从数组求和三角形-yiteyi-C++库

给定一个整数数组，从中打印一个和三角形，使第一级包含所有数组元素。从那时起，在每个级别上，元素的数量比前一级别少一个，并且该级别上的元素是前一级别上连续两个元素的总和。 例子：

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Input : A = {1, 2, 3, 4, 5}Output : [48]         [20, 28]          [8, 12, 16]          [3, 5, 7, 9]          [1, 2, 3, 4, 5] Explanation :Here,   [48]        [20, 28] -->(20 + 28 = 48)        [8, 12, 16] -->(8 + 12 = 20, 12 + 16 = 28)        [3, 5, 7, 9] -->(3 + 5 = 8, 5 + 7 = 12, 7 + 9 = 16)        [1, 2, 3, 4, 5] -->(1 + 2 = 3, 2 + 3 = 5, 3 + 4 = 7, 4 + 5 = 9)

推荐：请尝试你的方法 {IDE} 首先，在进入解决方案之前。

方法：

递归是关键。在每次迭代中，创建一个新数组，其中包含数组中作为参数传递的连续元素的总和。
进行递归调用，并在上一步中传递新创建的数组。
回溯时打印阵列（用于按相反顺序打印）。

下面是这个实施上述方法：

C++

                         // C++ program to create Special triangle.                       
                         #include<bits/stdc++.h>                       
                         using                                     namespace                                     std;                       
                                   
                         // Function to generate Special Triangle                       
                         void                                     printTriangle(                                     int                                     A[] ,                                     int                                     n)                       
                                                 {                       
                                                 // Base case                       
                                                 if                                     (n < 1)                       
                                                 return                                     ;                       
                                   
                                                 // Creating new array which contains the                       
                                                 // Sum of consecutive elements in                       
                                                 // the array passes as parameter.                       
                                                 int                                     temp[n - 1];                       
                                                 for                                     (                                     int                                     i = 0; i < n - 1; i++)                       
                                                 {                       
                                                 int                                     x = A[i] + A[i + 1];                       
                                                 temp[i] = x;                       
                                                 }                       
                                   
                                                 // Make a recursive call and pass                       
                                                 // the newly created array                       
                                                 printTriangle(temp, n - 1);                       
                                   
                                                 // Print current array in the end so                       
                                                 // that smaller arrays are printed first                       
                                                 for                                     (                                     int                                     i = 0; i < n ; i++)                       
                                                 {                       
                                                 if                                     (i == n - 1)                       
                                                 cout << A[i] <<                                     " "                                     ;                       
                                                 else                       
                                                 cout << A[i] <<                                     ", "                                     ;                       
                                                 }                       
                                   
                                                 cout << endl;                       
                                                 }                       
                                   
                                                 // Driver function                       
                                                 int                                     main()                       
                                                 {                       
                                                 int                                     A[] = { 1, 2, 3, 4, 5 };                       
                                                 int                                     n =                                     sizeof                                     (A) /                                     sizeof                                     (A[0]);                       
                                   
                                                 printTriangle(A, n);                       
                                                 }                       
                                   
                         // This code is contributed by Smitha Dinesh Semwal                       

JAVA

                         // Java program to create Special triangle.                       
                         import                                     java.util.*;                       
                         import                                     java.lang.*;                       
                                   
                         public                                     class                                     ConstructTriangle                       
                         {                       
                                                 // Function to generate Special Triangle.                       
                                                 public                                     static                                     void                                     printTriangle(                                     int                                     [] A)                       
                                                 {                       
                                                 // Base case                       
                                                 if                                     (A.length <                                     1                                     )                       
                                                 return                                     ;                       
                                   
                                                 // Creating new array which contains the                       
                                                 // Sum of consecutive elements in                       
                                                 // the array passes as parameter.                       
                                                 int                                     [] temp =                                     new                                     int                                     [A.length -                                     1                                     ];                       
                                                 for                                     (                                     int                                     i =                                     0                                     ; i < A.length -                                     1                                     ; i++)                       
                                                 {                       
                                                 int                                     x = A[i] + A[i +                                     1                                     ];                       
                                                 temp[i] = x;                       
                                                 }                       
                                   
