abc249_d Index Trio 题解

合集 - 题解(48)

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8.abc249_d Index Trio 题解2023-04-16

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Index Trio

题意

给定长度为 $n$ 的整数序列 $a=(a_1,a_2,\dots ,a_n)$。请你求出有多少个整数三元组 $(i,j,k)$ 满足：

• $1⩽i,j,k⩽N$
• $\frac{a_i}{a_j}=a_k$

数据范围

• $1⩽n,a_i⩽2\times {10}^5$

思路

转变式子：$\because \frac{a_i}{a_j}=a_k\therefore a_i=a_j\times a_k$。

这下就好办了，统计每个数的出现次数，对于每个数去枚举它的因数，统计答案即可，记得开long long。

复杂度

• 时间：$O(n\times \sqrt{V})$
• 空间：$O(V+n)$

Code

点击查看代码

#include <iostream>
#include <algorithm>
 
using namespace std;
using ll = long long;
 
const int N = 2e5 + 10;
 
int n, a[N], f[N];
ll ans;
 
int main () {
  ios::sync_with_stdio(0), cin.tie(0);
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
    f[a[i]]++; // 桶
  }
  for (int i = 1; i <= n; i++) {
    for (int k = 1; k * k <= a[i]; k++) { // 枚举约数
      if (a[i] % k == 0) {
        ans += 1ll * f[k] * f[a[i] / k] * (k * k != a[i] ? 2 : 1); // 统计答案
      }
    }
  }
  cout << ans;
  return 0;
}