螺旋奇次方阵的两条对角线之和-yiteyi-C++库

我们已经给出了一个奇数阶的螺旋矩阵，在这个矩阵中，我们以数字1为中心，顺时针向右移动。 例如：

null

Input : n = 3 Output : 25Explanation : spiral matrix = 7 8 96 1 25 4 3The sum of diagonals is 7+1+3+9+5 = 25Input : n = 5Output : 101Explanation : spiral matrix of order 521 22 23 23 2520  7  8  9 1019  6  1  2 1118  5  4  3 1217 16 15 14 13The sum of diagonals is 21+7+1+3+13+25+9+5+17 = 101

建议：请在“上解决” 实践 “首先，在讨论解决方案之前。

如果我们仔细观察nxn的螺旋矩阵，我们可以注意到右上角元素的值为n ^2. .左上角的值是（n^2）-（n-1）[为什么？不是因为我们在螺旋矩阵中顺时针移动蚂蚁，所以我们从右上角减去n-1后得到左上角的值]。类似地，左下角的值为（n^2）–2（n-1），右下角的值为（n^2）–3（n-1）。加上所有四个角，我们得到4[（n^2）]–6（n-1）。设f（n）是nxn矩阵的对角元素之和。利用上述观察结果，我们可以递归地将f（n）写成：

f(n) = 4[(n^2)] – 6(n-1) + f(n-2)

根据上述关系，我们可以用迭代法求出一个螺旋矩阵的所有对角元素之和。

spiralDiaSum(n){    if (n == 1)       return 1;    // as order should be only odd    // we should pass only odd-integers    return (4*n*n - 6*n + 6 + spiralDiaSum(n-2));}

下面是实现。

C++

                         // C++ program to find sum of                       
                         // diagonals of spiral matrix                       
                         #include<bits/stdc++.h>                       
                         using                                     namespace                                     std;                       
           
                         // function returns sum of diagonals                       
                         int                                     spiralDiaSum(                                     int                                     n)                       
                         {                       
                                                 if                                     (n == 1)                       
                                                 return                                     1;                       
           
                                                 // as order should be only odd                       
                                                 // we should pass only odd-integers                       
                                                 return                                     (4*n*n - 6*n + 6 + spiralDiaSum(n-2));                       
                         }                       
           
                         // Driver program                       
                         int                                     main()                       
                         {                       
                                                 int                                     n = 7;                       
                                                 cout <<  spiralDiaSum(n);                       
                                                 return                                     0;                       
                         }                       

JAVA

                         // Java program to find sum of                       
                         // diagonals of spiral matrix                       
           
                         class                                     GFG                       
                         {                       
                                                 // function returns sum of diagonals                       
                                                 static                                     int                                     spiralDiaSum(                                     int                                     n)                       
                                                 {                       
                                                 if                                     (n ==                                     1                                     )                       
                                                 return                                     1                                     ;                       
                                   
                                                 // as order should be only odd                       
                                                 // we should pass only odd-integers                       
                                                 return                                     (                                     4                                     * n * n -                                     6                                     * n +                                     6                                     +                       
                                                 spiralDiaSum(n -                                     2                                     ));                       
                                                 }                       
                                   
                                                 // Driver program to test                       
                                                 public                                     static                                     void                                     main (String[] args)                       
                                                 {                       
                                                 int                                     n =                                     7                                     ;                       
                                                 System.out.print(spiralDiaSum(n));                       
                                                 }                       
                         }                       
           
                         // This code is contributed by Anant Agarwal.                       

Python3

                         # Python3 program to find sum of                       
                         # diagonals of spiral matrix                       
           
                         # function returns sum of diagonals                       
                         def                                     spiralDiaSum(n):                       
                                   
                                                 if                                     n                                     =                                     =                                     1                                     :                       
                                                 return                                     1                       
           
                                                 # as order should be only odd                       
                                                 # we should pass only odd                       
                                                 # integers                       
                                                 return                                     (                                     4                                     *                                     n                                     *                                     n                                     -                                     6                                     *                                     n                                     +                                     6                                     +                       
                                                 spiralDiaSum(n                                     -                                     2                                     ))                       
                                   
                         # Driver program                       
                         n                                     =                                     7                                     ;                       
                         print                                     (spiralDiaSum(n))                       
           
                         # This code is contributed by Anant Agarwal.                       

C#

                         // C# program to find sum of                       
                         // diagonals of spiral matrix                       
                         using                                     System;                       
           
                         class                                     GFG  {                       
                                   
                                                 // function returns sum of diagonals                       
                                                 static                                     int                                     spiralDiaSum(                                     int                                     n)                       
                                                 {                       
                                                 if                                     (n == 1)                       
                                                 return                                     1;                       
                                   
                                                 // as order should be only odd                       
                                                 // we should pass only odd-integers                       
                                                 return                                     (4 * n * n - 6 * n + 6 +                       
                                                 spiralDiaSum(n - 2));                       
                                                 }                       
                                   
                                                 // Driver code                       
                                                 public                                     static                                     void                                     Main (String[] args)                       
                                                 {                       
                                                 int                                     n = 7;                       
                                                 Console.Write(spiralDiaSum(n));                       
                                                 }                       
                         }                       
           
                         // This code is contributed by parashar...                       

PHP

                         <?php                       
                         // PHP program to find sum of                       
                         // diagonals of spiral matrix                       
           
                         // function returns sum                       
                         // of diagonals                       
                         function                                     spiralDiaSum(                                     $n                                     )                       
                         {                       
                                                 if                                     (                                     $n                                     == 1)                       
                                                 return                                     1;                       
           
                                                 // as order should be only odd                       
                                                 // we should pass only odd-integers                       
                                                 return                                     (4 *                                     $n                                     *                                     $n                                     - 6 *                                     $n                                     + 6 +                       
                                                 spiralDiaSum(                                     $n                                     - 2));                       
                         }                       
           
                         // Driver Code                       
                         $n                                     = 7;                       
                         echo                                     spiralDiaSum(                                     $n                                     );                       
           
                         // This code is contributed by anuj_67.                       
                         ?>                       

Javascript

                         <script>                       
           
                         // Javascript program to find sum of                       
                         // diagonals of spiral matrix                       
           
                         // function returns sum of diagonals                       
                         function                                     spiralDiaSum(n)                       
                         {                       
                                                 if                                     (n == 1)                       
                                                 return                                     1;                       
           
                                                 // as order should be only odd                       
                                                 // we should pass only odd-integers                       
                                                 return                                     (4*n*n - 6*n + 6 +                       
                                                 spiralDiaSum(n-2));                       
                         }                       
           
                         // Driver program                       
                                                 let n = 7;                       
                                                 document.write(spiralDiaSum(n));                       
           
                         </script>                       

输出：

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