从n个缺失一个的求和方程中寻找n个变量-yiteyi-C++库

给出了一个数组a[]，其中n个值为[1]，a[2]…a[n]，它们是n变量中n个方程的一部分，其中方程为： Eqn1=>X2+X3++Xn=a1 Eqn2=>X1+X3++Xn=a2 Eqni=>X1+X2+…+X _i-1 +X _i+1 ..+Xn=ai Eqnn=>X1+X2++十、 _n-1 =安因为在n个变量中有n个方程，所以求所有变量（X1，X2…Xn）的值。 例如：

null

Input : a[] = {4, 4, 4, 4, 4}Output : X1 = 1         X2 = 1         X3 = 1         X4 = 1         X5 = 1Input : a[] = {2, 5, 6, 4, 8}Output : X1 = 4.25         X2 = 1.25         X3 = 0.25         X4 = 2.25         X5 = -1.75

推荐：请尝试你的方法 {IDE} 首先，在进入解决方案之前。

方法 : 设X1+X2+X3+…。Xn=总和使用值和，我们的方程如下

SUM - X1 = a1 -----(1)SUM - X2 = a2  -----(2)SUM - Xi = ai  -----(i)SUM - Xn = an -------(n)---------------------------------------------------------------Now, if we add all these equation we will have an equation as :n*SUM -(X1+X2+...Xn) = a1 + a2 + ...ann*SUM - SUM = a1 + a2 + ...anSUM = (a1+a2+...an)/(n-1)Calculate SUM from above equation.putting value of SUM in (i), (ii).... we haveX1 = SUM - a1X2 = SUM - a2

解决方案：

X1 = SUM - a1X2 = SUM - a2Xi = SUM - aiXn = SUM - an

C++

                         // CPP program to find n-variables                       
                         #include <bits/stdc++.h>                       
                         using                                     namespace                                     std;                       
           
                         // function to print n-variable values                       
                         void                                     findVar(                                     int                                     a[],                                     int                                     n)                       
                         {                       
                                                 // calculate value of array SUM                       
                                                 float                                     SUM = 0;                       
                                                 for                                     (                                     int                                     i = 0; i < n; i++)                       
                                                 SUM += a[i];                       
           
                                                 // Every variable contributes n-1                       
                                                 // times to sum. So dividing by                       
                                                 // n-1 to get sum of all.                       
                                                 SUM /= (n - 1);                       
           
                                                 // print the values of n-variables                       
                                                 for                                     (                                     int                                     i = 0; i < n; i++)                       
                                                 cout <<                                     "X"                                     << (i + 1)                       
                                                 <<                                     " = "                                     << SUM - a[i] << endl;                       
                         }                       
           
                         // driver program                       
                         int                                     main()                       
                         {                       
                                                 int                                     a[] = { 2, 5, 6, 4, 8 };                       
                                                 int                                     n =                                     sizeof                                     (a) /                                     sizeof                                     (a[0]);                       
                                                 findVar(a, n);                       
                                                 return                                     0;                       
                         }                       

JAVA

                         // Java program to                       
                         // find n-variables                       
                         import                                     java.io.*;                       
           
                         class                                     GFG                       
                         {                       
                                                 // function to print                       
                                                 // n-variable values                       
                                                 static                                     void                                     findVar(                                     int                                     []a,                       
                                                 int                                     n)                       
                                                 {                       
                                                 // calculate value+                       
                                                 // of array SUM                       
                                                 float                                     SUM =                                     0                                     ;                       
                                                 for                                     (                                     int                                     i =                                     0                                     ; i < n; i++)                       
                                                 SUM += a[i];                       
                                   
                                                 // Every variable contributes                       
                                                 // n-1 times to sum. So dividing                       
                                                 // by n-1 to get sum of all.                       
                                                 SUM /= (n -                                     1                                     );                       
                                   
                                                 // print the values                       
                                                 // of n-variables                       
                                                 for                                     (                                     int                                     i =                                     0                                     ; i < n; i++)                       
                                                 System.out.print(                                     "X"                                     + (i +                                     1                                     ) +                       
                                                 " = "                                     + (SUM -                       
                                                 a[i]) +                                     ""                                     );                       
                                                 }                       
                                   
                                                 // Driver Code                       
                                                 public                                     static                                     void                                     main(String args[])                       
                                                 {                       
                                                 int                                     []a =                                     new                                     int                                     []{                                     2                                     ,                                     5                                     ,                                     6                                     ,                                     4                                     ,                                     8                                     };                       
                                                 int                                     n = a.length;                       
                                                 findVar(a, n);                       
                                                 }                       
                         }                       
           
                         // This code is contributed by                       
                         // Manish Shaw(manishshaw1)                       

Python3

                         # Python3 program to                       
                         # find n-variables                       
           
                         # function to print                       
                         # n-variable values                       
                         def                                     findVar(a, n):                       
                                   
                                                 # calculate value of                       
                                                 # array SUM                       
                                                 SUM                                     =                                     0                                     ;                       
                                                 for                                     i                                     in                                     range                                     (n):                       
                                                 SUM                                     +                                     =                                     a[i];                       
           
