python CG练习题
输入方式
a, b, c = map(float, input().split())
alist = list(map(int, input().split()))
n = int(input())
#数组
for i in range(n):
Y[i] = int( input() )
import numpy A=numpy.array(list(map(int, input().split())))
s = str.split()
arr = np.array(s, dtype=int)
#二维数组
arr = [[0] * n] * n
for i in range(n):
arr[i] = input().split(" ")
arr[i] = [int(j) for j in arr[i]]
# 创建一个 5x3 的数组
x1 = np.arange(15).reshape((5, 3))
x1[2][2]= 999
print(x1)
#
递归-全排列
import numpy def Output(alist): res = numpy.array(alist) print(res) def PERM(alist,sta,end): if sta==end: Output(alist) else: for i in range(sta,end): alist[sta],alist[i] = alist[i] ,alist[sta] PERM(alist,sta+1,end) alist[sta], alist[i] = alist[i],alist[sta] alist = list(map(int, input().split())) PERM(alist,0,len(alist))
迭代法求函数的根
import numpy as np def cal(k): return k**5 - k*2 - 1 def Find( n ): Y = np.linspace(alist[0], alist[1], 9) # print(Y) for i in range(1,9): if cal( Y[i-1] )*cal(Y[i]) <0: # print(Y[i],Y[i-1],""choose",(Y[i]+Y[i-1])/2) Y0.append((Y[i]+Y[i-1])/2 ) if i<=7 and ( ( cal( Y[i+1] ) - cal( Y[i] ) )* ( cal( Y[i] ) - cal(Y[i-1]) ) ) < 0 and abs( cal(Y[i]) ) < 0.1: # print("find", Y[i]) Y0.append(Y[i]) def g1(x): while abs( (pow( (x*2+1) ,0.2) if(x*2+1>=0) else -pow( -(x*2+1) ,0.2) ) - x ) > delta : x = pow( (x*2+1) ,0.2) if(x*2+1>=0) else -pow( -(x*2+1) ,0.2) x = pow( (x*2+1) ,0.2) if(x*2+1>=0) else -pow( -(x*2+1) ,0.2) return x def g2(x): while abs( (pow(x,5)-1)/2-x ) > delta : x = (pow(x,5)-1)/2 x = (pow(x,5)-1)/2 return x def run(x): if x <-0.7 or x >0: res = g1(x) else : res = g2(x) # print("答案是",res) return res if __name__ == "__main__": # print("HI") alist = list(map(float,input().split())) delta = 10**(-int(alist[2])) Y0 = list() Find(8) Y0.sort() # print(Y0) for i in range(3): # print("Y0 is ",Y0[i]) print( "%.3f" %run( Y0[i] ) )
试值法求根
def cal(x): return 12 * 300 * ((1 + x / 12) ** 240 - 1) / x - 500000 def MID(x, y): return y - cal(y) * (y - x) / (cal(y) - cal(x)) a, b, c = map(float, input().split()) c = int(c) cnt = 0 res = a while b - a > pow(10, -c) / 2: mid = MID(a, b) if abs(cal(mid)) < 0.0001: break if (cal(mid) <= 0): a = mid else: b = mid cnt = cnt + 1 print(cnt) print(round(MID(a, b), c))
牛顿法求根
ee = 2.718281828459045235360287471 def f(x): return 9600*( 1 - ee**( -x/15 ) ) - 480 * x # y=f(t)=9600*(1-e**(-t/15.0)) - 480*t；x=r(t)=2400*(1-e**(-t/15.0)) def f_(x): return 9600/15* ( ee**(-x/15) ) - 480 def r(x): return 2400*( 1 - ee**( -x/15 ) ) def Cal(a): return a - f(a)/f_(a) if __name__ =="__main__": a,b,c = map( float,input().split( ) ) # print(a,b,c) b = 10**(-int(b)) c = 10**(-int(c)) # cnt = 0 while( abs( a-Cal(a) ) > b or abs( f( Cal(a) ) ) > c ): a = Cal(a) # cnt = cnt + 1 # print(cnt,a,abs( a-Cal(a) ) ,abs( f( Cal(a) ) ) ,b,c) print("%.5f"% a) print("%.5f" % r(a)) ''' 输出错误 错误输出： 8 1 1 期望输出： 9.08955 1090.69211 测试数据2 输出错误 错误输出： 8 3 3 期望输出： 9.08790 1090.54798 '''
快速排序