                                                 // Make a recursive call and pass                       
                                                 // the newly created array                       
                                                 printTriangle(temp);                       
                                   
                                                 // Print current array in the end so                       
                                                 // that smaller arrays are printed first                       
                                                 System.out.println(Arrays.toString(A));                       
                                                 }                       
                                   
                                                 // Driver function                       
                                                 public                                     static                                     void                                     main(String[] args)                       
                                                 {                       
                                                 int                                     [] A = {                                     1                                     ,                                     2                                     ,                                     3                                     ,                                     4                                     ,                                     5                                     };                       
                                                 printTriangle(A);                       
                                                 }                       
                         }                       

Python3

                         # Python3 program to create Special triangle.                       
                         # Function to generate Special Triangle.                       
                         def                                     printTriangle(A):                       
                                   
                                                 # Base case                       
                                                 if                                     (                                     len                                     (A) <                                     1                                     ):                       
                                                 return                       
                                   
                                                 # Creating new array which contains the                       
                                                 # Sum of consecutive elements in                       
                                                 # the array passes as parameter.                       
                                                 temp                                     =                                     [                                     0                                     ]                                     *                                     (                                     len                                     (A)                                     -                                     1                                     )                       
                                                 for                                     i                                     in                                     range                                     (                                     0                                     ,                                     len                                     (A)                                     -                                     1                                     ):                       
                                   
                                                 x                                     =                                     A[i]                                     +                                     A[i                                     +                                     1                                     ]                       
                                                 temp[i]                                     =                                     x                       
                                   
                                   
                                                 # Make a recursive call and pass                       
                                                 # the newly created array                       
                                                 printTriangle(temp)                       
                                   
                                                 # Print current array in the end so                       
                                                 # that smaller arrays are printed first                       
                                                 print                                     (A)                       
                                   
                                   
                         # Driver function                       
                         A                                     =                                     [                                     1                                     ,                                     2                                     ,                                     3                                     ,                                     4                                     ,                                     5                                     ]                       
                         printTriangle(A)                       
                                   
                         # This code is contributed by Smitha Dinesh Semwal                       

C#

                         // C# program to create Special triangle.                       
                                   
                         using                                     System;                       
                                   
                         public                                     class                                     ConstructTriangle                       
                         {                       
                         // Function to generate Special Triangle                       
                         static                                     void                                     printTriangle(                                     int                                     []A,                                     int                                     n)                       
                                                 {                       
                                                 // Base case                       
                                                 if                                     (n < 1)                       
                                                 return                                     ;                       
                                   
                                                 // Creating new array which contains the                       
                                                 // Sum of consecutive elements in                       
                                                 // the array passes as parameter.                       
                                                 int                                     []temp =                                     new                                     int                                     [n - 1];                       
                                                 for                                     (                                     int                                     i = 0; i < n - 1; i++)                       
                                                 {                       
                                                 int                                     x = A[i] + A[i + 1];                       
                                                 temp[i] = x;                       
                                                 }                       
                                   
                                                 // Make a recursive call and pass                       
                                                 // the newly created array                       
                                                 printTriangle(temp, n - 1);                       
                                   
                                                 // Print current array in the end so                       
                                                 // that smaller arrays are printed first                       
                                                 for                                     (                                     int                                     i = 0; i < n ; i++)                       
                                                 {                       
                                                 if                                     (i == n - 1)                       
                                                 Console.Write(A[i] +                                     " "                                     );                       
                                                 else                       
                                                 Console.Write(A[i] +                                     ", "                                     );                       
                                                 }                       
                                   
                                                 Console.WriteLine();                       
                                                 }                       
                                   
                                                 // Driver function                       
                                                 public                                     static                                     void                                     Main()                       
                                                 {                       
                                                 int                                     [] A = { 1, 2, 3, 4, 5 };                       
                                                 int                                     n = A.Length;                       
                                                 printTriangle(A,n);                       
                                                 }                       
                         }                       
                                   
