西北大学集训队选拔赛（重现赛）

A.坐飞机

代码：

#include <bits/stdc++.h>
using namespace std;
 
const int maxn = 1e5 + 10;
int n, t;
int a[maxn], b[maxn];
int p[maxn];
 
int main() {
  scanf("%d%d", &n, &t);
  for(int i = 1; i <= n; i ++) {
    scanf("%d%d", &a[i], &b[i]);
  }
 
  for(int i = 2; i <= n; i ++) {
    p[i - 1] = a[i] - b[i - 1] + 1;
  }
 
  n --;
 
  sort(p + 1, p + n + 1);
 
  int ans = 0;
  for(int i = 1; i <= n; i ++) {
    if(t >= p[i]) {
        ans ++;
        t -= p[i];
    }
  }
 
  printf("%d\n", ans);
  return 0;
}

B.饱和式救援

代码：

#include <bits/stdc++.h>
using namespace std;
 
const int maxn = 1e5 + 10;
int n, m, k;
 
double x[maxn];
 
double dp[2100][2100];
 
int main() {
  scanf("%d%d%d", &n, &m, &k);
 
  for(int i = 1; i <= m; i ++) x[i] = 1.0;
 
  for(int i = 1; i <= n; i ++) {
    int a; double p;
    scanf("%d%lf", &a, &p);
    x[a] = x[a] * (1.0 - p);
  }
 
  for(int i = 1; i <= m; i ++) x[i] = 1.0 - x[i];
 
  dp[1][1] = x[1];
  dp[1][0] = 1.0 - x[1];
 
  for(int i = 2; i <= m; i ++) {
    dp[i][0] = dp[i - 1][0] * (1.0 - x[i]);
    for(int j = 1; j <= i; j ++) {
      dp[i][j] = dp[i - 1][j] * (1.0 - x[i]) + dp[i - 1][j - 1] * x[i];
    }
  }
 
  double ans = 0.0;
 
  for(int j = k; j <= m; j ++) {
    ans += dp[m][j];
  }
 
  printf("%.3f\n", ans);
 
  return 0;
}

C.晾衣服

代码：

#include <bits/stdc++.h>
using namespace std;
 
const int maxn = 2e5 + 10;
int N;
long long L;
 
struct Node {
    int wet;
    int lena;
    int va;
    int tima;
    int lenb;
    int vb;
    int timb;
}node[maxn];
 
bool check(int x) {
    for(int i = 0; i < N; i ++)
        if(min(node[i].tima, node[i].timb) > x) return false;
    long long sum = 0;
    for(int i = 0; i < N; i ++) {
        if(node[i].tima <= x && node[i].timb <= x) {
            sum += min(node[i].lena, node[i].lenb);
        } else if(node[i].tima <= x){
            sum += node[i].lena;
        } else sum += node[i].lenb;
    }
    if(sum <= L) return true;
    else return false;
}
 
int main() {
    scanf("%d%lld", &N, &L);
    int T = 0;
    for(int i = 0; i < N; i ++) {
        scanf("%d%d%d%d%d", &node[i].wet, &node[i].lena, &node[i].va, &node[i].lenb, &node[i].vb);
 
        node[i].tima = node[i].wet / node[i].va;
        if(node[i].wet % node[i].va) node[i].tima ++;
        node[i].timb = node[i].wet / node[i].vb;
        if(node[i].wet % node[i].vb) node[i].timb ++;
        T = max(T, max(node[i].tima, node[i].timb));
    }
 
    int l = 0, r = T, mid, p = -1;
    while(l <= r) {
        mid = (l + r) / 2;
        if(check(mid)) {
            p = mid;
            r = mid - 1;
        } else l = mid + 1;
    }
 
    printf("%d\n", p);
 
    return 0;
}

D.温暖的签到题

代码：

#include <bits/stdc++.h>
using namespace std;
  
const int maxn = 1e5 + 10;
  
int n, m;
  
long long s[4 * maxn], f[maxn * 4], Q;
  
long long cal(long long first, int len) {
  return (first + first + len - 1) * len / 2;
}
  
void pushUp(int rt) {
  s[rt] = s[2 * rt] + s[2 * rt + 1];
}
  
void pushDown(int rt, int l, int r) {
  if(f[rt] == 0) return;
  
  int mid = (l + r) / 2;
  
