Question

我正在练习解决以下问题。我在python 3中编写代码，已经在这里停留了很长时间。请帮助我优化代码

Akash对新函数F感兴趣，例如，

F(x) = GCD(1, x) + GCD(2, x) + ... + GCD(x, x)

其中GCD是最大公约数。现在，问题很简单。给定大小为N的数组A，有两种查询类型： 1. CXY：计算F（A [X]）+ F（A [X + 1]）+ F（A [X + 2]）+ .... + F（A [Y]）（mod 10 ^ 9 + 7） 2. U X Y：更新数组A [X] = Y

的元素

输入输入的第一行包含整数N，即数组的大小。下一行包含A个元素的N个空格分隔的整数。下一行包含整数Q，即查询数量。接下来的Q行包含两个查询之一。

Output:
For each of the first type of query, output the required sum (mod 10^9 + 7).

Constraints:
1 <= N <= 106
1 <= Q <= 105
1 <= Ai <= 5*105

For Update ,
1 <= X <= N
1 <= Y <= 5*105

For Compute ,
1 <= X <= Y <= N

SAMPLE INPUT 
3
3 4 3
6
C 1 2
C 1 3
C 3 3
U 1 4
C 1 3
C 1 2
SAMPLE OUTPUT 
13
18
5
21
16
Explanation
A[1] = 3, A[2] = 4, A[3] = 3
F(3) = GCD(1, 3) + GCD(2, 3) + GCD(3, 3) = 1 + 1 + 3 = 5.
F(4) = GCD(1, 4) + GCD(2, 4) + GCD(3, 4) + GCD(4, 4) = 1 + 2 + 1 + 4 = 8.

First query, the sum will be F(3) + F(4) = 5 + 8 = 13 (mod 10^9 + 7).
Second query, the sum will be F(3) + F(4) + F(3) = 5 + 8 + 5 = 18 (mod 10^9 + 7).
Third query, the sum will be F(3) = 5 (mod 10^9 + 7).
Fourth query will update A[1] = 4.
Fifth query, the sum will be F(4) + F(4) + F(3) = 8 + 8 + 5 = 21 (mod 10^9 + 7).
Sixth query, the sum will be F(4) + F(4) = 8 + 8 = 16 (mod 10^9 + 7).

import math
def ft(t):
    s=0
    for i in range(1,t+1):
        s+=math.gcd(i , t)
    #print(s)
    return s



n=int(input())
a=list(map(int,input().split()))
q=int(input())

def f(a):
    su =0
    for i in range(1,a+1):
        su+=math.gcd(i,a)
    return su
for _ in range(q):
    t = list(input().split())
    t[1],t[2] = int(t[1]),int(t[2])
    if t[0] == 'U':
        a[t[1]-1] = t[2]
    else:
        #fq(t[1]-1,t[2]-1,a)
        sm = 0

        for i in range(t[1]-1,t[2]):
                #print(i,a,f)

                sm += f(a[i])
        print(sm%(10**9+7))

I am getting time limit exceeded for majority of the test cases.How can i optimize the code.

针对GCD相关竞争性编程问题优化python3代码

0 个答案: