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添加查找算法和SingleProblem
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36
Problems/NeumannNeighborProblem/Recursive/Neumann2_4_12.cpp
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36
Problems/NeumannNeighborProblem/Recursive/Neumann2_4_12.cpp
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#include <stdio.h>
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//递归法
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int Neumann2_4_12(int n) {
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//由图可知第0次有1个方格
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if (n == 0) return 1;
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//递推关系的求解请查看说明文档
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return Neumann2_4_12(n - 1) + 4 * n;
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}
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int main() {
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int n = 0, a = 0;
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printf("------冯诺依曼邻居问题------\n");
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printf("已知:\n");
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printf(" 0 阶冯诺依曼邻居的元胞数为 1 \n");
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printf(" 1 阶冯诺依曼邻居的元胞数为 5 \n");
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printf(" 2 阶冯诺依曼邻居的元胞数为 13 \n");
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printf("求:\n");
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printf(" n 阶冯诺依曼邻居的元胞数\n");
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printf("----------------------------\n");
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printf("请输入n\n");
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scanf("%d", &n);
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//建立递推关系,使用递归求解
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a = Neumann2_4_12(n);
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printf("------------通项法-------------\n");
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printf(" %d 阶冯诺依曼邻居的元胞数为 %d\3n", n, a);
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getchar();
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getchar();
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return 0;
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}
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BIN
Problems/NeumannNeighborProblem/Recursive/Neumann2_4_12.exe
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BIN
Problems/NeumannNeighborProblem/Recursive/Neumann2_4_12.exe
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Binary file not shown.
38
Problems/NeumannNeighborProblem/Recursive/README.md
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38
Problems/NeumannNeighborProblem/Recursive/README.md
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## 冯诺依曼邻居问题(递推关系)
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### 代码
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[冯诺依曼邻居问题(递推关系)代码](Neumann2_4_12.cpp)
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### 问题说明
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某算法从一个1×1的方格开始,每次都会在上次图形的周围再加上一圈方格,在第n次的时候要生成多少个方格?下图给出了n = 0,1,2是的结果。
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### 功能说明
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本程序使用递推关系求解。
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### 代码简述
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若设第n次生成的方格数是a(n),则:
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a(1) = a(0) + 4 * 1
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a(2) = a(1) + 4 * 2
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a(3) = a(2) + 4 * 3
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...
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a(n) = a(n-1) + 4 * n
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则可得:
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a(n) = a(n - 1) + 4 * n
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然后在代码中使用递归法,递归结束条件为n = 0,即
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if (n == 0) return 1;
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则可写出递归法的代码。
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在程序中用Neumann2_4_12函数进行递归求解。
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