CGCDSSQ (Codeforces 475D)
Tags: Math, data structures

Given a sequence of integers a1, ..., an and q queries x1, ..., xq on it. For each query xi you have to count the number of pairs (l, r) such that 1 ≤ l ≤ r ≤ n and gcd(al, al + 1, ..., ar) = xi. is a greatest common divisor of v1, v2, ..., vn, that is equal to a largest positive integer that divides all vi.

Input: The first line of the input contains integer n, (1 ≤ n ≤ 105), denoting the length of the sequence. The next line contains n space separated integers a1, ..., an, (1 ≤ ai ≤ 109).The third line of the input contains integer q, (1 ≤ q ≤ 3 × 105), denoting the number of queries. Then follows q lines, each contain an integer xi, (1 ≤ xi ≤ 109).

Output: For each query print the result in a separate line.


Sample Inputs:
3
2 6 3
5
1
2
3
4
6

7
10 20 3 15 1000 60 16
10
1
2
3
4
5
6
10
20
60
1000

Sample Outputs:
1
2
2
0
1

14
0
2
2
2
0
2
2
1
1

Solution (Python):
import sys
import math
if __name__ == '__main__':
    n = int(input())
    a = list(map(int, input().split()))
    mp2 = {}
    ans = {}
    for x in a:
        mp = {}
        for (key, value) in mp2.items():
            z = math.gcd(key, x)
            if z in mp:
                mp[z] += value
            else:
                mp[z] = 1
                mp[z] += value - 1
        if x in mp:
            mp[x] += 1
        else:
            mp[x] = 1
        (mp, mp2) = (mp2, mp)
        for (key, value) in mp2.items():
            if key in ans:
                ans[key] += value
            else:
                ans[key] = 1
                ans[key] += value - 1
    q = int(input())
    for i in range(q):
        val = int(input())
        if val in ans:
            print(ans[val])
        else:
            print(0)

Solution (Python):
import sys
import math
if __name__ == '__main__':
    n = int(input())
    a = list(map(int, input().split()))
    mp2 = {}
    ans = {}
    for x in a:
        mp = {}
        for (key, value) in mp2.items():
            z = math.gcd(key, x)
            if z in mp:
                mp[z] += value
            else:
                mp[z] = 1
                mp[z] += value - 1
        if x in mp:
            mp[x] += 1
        else:
            mp[x] = 1
        (mp, mp2) = (mp2, mp)
        for (key, value) in mp2.items():
            if key in ans:
                ans[key] += value
            else:
                ans[key] = 1
                ans[key] += value - 1
    q = int(input())
    for i in range(q):
        val = int(input())
        if val in ans:
            print(ans[val])
        else:
            print(0)

Solution (Python):
def gcd(a, b):
    if b == 0:
        return a
    return gcd(b, a % b)
n = int(input())
mp = [{} for i in range(n + 1)]
tp = [int(i) for i in input().split()]
for i in range(1, n + 1):
    ex = tp[i - 1]
    mp[i][ex] = 1
    for (gcdcurr, len) in mp[i - 1].items():
        v = gcd(gcdcurr, ex)
        mp[i][v] = mp[i].get(v, 0) + len
real = {}
for i in range(1, n + 1):
    for (gcdcurr, len) in mp[i].items():
        real[gcdcurr] = real.get(gcdcurr, 0) + len
q = int(input())
for i in range(q):
    ex = int(input())
    print(real.get(ex, 0))