牛客-小w的a=b问题

题目传送门

sol1：老实做，预处理出所有2到1e5的素数，对所有数进行分解质因数，然后对比因子个数。感觉有点卡常，用了快读然后多次优化之后才过的，map也用上了。

• 素数筛，快速分解质因数

  #include "bits/stdc++.h"
  using namespace std;
  typedef long long LL;
  const int MAXN = 1e5 + 10;
  bool v[MAXN];
  map<int, int> mp;
  int p[MAXN], pos;
  int a[MAXN], b[MAXN];
  LL ca[MAXN], cb[MAXN];
  void init() {
      for (int i = 2; i <= 1e5; i++) {
          if (v[i] == false) {
              p[++pos] = i;
              mp[i] = pos;
              for (int j = i << 1; j <= 1e5; j += i)
                  v[j] = true;
          }
      }
  }
  inline int read() {
      int n = 0;
      char c = getchar();
      while (c < '0' || c > '9') c = getchar();
      while (c >= '0' && c <= '9') {
          n = n * 10 + (c ^ '0');
          c = getchar();
      }
      return n;
  }
  void fun(int k, int c, LL* a) {
      for (int i = 1; v[k]; i++) {
          while (k % p[i] == 0) {
              k /= p[i];
              a[i] += c;
          }
      }
      if (k != 1) a[mp[k]] += c;
  }
  int main() {
      init();
      int t, n, m, k;
      t = read();
      while (t--) {
          n = read(), m = read();
          memset(ca, 0, sizeof(LL) * (pos + 1));
          memset(cb, 0, sizeof(LL) * (pos + 1));
          for (int i = 1; i <= n; i++) a[i] = read();
          for (int i = 1; i <= m; i++) b[i] = read();
          sort(a + 1, a + 1 + n);
          sort(b + 1, b + 1 + m);
          k = 1;
          for (int i = 1; i <= a[n]; i++) {
              while (i > a[k]) k++;
              fun(i, n - k + 1, ca);
          }
          k = 1;
          for (int i = 1; i <= b[m]; i++) {
              while (i > b[k]) k++;
              fun(i, m - k + 1, cb);
          }
          bool ok = true;
          for (int i = 1; i <= pos; i++) {
              if (ca[i] != cb[i]) {
                  ok = false;
                  break;
              }
          }
          if (ok) puts("equal");
          else puts("unequal");
      }
      return 0;
  }

sol2：题解上说用哈希。虽然一开始也有想到哈希，但是怕哈希冲突，没怎么在比赛中用过哈希，没有哈希的意识。知道用哈希之后代码就信手拈来了，不过还是产生了一次哈希冲突，不要用1e9 + 7这种特殊素数，决定还是使用2147483587（int范围第二大的素数，怕最大的会被卡）。

• 哈希

  #include "bits/stdc++.h"
  using namespace std;
  const int MAXN = 1e5 + 10;
  const int MOD = 2147483587;
  int a[MAXN], b[MAXN];
  int quick_pow(int n, int k) {
      int ans = 1;
      while (k) {
          if (k & 1) ans = 1LL * ans * n % MOD;
          n = 1LL * n * n % MOD;
          k >>= 1;
      }
      return ans;
  }
  int main() {
      int t, n, m, k;
      scanf("%d", &t);
      while (t--) {
          scanf("%d%d", &n, &m);
          for (int i = 1; i <= n; i++)
              scanf("%d", &a[i]);
          for (int i = 1; i <= m; i++)
              scanf("%d", &b[i]);
          sort(a + 1, a + 1 + n);
          sort(b + 1, b + 1 + m);
          int ha = 1, hb = 1;
          k = 1;
          for (int i = 1; i <= a[n]; i++) {
              while (i > a[k]) k++;
              ha = 1LL * ha * quick_pow(i, n - k + 1) % MOD;
          }
          k = 1;
          for (int i = 1; i <= b[m]; i++) {
              while (i > b[k]) k++;
              hb = 1LL * hb * quick_pow(i, m - k + 1) % MOD;
          }
          if (ha == hb) puts("equal");
          else puts("unequal");
      }
      return 0;
  }