66-64: 模拟赛

等比数列求和

#include <iostream>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <string>
#include <algorithm>

using namespace std;

#define gc getchar()
inline int read() {
    int x = 0; char c = gc;
    while(c < '0' || c > '9') c = gc;
    while(c >= '0' && c <= '9') x = x * 10 + c - '0', c = gc;
    return x;
}

#define LL long long

const int Mod = 1e9 + 7;

LL Ksm(LL a, LL b) {
    LL ret = 1;
    while(b) {
        if(b & 1) ret = ret * a % Mod;
        a = a * a % Mod;
        b >>= 1;
    }
    return ret;
}

LL Calc(LL n, LL m) {
    LL Answer = 0;
    for(int i = 1; i <= n; i ++) {
        for(int j = 1; j <= m; j ++) {
            (Answer += Ksm(i, j)) %= Mod;
        }
    }
    return Answer % Mod;
}

int main() {
    freopen("sum.in", "r", stdin);
    freopen("sum.out", "w", stdout);
    LL n, m;
    cin >> n >> m;
    LL Answer = 0;
    for(int i = 1; i <= n; i ++) {
        LL up = i * (Ksm(i, m) - 1) % Mod;
        LL dow = i - 1;
        while(up < 0) up += Mod;
        while(dow < 0) dow += Mod;
        dow = Ksm(dow, Mod - 2);
        (Answer += (up * dow % Mod)) %= Mod;
    }
    (Answer += m) %= Mod;
    while(Answer < 0) Answer += Mod;
    cout << Answer;
    
    return 0;
}

边权和的两倍 - 距离1最远的距离

#include <iostream>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <string>
#include <algorithm>

using namespace std;

const int N = 5e4 + 10;

#define Rep(i, a, b) for(int i = a; i <= b; i ++)
#define gc getchar()
inline int read() {
    int x = 0; char c = gc;
    while(c < '0' || c > '9') c = gc;
    while(c >= '0' && c <= '9') x = x * 10 + c - '0', c = gc;
    return x;
}

#define LL long long

struct Node {
    int u, v, w, nxt;
} G[N << 1];
int cnt, head[N];
int n;

LL Answer;

void Link(int u, int v, int w) {
    G[++ cnt].v = v, G[cnt].w = w, G[cnt].nxt = head[u], head[u] = cnt;
}

LL dis[N];

void Dfs(int u, int f) {
    for(int i = head[u]; ~ i; i = G[i].nxt) {
        int v = G[i].v;
        if(v == f) continue;
        dis[v] = dis[u] + G[i].w;
        Dfs(v, u);
    }
}

int main() {
    freopen("tour.in", "r", stdin);
    freopen("tour.out", "w", stdout);
    
    n = read();
    Rep(i, 1, n) head[i] = -1;
    Rep(i, 1, n - 1) {
        int u = read(), v = read(), w = read();
        Link(u, v, w), Link(v, u, w);
        Answer += w + w;
    }
//    cout << Answer << "\n";
    Dfs(1, 0);
    LL cut = -1;
    Rep(i, 1, n) cut = max(cut, dis[i]);
    cout << Answer - cut;
    
    return 0;
}

dp + 数论

#include <cstdlib>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <iostream>
#include <vector>
#include <map>

using std::min;
using std::max;

typedef long long i64;
const i64 modulo = i64(1e9) + 7;
const int MaxN = 100005;
const int MaxM = 1024;

i64 power(i64 base, i64 k) {
    i64 res = 1;
    for ( ; k; k >>= 1) {
        if (k & 1) res = (res * base) % modulo;
        base = (base * base) % modulo;
    }
    return res;
}

i64 inv(i64 k) {
    return power(k, modulo - 2);
}

std::vector<i64> gen_lucky(i64 upper) {
    std::vector<i64> res; res.clear();
    std::vector<i64> a; a.clear(); a.push_back(0);
    for (int i = 0; i < 10; ++i) {
        std::vector<i64> b; b.clear();
        for (size_t j = 0; j < a.size(); ++j) {
            b.push_back(a[j] * 10 + 4);
            b.push_back(a[j] * 10 + 7);
        }
        if (b[0] < upper) {
            res.insert(res.end(), b.begin(), b.end());
            a = b;
        } else {
            return res;
        }
    }
    return res;
}

std::vector<i64> lucky;
std::map<i64, int> lucky2idx;
int n, m, unlucky, k, a[MaxN], cnt[MaxM];
i64 dp[MaxM][MaxM];
i64 f[MaxN];

i64 bincoef(int a, int b) {
    i64 tmp = f[a];
    tmp = tmp * inv(f[b]) % modulo;
    tmp = tmp * inv(f[a-b]) % modulo;
    return tmp;
}

int main(void) 
{   freopen("lucky.in","r",stdin);
    freopen("lucky.out","w",stdout);
    lucky = gen_lucky(1e9);
    m = lucky.size();
    for (int i = 0; i < m; ++i) {
        lucky2idx[lucky[i]] = i;
    }

    scanf("%d%d", &n, &k);
    unlucky = n;
    for (int i = 0; i < n; ++i) {
        scanf("%d", a+i);
        std::map<i64, int>::iterator it = lucky2idx.find(a[i]);
        if (it != lucky2idx.end()) ++cnt[it->second], --unlucky;
    }

    dp[0][0] = 1;
    for (int i = 0; i < m; ++i) {
        for (int j = 0; j <= i; ++j) {
            dp[i+1][j] = (dp[i+1][j] + dp[i][j]) % modulo;
            dp[i+1][j+1] += (dp[i+1][j+1] + (dp[i][j] * cnt[i] % modulo)) % modulo;
        }
    }

    f[0] = 1;
    for (int i = 1; i <= n; ++i) {
        f[i] = f[i-1] * i % modulo;
    }

    i64 ans = 0;
    int st = max(0, k-m);
    int ed = min(k, unlucky);
    for (int i = st; i <= ed; ++i) {
        ans += dp[m][k-i] * bincoef(unlucky, i) % modulo;
        ans %= modulo;
    }

    printf("%d\n", (int) ans);
    fclose(stdin);
    fclose(stdout);

    return 0;
}