多项式求和算法对比_求和对比-优快云博客

本文链接：https://blog.youkuaiyun.com/adaadadsa/article/details/126915038

本文通过C++实现两种不同的多项式求和算法，并对其执行效率进行比较。第一种算法采用直接逐项累加的方式，而第二种算法则利用提取公因式的方法。通过对这两种算法的时间消耗进行测量，展示不同算法在实际运行中的性能差异。

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#include<stdio.h>
#include<conio.h>
#include<random>
#include<windows.h>
#include<time.h>
#include<math.h>


double getSum1(double x_, int n_, double nums[]);
double getSum2(double x_, int n_, double nums[]);

clock_t time1;
clock_t time2;
clock_t time3;

int main() {

	// 测试多项式的和
	// f(x) = a1 + a2*x +a3*x^2 + ... + an*x^(n-1)
	/*
	srand(unsigned(time(NULL)));
	int randomize(void);
	int a = rand() % 50;
	printf("a: %d\n", a);
	*/

	int n = 10;
	double x = 3.1;
	int run_Cycle = 1000000;
	double nums[10] = {};
	
	for (int i = 0; i < n; i++) {
		nums[i] = (double)(rand() % 10);
		//printf("number %d: %d\n", i, nums[i]);
	}

	time1 = clock();
	double result1;
	for (int i = 0; i < run_Cycle; i++) {
		result1 = getSum1(x, n, nums);
	}
	
	time2 = clock();
	printf("ticks1 %f\n", (double)(time2 - time1));
	printf("function a takes %6.2e s, result = %f\n", (double)(time2-time1)/CLOCKS_PER_SEC/run_Cycle, result1);

	double result2;
	for (int i = 0; i < run_Cycle; i++) {
		result2 = getSum2(x, n, nums);
	}
	time3 = clock();
	printf("ticks2 %f\n", (double)(time3 - time2));
	printf("function b takes %6.2e s, result = %f\n", (double)(time3 - time2)/CLOCKS_PER_SEC/run_Cycle, result2);

	_getch();
	return 0;
}

// 加号前各项相加
double getSum1(double x, int n, double nums[]) {

	double sum = 0;
	for (int i = 0; i < n; i++) {
		sum += (pow(x, i) * nums[i]);
	}
	
	return sum;
}

// 提取公因式算法
double getSum2(double x, int n, double nums[]) {

	double p = nums[n - 1];
	for (int i = n - 2; i >= 0; i--) {
		p = p * x + nums[i];
	}

	return p;
}