均为0或1,是1的话,表示这块土地足够肥沃,0则表示这块土地不适合种草。
输出格式:
一个整数,即牧场分配总方案数除以100,000,000的余数。
输入输出样例
输入样例#1: 复制
2 3 1 1 1 0 1 0
输出样例#1: 复制
9 题解:
#include <bits/stdc++.h> using namespace std; const int M = 1e9; int m, n, f[13][4096], F[13], field[13][13]; // max state: (11111111111)2 = (4095)10 bool state[4096]; int main() { cin >> m >> n; for (int i = 1; i <= m; i++) for (int j = 1; j <= n; j++) cin >> field[i][j]; for (int i = 1; i <= m; i++) for (int j = 1; j <= n; j++) F[i] = (F[i] << 1) + field[i][j];//用F数组存每行的状态,例如field[1][1]=1,所以F[i]=0<<1+1,即01......以此类推 // F[i]: state on line i int MAXSTATE = 1 << n; for (int i = 0; i < MAXSTATE; i++) state[i] = ((i&(i<<1))==0) && ((i&(i>>1))==0);//每一行的单独的预处理(即不考虑上下行对本行的影响),因为它无需考虑上下行是否满足不相邻;所以这句话的意思是判断该行某种排列情况是否满足左右不相邻 /* 样例: 2 3 1 1 1 0 1 0 第一行满足的情况:0 0 0,0 0 1,0 1 0,1 0 0,1 0 1 (共有2的n次方种情况,但满足的只有5种。 */ f[0][0] = 1;//初始化第0行 for (int i = 1; i <= m; i++) for (int j = 0; j < MAXSTATE; j++)// 枚举第i行每种状态 if (state[j] && ((j & F[i]) == j))//当state[j]==1(即这种状态满足不相邻)并且这种方案在本行可以实行(有可能本行没有j状态能耕草的地) /* 比如j的状态此时是1 0 0 1,但本行F[i](可作为草地的)为0 0 1 1,所以不满足 */ for (int k = 0; k < MAXSTATE; k++)//枚举上一行的状态 if ((k & j) == 0)//如果本行状态与上一行不冲突,则dp下去 /* 例: k:0010 j:1001 k&j=0 即k状态与j状态不冲突 */ f[i][j] = (f[i][j] + f[i-1][k]) % M;// 前i行的状态为j时的合法方案数,如果满足j&k==0则累加方案数 int ans = 0; for (int i = 0; i < MAXSTATE; i++)//将最后一行的状态为i时的合法方案全部累加,即最终答案 ans += f[m][i], ans %= M; cout << ans << endl; getchar();//可要可不要 getchar();//可要可不要 return 0; }
感谢洛谷https://www.luogu.org/space/show?uid=9671提供的代码!
注释是我理解后加上去的,希望对不懂题解的你们有用!
原文地址:https://www.cnblogs.com/tfyzs/p/11200174.html