给定一个多项式函数f（x）=1+a1*x+a2*（x^2）+…an（x^n）。找到 Sgn 这些函数的值，当x给定时，所有的系数也是。
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If value of polynomial greater than 0 Sign = 1Else If value of polynomial less than 0 Sign = -1Else if value of polynomial is 0 Sign = 0
例如：
Input: poly[] = [1, 2, 3] x = 1 Output: 1 Explanation: f(1) = 6 which is > 0 hence 1.Input: poly[] = [1, -1, 2, 3] x = -2 Output: -1 Explanation: f(-2)=-11 which is less then 0, hence -1.
A. 缺乏经验的 方法是计算x的每一次幂，然后将其与系数相乘，将其加到答案中。计算x的幂需要O（n）个时间，计算n个系数需要O（n）个时间。因此，将总复杂度设为O（n*n） 一 有效率的 方法是使用 霍纳法 我们用霍纳的方法计算多项式的值。然后我们根据值的符号返回值。 下面是上述方法的实现
C++
// CPP program to find sign value of a // polynomial #include <iostream> using namespace std; // returns value of poly[0]x(n-1) + poly[1]x(n-2) // + .. + poly[n-1] int horner( int poly[], int n, int x) { int result = poly[0]; // Initialize result // Evaluate value of polynomial // using Horner's method for ( int i=1; i<n; i++) result = result*x + poly[i]; return result; } // Returns sign value of polynomial int findSign( int poly[], int n, int x) { int result = horner(poly, n, x); if (result > 0) return 1; else if (result < 0) return -1; return 0; } // Driver program to test above function. int main() { // Let us evaluate value of 2x3 - 6x2 // + 2x - 1 for x = 3 int poly[] = {2, -6, 2, -1}; int x = 3; int n = sizeof (poly)/ sizeof (poly[0]); cout << "Sign of polynomial is " << findSign(poly, n, x); return 0; } |
JAVA
// Java program to find sign value of a // polynomial class GFG { // returns value of poly[0]x(n-1) + poly[1]x(n-2) // + .. + poly[n-1] static int horner( int poly[], int n, int x) { // Initialize result int result = poly[ 0 ]; // Evaluate value of polynomial // using Horner's method for ( int i = 1 ; i < n; i++) result = result * x + poly[i]; return result; } // Returns sign value of polynomial static int findSign( int poly[], int n, int x) { int result = horner(poly, n, x); if (result > 0 ) return 1 ; else if (result < 0 ) return - 1 ; return 0 ; } // Driver code public static void main (String[] args) { // Let us evaluate value of 2x3 - 6x2 // + 2x - 1 for x = 3 int poly[] = { 2 , - 6 , 2 , - 1 }; int x = 3 ; int n = poly.length; System.out.print( "Sign of polynomial is " + findSign(poly, n, x)); } } // This code is contributed by Anant Agarwal. |
Python3
# Python3 program to find # sign value of a # polynomial # returns value of poly[0]x(n-1) + # poly[1]x(n-2) + .. + poly[n-1] def horner( poly, n, x): # Initialize result result = poly[ 0 ]; # Evaluate value of # polynomial using # Horner's method for i in range ( 1 ,n): result = (result * x + poly[i]); return result; # Returns sign value # of polynomial def findSign(poly, n, x): result = horner(poly, n, x); if (result > 0 ): return 1 ; elif (result < 0 ): return - 1 ; return 0 ; # Driver Code # Let us evaluate value # of 2x3 - 6x2 # + 2x - 1 for x = 3 poly = [ 2 , - 6 , 2 , - 1 ]; x = 3 ; n = len (poly); print ( "Sign of polynomial is " , findSign(poly, n, x)); # This code is contributed by mits |
C#
// C# program to find sign value of a // polynomial using System; class GFG { // returns value of poly[0]x(n-1) // + poly[1]x(n-2) + .. + poly[n-1] static int horner( int []poly, int n, int x) { // Initialize result int result = poly[0]; // Evaluate value of polynomial // using Horner's method for ( int i = 1; i < n; i++) result = result * x + poly[i]; return result; } // Returns sign value of polynomial static int findSign( int []poly, int n, int x) { int result = horner(poly, n, x); if (result > 0) return 1; else if (result < 0) return -1; return 0; } // Driver code public static void Main () { // Let us evaluate value of 2x3 - 6x2 // + 2x - 1 for x = 3 int []poly = {2, -6, 2, -1}; int x = 3; int n = poly.Length; Console.Write( "Sign of polynomial is " + findSign(poly, n, x)); } } // This code is contributed by vt_m. |
PHP
<?php // PHP program to find // sign value of a // polynomial // returns value of poly[0]x(n-1) + // poly[1]x(n-2) + .. + poly[n-1] function horner( $poly , $n , $x ) { // Initialize result $result = $poly [0]; // Evaluate value of polynomial // using Horner's method for ( $i = 1; $i < $n ; $i ++) $result = $result * $x + $poly [ $i ]; return $result ; } // Returns sign value // of polynomial function findSign( $poly , $n , $x ) { $result = horner( $poly , $n , $x ); if ( $result > 0) return 1; else if ( $result < 0) return -1; return 0; } // Driver Code // Let us evaluate value // of 2x3 - 6x2 // + 2x - 1 for x = 3 $poly = array (2, -6, 2, -1); $x = 3; $n = count ( $poly ); echo "Sign of polynomial is " , findSign( $poly , $n , $x ); // This code is contributed by anuj_67. ?> |
Javascript
<script> // Javascript program to find sign value of a // polynomial // Returns value of poly[0]x(n-1) + poly[1]x(n-2) // + .. + poly[n-1] function horner(poly, n, x) { // Initialize result var result = poly[0]; // Evaluate value of polynomial // using Horner's method for ( var i = 1; i < n; i++) result = result * x + poly[i]; return result; } // Returns sign value of polynomial function findSign(poly, n, x) { var result = horner(poly, n, x); if (result > 0) return 1; else if (result < 0) return -1; return 0; } // Driver Code // Let us evaluate value of 2x3 - 6x2 // + 2x - 1 for x = 3 var poly = [ 2, -6, 2, -1 ]; var x = 3; var n = poly.length; document.write( "Sign of polynomial is " + findSign(poly, n, x)); // This code is contributed by kirti </script> |
输出：
Sign of polynomial is 1
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