  // [l, mid]
  f[2 * rt] = f[rt];
  s[2 * rt] = cal(f[rt], mid - l + 1);
  
  // [mid + 1, r]
  f[2 * rt + 1] = f[rt] + mid + 1 - l;
  s[2 * rt + 1] = cal(f[rt] + mid + 1 - l, r - (mid + 1) + 1);
  
  f[rt] = 0;
}
  
void Input(int rt, int l, int r) {
  if(l == r) {
    s[rt] = r;
    return;
  }
  
  int mid = (l + r) / 2;
  
  Input(rt * 2, l, mid);
  Input(rt * 2 + 1, mid + 1, r);
  
  pushUp(rt);
}
  
long long Sum(int L, int R, int rt, int l, int r) {
  if(L <= l && r <= R) {
    return s[rt];
  }
  
  pushDown(rt, l, r);
  
  int mid = (l + r) / 2;
  
  long long left = 0;
  long long right = 0;
  
  if(L <= mid) left = Sum(L, R, 2 * rt, l, mid);
  if(R > mid) right = Sum(L, R, 2 * rt + 1, mid + 1, r);
  
  pushUp(rt);
  
  return left + right;
}
  
void Update(int L, int R, int rt, int l, int r) {
  if(L <= l && r <= R) {
    f[rt] = Q;
    s[rt] = cal(Q, r - l + 1);
    Q += (r - l + 1);
    return;
  }
  
  pushDown(rt, l, r);
  
  int mid = (l + r) / 2;
  
  if(L <= mid) Update(L, R, 2 * rt, l, mid);
  if(R > mid) Update(L, R, 2 * rt + 1, mid + 1, r);
  
  pushUp(rt);
}
  
int main() {
  scanf("%d%d", &n, &m);
  Input(1, 1, n);
  
  while(m --) {
    int op, L, R;
    scanf("%d%d%d", &op, &L, &R);
    if(op == 1) {
      Q = 1;
      Update(L, R, 1, 1, n);
    } else {
      printf("%lld\n", Sum(L, R, 1, 1, n));
    }
  }
  
  return 0;
}

E.西湖奇遇记

代码：

#include <bits/stdc++.h>
using namespace std;
 
const int maxn = 4e5 + 10;
 
long long INF = 1e9;
 
int n, m, k;
 
long long dis[maxn][7];
 
int h[maxn], a[maxn], b[maxn], cost[maxn], nx[maxn], sz;
 
void add(int x, int y, long long z) {
  a[sz] = x;
  b[sz] = y;
  cost[sz] = z;
  nx[sz] = h[x];
  h[x] = sz ++;
}
 
void dij() {
  for(int i = 1; i <= n; i ++) {
    for(int j = 0; j <= k; j ++) {
      dis[i][j] = INF;
    }
  }
 
  for(int j = 0; j <= k; j ++) {
    dis[1][0] = 0;
  }
 
  priority_queue<pair<long long, int> > q;
  q.push(make_pair(0LL, 1 * 10 + 0));
 
  while(!q.empty()) {
    pair<long long, int> tp = q.top();
    q.pop();
 
    int d = -tp.first;
    int v = tp.second / 10;
    int f = tp.second % 10;
 
    for (int i = h[v]; i != -1; i = nx[i]) {
      if (dis[v][f] + cost[i] < dis[b[i]][f]) {
        dis[b[i]][f] = dis[v][f] + cost[i];
        q.push(make_pair(-dis[b[i]][f], b[i] * 10 + f));
      }
 
      if (f + 1 <= k && dis[v][f] + 1 < dis[b[i]][f + 1]) {
        dis[b[i]][f + 1] = dis[v][f] + 1;
        q.push(make_pair(-dis[b[i]][f + 1], b[i] * 10 + f + 1));
      }
    }
  }
 