                                                 # Every variable contributes                       
                                                 # n-1 times to sum. So                       
                                                 # dividing by n-1 to get sum                       
                                                 # of all.                       
                                                 SUM                                     =                                     SUM                                     /                                     (n                                     -                                     1                                     );                       
           
                                                 # print the values                       
                                                 # of n-variables                       
                                                 for                                     i                                     in                                     range                                     (n):                       
                                                 print                                     (                                     "X"                                     , (i                                     +                                     1                                     ),                       
                                                 " = "                                     ,                                     SUM                                     -                                     a[i]);                       
           
                         # Driver Code                       
                         a                                     =                                     [                                     2                                     ,                                     5                                     ,                                     6                                     ,                                     4                                     ,                                     8                                     ];                       
                         n                                     =                                     len                                     (a);                       
                         findVar(a, n);                       
                                   
                         # This code is contributed                       
                         # by mits                       

C#

                         // C# program to find n-variables                       
                         using                                     System;                       
                         using                                     System.Linq;                       
                         using                                     System.Collections.Generic;                       
           
                         class                                     GFG                       
                         {                       
                                                 // function to print                       
                                                 // n-variable values                       
                                                 static                                     void                                     findVar(                                     int                                     []a,                       
                                                 int                                     n)                       
                                                 {                       
                                                 // calculate value+                       
                                                 // of array SUM                       
                                                 float                                     SUM = 0;                       
                                                 for                                     (                                     int                                     i = 0; i < n; i++)                       
                                                 SUM += a[i];                       
                                   
                                                 // Every variable contributes                       
                                                 // n-1 times to sum. So dividing                       
                                                 // by n-1 to get sum of all.                       
                                                 SUM /= (n - 1);                       
                                   
                                                 // print the values                       
                                                 // of n-variables                       
                                                 for                                     (                                     int                                     i = 0; i < n; i++)                       
                                                 Console.Write(                                     "X"                                     + (i + 1) +                       
                                                 " = "                                     + (SUM - a[i]) +                                     ""                                     );                       
                                                 }                       
                                   
                                                 // Driver Code                       
                                                 static                                     void                                     Main()                       
                                                 {                       
                                                 int                                     []a = { 2, 5, 6, 4, 8 };                       
                                                 int                                     n = a.Length;                       
                                                 findVar(a, n);                       
                                                 }                       
                         }                       
           
                         // This code is contributed by                       
                         // Manish Shaw(manishshaw1)                       

PHP

                         <?php                       
                         // PHP program to                       
                         // find n-variables                       
           
                         // function to print                       
                         // n-variable values                       
                         function                                     findVar(                                     $a                                     ,                                     $n                                     )                       
                         {                       
                                   
                                                 // calculate value of                       
                                                 // array SUM                       
                                                 $SUM                                     = 0;                       
                                                 for                                     (                                     $i                                     = 0;                                     $i                                     <                                     $n                                     ;                                     $i                                     ++)                       
                                                 $SUM                                     +=                                     $a                                     [                                     $i                                     ];                       
           
                                                 // Every variable contributes n-1                       
                                                 // times to sum. So dividing by                       
                                                 // n-1 to get sum of all.                       
                                                 $SUM                                     /= (                                     $n                                     - 1);                       
           
                                                 // print the values                       
                                                 // of n-variables                       
                                                 for                                     (                                     $i                                     = 0;                                     $i                                     <                                     $n                                     ;                                     $i                                     ++)                       
                                                 echo                                     "X"                                     , (                                     $i                                     + 1)                       
                                                 ,                                     " = "                                     ,                                     $SUM                                     -                                     $a                                     [                                     $i                                     ];                       
                         }                       
           
                                                 // Driver Code                       
                                                 $a                                     =                                     array                                     (2, 5, 6, 4, 8);                       
                                                 $n                                     =                                     count                                     (                                     $a                                     );                       
                                                 findVar(                                     $a                                     ,                                     $n                                     );                       
                                   
                         // This code is contributed by anuj_67.                       
                         ?>                       

Javascript

                         <script>                       
           
                         // function to print                       
                         // n-variable values                       
                         function                                     findVar(a,n)                       
                         {                       
           
                                                 // calculate value+                       
                                                 // of array SUM                       
                                                 let SUM = 0;                       
                                                 for                                     (let i = 0; i < n; i++)                       
                                                 SUM += a[i];                       
           
                                                 // Every variable contributes                       
                                                 // n-1 times to sum. So dividing                       
                                                 // by n-1 to get sum of all.                       
                                                 SUM /= (n - 1);                       
           
                                                 // print the values                       
                                                 // of n-variables                       
                                                 for                                     (let i = 0; i < n; i++)                       
                                                 document.write(                                     "X"                                     + (i + 1) +                                     " = "                                     + (SUM - a[i]) +                                     "<br>"                                     );                       
                         }                       
                                   
           
                         let a = [2, 5, 6, 4, 8 ];                       
                         let n = a.length;                       
                         findVar(a, n);                       
           
                         // This code is contributed by mohit kumar 29.                       
           
                         </script>                       

输出：

X1 = 4.25X2 = 1.25X3 = 0.25X4 = 2.25X5 = -1.75

时间复杂性： O（n） 辅助空间： O（1）

文章版权归作者所有，未经允许请勿转载。

THE END

技术文章