問題描述

分別實現多項式求值的四種運算，若針對不同規模的輸入值$a$，各演算法的執行時間，問題規模$n$分別取10，50，100，150，200，300，400，500，10000，20000，50000，100000時繪製四種演算法執行時間的比較圖。

解題方法

需要用四種不同的方法實現對多項式的求值，這裡採用的是直接代入以及三種不同的遞迴演算法。三種不同的遞迴思想分別為：
$1){P_n}(x) = {P_{n - 1}}(x) + {a_n}{x^n}$
2)P=a0,Q=1,Q=Qx,P=P+a

具體程式碼

import numpy as np
import time
import math
import random
# root = np.array([1, 2, 1])
# p = np.poly1d(root)
# r = np.roots(p)
# print(r)
n = [10,50,100,150,200,300,400,500]
x = 1.2 #將多項式中x的值設為1.2
 

Sum_time1 = []
Sum_time2 = []
Sum_time3 = []
Sum_time4 = []
for ele in n:
    a =  np.random.random(ele)
    p = np.poly1d(a)
    time_start = time.time()
    temp = np.polyval(p, x)
    time_end = time.time()
    Sum_time1.append(time_end - time_start)

    temp = float('Inf')
    time_start = time
 
.time()
    for i in range(0, ele, 1):
        temp = temp + a[i] * x**i
    time_end = time.time()
    Sum_time2.append(time_end - time_start)

   # temp = int()
    time_start = time.time()
    q = 1
    for i in range(0, ele, 1):
        q = q * x
        temp = temp + a[i] * q
    time_end = time.time()
    Sum_time3.append(time_end - time_start)

    #temp = int()
    time_start = time.time()
    for i in range(0, ele, 1):
        temp = temp * x + a[ele - i - 1]
    time_end = time.time()
    Sum_time4.append(time_end - time_start)
print(Sum_time1)
print(Sum_time2)
print(Sum_time3)
print(Sum_time4)