}
 
int main() {
 
  INF = INF * INF;
 
  scanf("%d%d%d", &n, &m, &k);
 
  for(int i = 1; i <= n; i ++) h[i] = -1;
 
  for(int i = 1; i <= m; i ++) {
    int x, y; long long c;
    scanf("%d%d%lld", &x, &y, &c);
    add(x, y, c);
    add(y, x, c);
  }
 
  dij();
 
  long long ans = INF;
 
  for(int j = 0; j <= k; j ++) {
    ans = min(ans, dis[n][j]);
  }
 
  printf("%lld\n", ans);
 
  return 0;
}

F.三生三世

代码：

#include <bits/stdc++.h>
using namespace std;
 
int N;
string s, t;
map<char, int> mp;
 
int main() {
    scanf("%d", &N);
    cin >> s >> t;
    bool flag = true;
    if(s == t || s.length() != t.length()) flag = false;
    else {
        for(int i = 0; s[i]; i ++)
            mp[s[i]] ++;
        for(int i = 0; t[i]; i ++)
            mp[t[i]] --;
        for(int i = 0; i < 26; i ++) {
            if(mp['a' + i] < 0 || mp['A' + i] < 0) {
                flag = false;
                break;
            }
        }
    }
 
    if(flag) printf("yes\n");
    else printf("no\n");
 
    return 0;
}

G.序列长度Ⅰ

代码：

#include <bits/stdc++.h>
using namespace std;
 
const int maxn = 2e6 + 10;
int n, k;
int m;
int b[maxn], st[maxn], top;
 
int main() {
  scanf("%d%d%d", &n, &m, &k);
  for(int i = 1; i <= n; i ++) {
    scanf("%d", &b[i]);
  }
 
  top = -1;
 
  long long ans = 0;
  long long sum = 0;
 
  for(int i = 1; i <= k - 1; i ++) {
    sum += b[i];
    if(b[i] != -m) {
      st[++ top] = i;
    }
  }
 
  for(int i = k; i <= n; i ++) {
    sum += b[i];
 
    if(b[i] != -m) {
      st[++ top] = i;
    }
 
    while(sum >= 0) {
      int pos = st[top];
      top --;
 
      if(sum - (b[pos] + m) < 0) {
        b[pos] = (int)(1LL * b[pos] - (sum + 1));
        ans += (sum + 1);
        sum = -1LL;
        if(b[pos] != -m) st[++ top] = i;
      } else {
        sum -= (1LL * b[pos] + m);
        ans += (1LL * b[pos] + m);
        b[pos] = -m;
      }
    }
    sum -= b[i - k + 1];
  }
 
  printf("%lld\n", ans);
 
  return 0;
}

H.偶数计算

代码：

#include <iostream>
using namespace std;
 
long long N, L, R;
 
long long b[100], len, one;
 
long long get(long long x) {
    long long res = 0LL;
    long long p = one - 1LL;
 
    for (long long i = len - 1; i >= 0; i--) {
        long long act = b[i];
        if (act == 1LL) {
            act = (x&(1LL << p)) ? 1LL : 0LL;
            p--;
        }
        res = res * 2LL + act;
    }
 
    return res;
}
 
long long cal(long long x) {
    long long left = 0LL;
    long long right = (1LL << one) - 1LL;
    long long pos = 0;
 
    while (left <= right) {
        long long mid = (left + right) / 2LL;
        if (get(mid) <= x) {
            pos = mid;
            left = mid + 1LL;
        }
        else {
            right = mid - 1LL;
        }
    }
 
    return pos;
}
 
int main() {
    cin >> N >> L >> R;
 
    len = one = 0;
    long long t = N;
 
    while (t) {
        if (t % 2LL == 1LL) {
            one++;
        }
 
        b[len++] = t % 2LL;
        t = t / 2LL;
    }
 
    cout << R - L + 1LL - (cal(R) - cal(L - 1LL)) << endl;
 
    return 0;
}

J.西湖奇遇记Ⅱ

代码：

#include <bits/stdc++.h>
using namespace std;
 
const int INF = 1e8;
const int maxn = 310;
int n, m, k;
int a[maxn][maxn];
int v[maxn][maxn], id;
int dis[maxn][maxn];
 
