日常训练2025-1-11

日常训练2025-1-11

P1091 [NOIP2004 提高组] 合唱队形

https://www.luogu.com.cn/problem/P1091

思路

枚举一条分界线，分界线左边是从左到右求最长上升子序列，分界线右边从右到左求最长上升子序列。

然后计算答案即可。

代码

#include <bits/stdc++.h>typedef std::pair<long long, long long> pll;
typedef std::pair<int, int> pii;
#define INF 0x3f3f3f3f
#define MOD 998244353
using i64 = long long;
const int N = 1e5+5;void solve(){int n = 0;std::cin >> n;std::vector<int> v(n+1);for (int i = 1; i <= n; i++) std::cin >> v[i];std::vector<int> f(n+1, 1), g(n+1, 1);f[1] = 1;for (int i = 2; i <= n; i++){for (int j = i - 1; j >= 1; j--){if (v[i] > v[j] && f[i] <= f[j] + 1){f[i] = f[j] + 1;}}}g[n] = 1;for (int i = n - 1; i >= 1; i--){for (int j = i + 1; j <= n; j++){if (v[i] > v[j] && g[i] <= g[j] + 1){g[i] = g[j] + 1;}}}int ans = 0;for (int i = 1; i <= n; i++){ans = std::max(ans, f[i]+g[i]-1);}std::cout << n - ans << '\n';
}signed main()
{std::ios::sync_with_stdio(false);std::cin.tie(nullptr);std::cout<<std::setiosflags(std::ios::fixed)<<std::setprecision(2);int t = 1, i;for (i = 0; i < t; i++){solve();}return 0;
}

P1541 [NOIP2010 提高组] 乌龟棋

https://www.luogu.com.cn/problem/P1541

思路

多维背包问题

题解：https://www.luogu.com.cn/article/6maja666

题解已经讲的非常清楚，不再过多赘述。

代码

#include <bits/stdc++.h>typedef std::pair<long long, long long> pll;
typedef std::pair<int, int> pii;
#define INF 0x3f3f3f3f
#define MOD 998244353
using i64 = long long;
const int N = 1e5+5;int f[41][41][41][41];
void solve(){int n, m;std::cin >> n >> m;std::vector<int> v(n+1);for (int i = 1; i <= n; i++){std::cin >> v[i];}int count[5] = {0};for (int i = 0; i < m; i++){int a;std::cin >> a;count[a]++;}f[0][0][0][0] = v[1];for (int a = 0; a <= count[1]; a++){for (int b = 0; b <= count[2]; b++){for (int c = 0; c <= count[3]; c++){for (int d = 0; d <= count[4]; d++){int r = 1 + a + b*2 + c*3 + d*4;if (a != 0) f[a][b][c][d] = std::max(f[a][b][c][d], f[a-1][b][c][d] + v[r]);if (b != 0) f[a][b][c][d] = std::max(f[a][b][c][d], f[a][b-1][c][d] + v[r]);if (c != 0) f[a][b][c][d] = std::max(f[a][b][c][d], f[a][b][c-1][d] + v[r]);if (d != 0) f[a][b][c][d] = std::max(f[a][b][c][d], f[a][b][c][d-1] + v[r]);}}}}std::cout << f[count[1]][count[2]][count[3]][count[4]];
}signed main()
{std::ios::sync_with_stdio(false);std::cin.tie(nullptr);std::cout<<std::setiosflags(std::ios::fixed)<<std::setprecision(2);int t = 1, i;for (i = 0; i < t; i++){solve();}return 0;
}