计算建造建筑物的方法


此处给出了 n 个部分,每个部分的道路两侧可以建两座建筑物。如果两所房屋之间需要一个空位,则在地块上建造建筑物的可能方法有多少。

建造建筑物有四种可能性

  •  道路的一侧
  •  道路的另一侧
  •  不能建造建筑物
  •  道路的两侧

输入和输出

Input:
It takes the number of sections to construct buildings. Say the input is 3.
Output:
Enter Number of sections: 3
Buildings can be constructed in 25 different ways.

算法

constructionWays(n)

输入:有 n 个部分。

输出 −可能的方案数。

Begin
   if n = 1, then
      return 4
   countEnd := 1
   countEndSpace := 1

   for i := 2 to n, do
      prevCountEnd := countEnd
      prevCountEndSpace := countEndSpace
      countEndSpace := countEnd + prevCountEndSpace
      countEnd := prevCountEndSpace
   done

   answer := countEndSpace + countEnd
   return answer^2
End

示例

#include<iostream>
using namespace std;

int constructionWays(int n) {
   if (n == 1)        //if there is one section
      return 4;       //4 possible ways to construct building in that section

   //set counting values for place at the end and end with space
   int countEnd=1, countEndSpace=1, prevCountEnd, prevCountEndSpace;

   for (int i=2; i<=n; i++) {       //fot the second section to nth section
      prevCountEnd = countEnd;
      prevCountEndSpace = countEndSpace;

      countEndSpace = countEnd + prevCountEndSpace;
      countEnd = prevCountEndSpace;
   }

   //possible ways to end with space and building at the end
   int answer = countEndSpace + countEnd;

   return (answer*answer);     //for two sides the answer will be squared
}

int main() {
   int n;
   cout << "Enter Number of sections: ";
   cin >> n;
   cout << "Buildings can be constructed in " << constructionWays(n) <<" different ways." ;
}

输出

Enter Number of sections: 3
Buildings can be constructed in 25 different ways.

更新日期:16-Jun-2020

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