                         //This code contributed by 29AjayKumar                       

PHP

                         <?php                       
                         // PHP program to create                       
                         // Special triangle.                       
                                   
                         // Function to generate                       
                         // Special Triangle                       
                         function                                     printTriangle(                                     $A                                     ,                                     $n                                     )                       
                                                 {                       
                                   
                                                 // Base case                       
                                                 if                                     (                                     $n                                     < 1)                       
                                                 return                                     ;                       
                                   
                                                 // Creating new array which                       
                                                 // contains the Sum of                       
                                                 // consecutive elements in                       
                                                 // the array passes as parameter.                       
                                                 $temp                                     [                                     $n                                     - 1] = 0;                       
                                                 for                                     (                                     $i                                     = 0;                                     $i                                     <                                     $n                                     - 1;                                     $i                                     ++)                       
                                                 {                       
                                                 $x                                     =                                     $A                                     [                                     $i                                     ] +                                     $A                                     [                                     $i                                     + 1];                       
                                                 $temp                                     [                                     $i                                     ] =                                     $x                                     ;                       
                                                 }                       
                                   
                                                 // Make a recursive call and                       
                                                 // pass the newly created array                       
                                                 printTriangle(                                     $temp                                     ,                                     $n                                     - 1);                       
                                   
                                                 // Print current array in the                       
                                                 // end so that smaller arrays                       
                                                 // are printed first                       
                                                 for                                     (                                     $i                                     = 0;                                     $i                                     <                                     $n                                     ;                                     $i                                     ++)                       
                                                 {                       
                                                 if                                     (                                     $i                                     ==                                     $n                                     - 1)                       
                                                 echo                                     $A                                     [                                     $i                                     ] ,                                     " "                                     ;                       
                                                 else                       
                                                 echo                                     $A                                     [                                     $i                                     ] ,                                     ", "                                     ;                       
                                                 }                       
                                   
                                                 echo                                     ""                                     ;                       
                                                 }                       
                                   
                         // Driver Code                       
                         $A                                     =                                     array                                     ( 1, 2, 3, 4, 5 );                       
                         $n                                     = sizeof(                                     $A                                     );                       
                                   
                         printTriangle(                                     $A                                     ,                                     $n                                     );                       
                                   
                         // This code is contributed                       
                         // by nitin mittal.                       
                         ?>                       

Javascript

                         <script>                       
           
                         // JavaScript program to create Special triangle.                       
           
                         // Function to generate Special Triangle                       
                                                 function                                     printTriangle(A,  n)                       
                                                 {                       
                                                 // Base case                       
                                                 if                                     (n < 1)                       
                                                 return                                     ;                       
                                   
                                                 // Creating new array which contains the                       
                                                 // Sum of consecutive elements in                       
                                                 // the array passes as parameter.                       
                                                 var                                     temp =                                     new                                     Array(n - 1);                       
                                                 for                                     (                                     var                                     i = 0; i < n - 1; i++)                       
                                                 {                       
                                                 var                                     x = A[i] + A[i + 1];                       
                                                 temp[i] = x;                       
                                                 }                       
                                   
                                                 // Make a recursive call and pass                       
                                                 // the newly created array                       
                                                 printTriangle(temp, n - 1);                       
                                   
                                                 // Print current array in the end so                       
                                                 // that smaller arrays are printed first                       
                                                 for                                     (                                     var                                     i = 0; i < n ; i++)                       
                                                 {                       
                                                 if                                     (i == n - 1)                       
                                                 document.write( A[i]  +                                     " "                                     );                       
                                                 else                       
                                                 document.write( A[i]  +                                     ", "                                     );                       
                                                 }                       
                                   
                                                 document.write(                                     "<br>"                                     );                       
                                                 }                       
                                   
                                                 // Driver function                       
           
                                                 var                                     A = [ 1, 2, 3, 4, 5 ];                       
                                                 var                                     n = A.length;                       
                                                 printTriangle(A,n);                       
           
                         </script>                       

输出：

4820, 288, 12, 163, 5, 7, 91, 2, 3, 4, 5

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