Equilateral numbers

#include <bits/stdc++.h>

// g++ -std=c++17 e.cpp -o e
using namespace std;
unordered_map<int64_t, int> d;
int hae(int64_t n, int level){
    if (n==1) return 1;
    if (n==2) return 2;
    if (n==3) return 1;
    if (n==4) return 2;
    if (n==5) return 3;
    if (n==7) return 2;
    if (n==8) return 3;
    if (n==9) return 2;

    int64_t b = (-1+sqrt(1+8*n))/2-5;
    //cout << n <<  " " << b <<endl;
    //return 0;
    while((b*(b+1))/2 < n){
        b += 1;
    }
    while((b*(b+1))/2 > n){
        b -= 1;
    }
    if ((b*(b+1))/2 == n){
        return 1;
    }
    if (d.find(n) != d.end()) return d[n];
    
    if (level >= 2) return 100000;
    while((b*(b+1))/2 > n) {
        b--;
    }
    int mi = 100000;
    while(b > 0){
        int h = hae(n-(b*(b+1))/2, level+1);
        mi = min(mi, h);
        --b;
    }
    d[n] = mi+1;
    return mi+1;
}

int main() {
    int64_t n; cin >> n;
    
    //for (int64_t i = 1; i <= 28; ++i){
    //    cout << i << " " << hae(i) << endl;
    //}
    auto ans = hae(n, 0);
    if (ans >= 100000){
        cout << 3 << endl;
        return 0;
    }
    cout << ans << endl;
    return 0;
}

Test 1

Verdict: ACCEPTED

Test 2

Verdict: ACCEPTED

Test 3

Verdict: ACCEPTED

Test 4

Verdict: ACCEPTED

Test 5

Verdict: ACCEPTED

Test 6

Verdict: TIME LIMIT EXCEEDED

Test 7

Verdict: TIME LIMIT EXCEEDED

Test 8

Verdict: TIME LIMIT EXCEEDED

Test 9

Verdict: TIME LIMIT EXCEEDED

Test 10

Verdict: ACCEPTED

Test 11

Verdict: TIME LIMIT EXCEEDED

Test 12

Verdict: TIME LIMIT EXCEEDED