int cost[30][30];
 
int dp[100000][30];
 
int dir[4][2] = {
  {1, 0}, {-1, 0}, {0, 1}, {0, -1}
};
 
int out(int cx, int cy) {
  if(cx < 0 || cx > n - 1 || cy < 0 || cy > m - 1) return 1;
  return 0;
}
 
void bfs(int sx, int sy) {
  for(int i = 0; i < n; i ++) {
    for(int j = 0; j < m; j ++) {
      dis[i][j] = INF;
    }
  }
 
  dis[sx][sy] = 0;
 
  queue<int> q;
  q.push(sx * m + sy);
  while(!q.empty()) {
    int tp = q.front();
    q.pop();
 
    int cx = tp / m;
    int cy = tp % m;
 
    for(int i = 0; i < 4; i ++) {
      int nx = cx + dir[i][0];
      int ny = cy + dir[i][1];
 
      if(out(nx, ny)) continue;
      if(a[nx][ny] == 1) continue;
 
      if(dis[cx][cy] + 1 < dis[nx][ny]) {
        dis[nx][ny] = dis[cx][cy] + 1;
        q.push(nx * m + ny);
      }
    }
  }
/*
  printf("------\n");
  for(int i = 0; i < n; i ++) {
    for(int j = 0; j < m; j ++) {
      printf("%d ", dis[i][j]);
    }
    cout << endl;
  }
*/
  int op = v[sx][sy];
  if(sx == 0 && sy == 0) op = 0;
 
  for(int i = 0; i < n; i ++) {
    for(int j = 0; j < m; j ++) {
      if(i == 0 && j == 0) cost[op][0] = dis[i][j];
      if(v[i][j] != 0) cost[op][v[i][j]] = dis[i][j];
    }
  }
}
 
int lowbit(int x) {
  return x & (-x);
}
 
int main() {
  scanf("%d%d%d", &n, &m, &k);
 
  for(int i = 0; i < n; i ++) {
    for(int j = 0; j < m; j ++) {
      scanf("%d", &a[i][j]);
      if(a[i][j] == 2) {
        id ++;
        v[i][j] = id;
      }
    }
  }
 
  for(int i = 0; i <= id; i ++) {
    for(int j = 0; j <= id; j ++) {
      cost[i][j] = INF;
    }
  }
 
  for(int i = 0; i < n; i ++) {
    for(int j = 0; j < m; j ++) {
      if(i == 0 && j == 0) bfs(i, j);
      if(v[i][j] != 0) bfs(i, j);
    }
  }
/*
  cout << "!!!" << endl;
  for(int i = 0; i < n; i ++) {
    for(int j = 0; j < m; j ++) {
      cout << v[i][j] << " ";
    }
    cout << endl;
  }
 
  for(int i = 0; i <= id; i ++) {
    for(int j = 0; j <= id; j ++) {
      printf("%d -> %d: %d\n", i, j, cost[i][j]);
    }
  }
*/
  // dp
 
  for(int i = 0; i < (1 << (id + 1)); i ++) {
    for(int j = 0; j <= id; j ++) {
      dp[i][j] = INF;
    }
  }
 
  dp[1][0] = 0;
  for(int i = 2; i < (1 << (id + 1)); i ++) {
    for(int j = 0; j <= id; j ++) {
      if(((1 << j) & i) == 0) continue;
 
      int pre = i ^ (1 << j);
      for(int k = 0; k <= id; k ++) {
        if(((1 << k) & pre) == 0) continue;
        dp[i][j] = min(dp[i][j], dp[pre][k] + cost[k][j]);
      }
    }
  }
 
  int ans = 0;
 
 
  for(int i = 1; i < (1 << (id + 1)); i ++) {
    for(int j = 0; j <= id; j ++) {
      if(dp[i][j] > k) continue;
 
      int t = 0;
      int temp = i;
      while(temp) {
        t ++;
        temp -= lowbit(temp);
      }
 
      ans = max(ans, t - 1);
    }
  }
 
  printf("%d\n", ans);
 
  return 0;
}