python二分迭代法代码
时间: 2023-03-31 22:03:05 浏览: 64
以下是 Python 的二分迭代法代码:
def binary_search(arr, target):
left, right = , len(arr) - 1
while left <= right:
mid = (left + right) // 2
if arr[mid] == target:
return mid
elif arr[mid] < target:
left = mid + 1
else:
right = mid - 1
return -1
请问,这个函数的时间复杂度是多少?
相关问题
二分迭代法解方程python
您好!谢谢您对ChitGPT的关注和使用。关于您的问题,二分迭代法是一种求解方程的方法,其原理是通过迭代逼近函数零点的过程来获得方程的解。在Python中,我们可以通过编写函数来实现二分迭代法,具体的实现方式可以参考以下代码:
```python
def binary_search(f, a, b, eps=1e-6):
"""
二分迭代法求解方程f(x)=0在区间[a, b]上的根,精确度为eps
:param f: 函数对象,输入x,返回f(x)
:param a: 区间左端点
:param b: 区间右端点
:param eps: 精确度
:return: 方程f(x)=0的一个近似解
"""
while b - a > eps:
c = (a + b) / 2
if f(c) == 0:
return c
elif f(c) * f(a) < 0:
b = c
else:
a = c
return (a + b) / 2
```
在使用时,我们需要指定函数f、区间[a, b]和精确度eps,例如:
```python
f = lambda x: x ** 2 - 2 # 原方程
a, b = 0, 2 # 区间
x = binary_search(f, a, b) # 求根
print(x) # 输出结果
```
如果您有其他问题,欢迎随时向我提问哦!
怎么把二分迭代法解微分方程的迭代过程打印出来python
您可以使用以下代码将迭代过程打印出来:
```
import numpy as np
def bisection_iter(f, a, b, N):
"""
Solves f(x) = 0 on the interval [a,b] using N iterations of bisection method.
Returns a list of the intermediate bisection values.
"""
p = [] # list to store intermediate bisection values
for n in range(1, N+1):
c = (a + b)/2.0 # midpoint
p.append(c)
if f(c) == 0:
return p
elif f(c)*f(a) < 0:
b = c
else:
a = c
return p
def solve_differential_equation(f, x0, y0, x_range, N):
"""
Solves the differential equation y' = f(x,y) with initial condition y(x0) = y0
on the interval x_range = [x0, x1] using N iterations of bisection method.
Returns a list of tuples (x, y) representing the approximation of the solution.
"""
h = (x_range[1] - x_range[0])/float(N)
x = x0
y = y0
solution = [(x, y)]
for i in range(N):
p = bisection_iter(lambda z: z - y - h*f(x+h,z), y, y+h*f(x,y), 10)
y = p[-1]
x = x + h
solution.append((x, y))
return solution
# example usage
f = lambda x, y: x - y # differential equation y' = x - y
solution = solve_differential_equation(f, 0, 1, [0, 1], 10)
for x, y in solution:
print("x = {:.3f}, y = {:.3f}".format(x, y))
```
这里的函数 `solve_differential_equation` 使用二分迭代法来计算微分方程的解,其中参数 `f` 是微分方程的右侧,即 $y'(x) = f(x,y(x))$。将解的近似值存储在一个列表中返回,而函数 `bisection_iter` 是一个二分迭代法的实现,用于计算微分方程的每个步骤。