Project Euler

1 Longest Collatz sequence

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <algorithm>
#include <queue>
#include <vector>
#include <stack>
#include <map>
#include <set>
#include <cmath>
#include <cctype>
#include <ctime>

using namespace std;

#define REP(i, n) for (int i = 0; i < (n); ++i)
#define eps 1e-9

typedef long long ll;
typedef pair<int, int> pii;

const int INF = 0x7fffffff;
const int maxn = 1e7 + 10;
ll ans = 0;
map<ll, ll> ans_t, pre;

ll cal(ll x) {
    ll ret = 1, x_t = x, t = x; pre[x] = x;
    while (x != 1) {
        if (ans_t.count(x)) { ans_t[x_t] = ret + ans_t[x] - 1; break; }
        if (x % 2 == 0) { x /= 2; } else { x = x * 3 + 1; }
        pre[x] = t; t = x;
        ++ret;
    }
    if (x == 1) { ans_t[x_t] = ret; }
    for (ll i = pre[x], j = 1; i != x_t; i = pre[i], ++j) {
        ans_t[i] = ans_t[x] + j;
    }
    return ans_t[x_t];
}

int main() {
#ifdef __AiR_H
//    freopen("in.txt", "r", stdin);
//    freopen("out.txt", "w", stdout);
#endif // __AiR_H
    ll t; ll my_ans;
    for (int i = 1; i < 1000000; ++i) {
        t = cal(i);
        if (t > ans) { ans = t; my_ans = i; }
    }
    printf("%I64d
", my_ans);
#ifdef __AiR_H
    printf("Time used = %.2fs
", (double)clock() / CLOCKS_PER_SEC);
#endif // __AiR_H
    return 0;
}

2 P243 Resilience

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <algorithm>
#include <queue>
#include <vector>
#include <stack>
#include <map>
#include <set>
#include <cmath>
#include <cctype>
#include <ctime>

using namespace std;

#define REP(i, n) for (int i = 0; i < (n); ++i)
#define eps 1e-9

typedef long long ll;
typedef pair<int, int> pii;
const int maxn = 1e7;
const ll INF = 1e18;
int prime_cnt = 0;
int prime[maxn];
bool vis[maxn];
ll ans = INF;

void init() {
    for (int i = 2; i < maxn; ++i) {
        if (!vis[i]) {
            prime[prime_cnt++] = i;
            for (int j = i; j < maxn; j += i) { vis[j] = true; }
        }
    }
}
bool check(ll a, ll b) { return a * 94744 < b * 15499; }
ll euler(int x) {
    ll ret = x;
    for (int i = 0; prime[i] * prime[i] <= x; ++i) {
        if (x % prime[i] == 0) {
            ret = ret / prime[i] * (prime[i] - 1); x /= prime[i];
            while (x % prime[i] == 0) { x /= prime[i]; }
        }
    }
    if (x != 1) { ret = ret / x * (x - 1); }
    return ret;
}

// 6469693230
int main() {
#ifdef __AiR_H
    freopen("in.txt", "r", stdin);
    freopen("out.txt", "w", stdout);
#endif // __AiR_H
    init(); ll t = 1;
    for (int i = 2; i < prime[9]; ++i) {
        t = 1ll * 223092870 * i;
        if (check(euler(t), t - 1)) { ans = t; break; }
    }
    printf("%I64d
", ans);
#ifdef __AiR_H
    printf("Time used = %.2fs
", (double)clock() / CLOCKS_PER_SEC);
#endif // __AiR_H
    return 0;
}

3 P32 Pandigital products

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <algorithm>
#include <queue>
#include <vector>
#include <stack>
#include <map>
#include <set>
#include <cmath>
#include <cctype>
#include <ctime>

using namespace std;

#define REP(i, n) for (int i = 0; i < (n); ++i)
#define eps 1e-9

typedef long long ll;
typedef pair<int, int> pii;
const int maxn = 210;
int key[] = {1, 2, 3, 4, 5, 6, 7, 8, 9};
ll ans = 0;
set<ll> s;

void print() {
    for (int i = 0; i < 9; ++i) { printf("%d ", key[i]); } printf("
");
}
int cal_tt(int l, int r) {
    int ret = 0;
    for (int i = l; i < r; ++i) { ret = ret * 10 + key[i]; }
    return ret;
}
void cal_t(int x, int y) {
    ll t1 = cal_tt(0, x), t2 = cal_tt(x, y), t3 = cal_tt(y, 9);
    if (t1 * t2 == t3) {
        if (s.find(t3) != s.end()) { return; }
        printf("%I64d %I64d %I64d
", t1, t2, t3); s.insert(t3);
        ans += t3;
    }
}
void cal() {
    for (int i = 1; i <= 7; ++i) {
        for (int j = i + 1; j <= 8; ++j) {
            cal_t(i, j);
        }
    }
}

int main() {
#ifdef __AiR_H
    freopen("in.txt", "r", stdin);
    freopen("out.txt", "w", stdout);
#endif // __AiR_H
    do {
        cal();
//        print();
    } while (next_permutation(key, key + 9));
    printf("%I64d
", ans);
#ifdef __AiR_H
    printf("Time used = %.2fs
", (double)clock() / CLOCKS_PER_SEC);
#endif // __AiR_H
    return 0;
}