Problem p00820 (C++) — buggy submission, verdict: Memory Limit Exceeded

#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef long double ld;
typedef tuple<int, int> duo;
const int dx[] = {0, 0, 1, -1, 1, 1, -1, -1};
const int dy[] = {1, -1, 0, 0, 1, -1, 1, -1};
const int Mod = 1000000000 + 0;
//{{{ templates
#define TT_ template <typename T> inline
#define TTF_ template <typename T, typename F> inline
TT_ T sq(T x) { return x * x; }
TT_ T In() {
  T x;
  cin >> x;
  return x;
}
TT_ void Out(T &x) { cout << x; }
TT_ void sort(T &v) { sort(begin(v), end(v)); }
TT_ void revs(T &v) { reverse(begin(v), end(v)); }
TT_ void uniq(T &v) {
  sort(v);
  v.erase(unique(begin(v), end(v)), end(v));
}
TT_ int ubnd(T &v, typename T::value_type x) {
  return upper_bound(begin(v), end(v), x) - begin(v);
}
TT_ int lbnd(T &v, typename T::value_type x) {
  return lower_bound(begin(v), end(v), x) - begin(v);
}
TTF_ void inpt(T &v, int n, F f) {
  for (v.reserve(n); n--; v.emplace_back(f()))
    ;
}
TTF_ void show(T &v, F f, string d = " ", string e = "\\n") {
  int i = 0;
  for (auto &x : v)
    i++ && (cout << d), f(x);
  cout << e;
}
TT_ typename T::iterator minel(T &v) { return min_element(begin(v), end(v)); }
TT_ typename T::iterator maxel(T &v) { return max_element(begin(v), end(v)); }

inline void fast_io() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
}
inline int in() {
  int x;
  scanf("%d", &x);
  return x;
}
inline ll pow_mod(ll a, ll k, ll m) {
  ll r = 1;
  for (; k > 0; a = a * a % m, k >>= 1)
    if (k & 1)
      r = r * a % m;
  return r;
}
inline ll mod_inv(ll a, ll p) { return pow_mod(a, p - 2, p); }
//}}} priority_queue queue deque front stringstream max_element min_element
//insert count make_tuple

const int MAX_N = 1 << 16;
int dp[5][MAX_N];

int main() {
  dp[0][0] = 1;
  for (int i = 0; i * i < MAX_N; i++) {
    int x = i * i;
    for (int j = 1; j <= 4; j++) {
      for (int k = 0; k < MAX_N - x; k++) {
        if (!dp[j - 1][k])
          continue;
        dp[j][k + x] += dp[j - 1][k];
      }
    }
  }
  while (int n = in()) {
    printf("%d\\n", dp[4][n]);
  }
  return 0;
}

Error: MLE

Fixed submission:

#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef long double ld;
typedef tuple<int, int> duo;
typedef tuple<int, int, int> tri;
const int dx[] = {0, 0, 1, -1, 1, 1, -1, -1};
const int dy[] = {1, -1, 0, 0, 1, -1, 1, -1};
const int Mod = 1000000000 + 0;
//{{{ templates
#define TT_ template <typename T> inline
#define TTF_ template <typename T, typename F> inline
TT_ T sq(T x) { return x * x; }
TT_ T In() {
  T x;
  cin >> x;
  return x;
}
TT_ void Out(T &x) { cout << x; }
TT_ void sort(T &v) { sort(begin(v), end(v)); }
TT_ void revs(T &v) { reverse(begin(v), end(v)); }
TT_ void uniq(T &v) {
  sort(v);
  v.erase(unique(begin(v), end(v)), end(v));
}
TT_ int ubnd(T &v, typename T::value_type x) {
  return upper_bound(begin(v), end(v), x) - begin(v);
}
TT_ int lbnd(T &v, typename T::value_type x) {
  return lower_bound(begin(v), end(v), x) - begin(v);
}
TTF_ void inpt(T &v, int n, F f) {
  for (v.reserve(n); n--; v.emplace_back(f()))
    ;
}
TTF_ void show(T &v, F f, string d = " ", string e = "\\n") {
  int i = 0;
  for (auto &x : v)
    i++ && (cout << d), f(x);
  cout << e;
}
TT_ typename T::iterator minel(T &v) { return min_element(begin(v), end(v)); }
TT_ typename T::iterator maxel(T &v) { return max_element(begin(v), end(v)); }

inline void fast_io() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
}
inline int in() {
  int x;
  scanf("%d", &x);
  return x;
}
inline ll pow_mod(ll a, ll k, ll m) {
  ll r = 1;
  for (; k > 0; a = a * a % m, k >>= 1)
    if (k & 1)
      r = r * a % m;
  return r;
}
inline ll mod_inv(ll a, ll p) { return pow_mod(a, p - 2, p); }
//}}} priority_queue queue deque front stringstream max_element min_element
//insert count make_tuple

map<tri, int> memo;
int dfs(int x, int c = 4, int a = 1) {
  if (x == 0)
    return 1;
  if (c == 0)
    return 0;
  auto t = tri(x, c, a);
  if (memo.count(t))
    return memo[t];
  int tot = 0;
  for (int i = a; i * i <= x; i++) {
    tot += dfs(x - i * i, c - 1, i);
  }
  return memo[t] = tot;
}

int main() {
  while (int n = in()) {
    printf("%d\\n", dfs(n));
  }
  return 0;
}