import numpy import math def find( Thelist,s,e ): if( s == e ): return s Mid = Thelist[e] MinId = s for i in range(s,e): if( Thelist[i]<=Mid ): Thelist[i],Thelist[MinId] = Thelist[MinId],Thelist[i] MinId = MinId+1 Thelist[e], Thelist[MinId] = Thelist[MinId], Thelist[e] print(Mid,MinId) return MinId def QuickSort( TheList,s,e ): if( s<e ): pos = find(TheList,s,e) QuickSort(TheList,s,pos-1) QuickSort(TheList,pos+1,e) alist = list(map(int,input().split())) LEN = len(alist) QuickSort(alist,0,LEN-1) print( numpy.array( alist )) ''' 【样例输入】 2 8 7 1 3 5 6 4 【样例输出】 4 3 3 2 1 0 8 7 6 5 [1 2 3 4 5 6 7 8] '''
二分找点
def find(l,r): mid = int( (l+r)/2 ) if( l>r ) :return int(-1) if( A[mid]== n): return mid else: if( A[mid]<n ): return find( mid+1,r ) return find(l,mid-1) A = list(map(int, input().split())) n = int(input()) print( find(0,len(A)-1)+1 )
归并排序
import numpy import math def Merge(Llist,Rlist): res = [] Lpos,Rpos,pos = 0,0,0 while Lpos<len(Llist) and Rpos<len(Rlist) : if( Llist[Lpos] < Rlist[Rpos] ): res.append(Llist[Lpos]) Lpos= Lpos + 1 else: res.append(Rlist[Rpos]) Rpos = Rpos + 1 pos = pos + 1 res += list( Llist[Lpos:] ) res += list( Rlist[Rpos:] ) return res def MergeSort( L ): print(numpy.array(L)) if( len(L)<=1 ) : return L mid = math.ceil( len(L)/2 ) return Merge( MergeSort( L[:mid] ), MergeSort( L[mid:] ) ) alist = list(map(int,input().split())) print( numpy.array(MergeSort(alist)))
二分
def cal(x): return 12 * 300 * ((1 + x / 12) ** 240 - 1)/ x - 500000 def MID(x,y): return x/2+y/2 # return y - cal(y)*(y-x)/( cal(y)-cal(x) ) a,b,c = map(float,input().split()) c = int(c) cnt = 0 while b-a > pow(10, -c): mid = MID(a,b) cnt = cnt + 1 if( cal(mid)>=0 ) : b = mid else: a = mid print(cnt) print( round(MID(a,b),c) )
上三角线性方程
import numpy as np if __name__ == "__main__": n = int(input()) arr = [[0] * n] * n for i in range(n): arr[i] = input().split(" ") arr[i] = [int(j) for j in arr[i]] Y = [0]*n res = [0.0]*n for i in range(n): Y[i] = int( input() ) i = int(n-1) res[i] = Y[i]/arr[n-1][n-1] i = i - 1 while i>=0: sum = int(0) for j in range(i+1,n): sum = sum + arr[i][j]*res[j] res[i] = ( Y[i]-sum )/arr[i][i] i = i-1 ans = np.array(res).reshape(n,1) print(ans)
select算法
import math flag = 1 def PARTITION(alist,l,r,x): pos = l posx = l for i in range(l,r+1): if alist[i] <= x: if( alist[i]==x ): posx = i alist[pos],alist[i] = alist[i],alist[pos] pos = pos + 1 alist[pos-1],alist[posx] = alist[posx],alist[pos-1] return max(pos-1,l) def SELECT( alist,l,r,n ): global flag Len = r - l + 1 if Len <= 10: alist[l:r+1] = sorted( alist[l:r+1] ) return alist[ max(int(l+n-1),l)] #分组递归求中位数的中位数,其实就是找基准的过程 Groups = Len//5 #这么多组 L = l TemList = [] for i in range(Groups-1): TemList.append( SELECT( alist,L,L+4,3 ) ) L = L+5 TemList.append( SELECT(alist, L, r, (r-L+2)//2 ) ) x = SELECT(TemList , 0 , Groups-1 ,(Groups+1)//2 ) #分组后的中位数取第（num_group/2向上取整）小的元素。 if flag == 1 : print(x) flag = 0 #以x为基准寻找小于基准的下标位置q q = PARTITION( alist,l,r,x) nums = q-l+1 if nums == n: return x elif nums>n: return SELECT(alist,l,q-1,n) return int(SELECT(alist,q+1,r,n-nums)) if __name__ == "__main__": alist = list( map(int,input().split()) ) n = int( input() ) # print(alist,n) print( SELECT( alist,int(0),int(len(alist)-1),int(n) ) ) ''' 测试数据1 输出错误 错误输出： 2 9 8 0 7 10 1 12 3 14 5 13 6 11 4 3 期望输出： 7 2 测试数据2 输出错误 错误输出： 32 22 28 11 24 8 9 12 10 19 36 16 39 50 14 30 21 23 3 43 46 35 17 31 18 42 44 34 27 33 15 45 29 5 13 38 26 6 0 1 47 40 41 25 7 20 2 4 37 49 48 20 期望输出： 23 19 '''
