5.8线性动态规划2

KuaCpp2025-05-11 17:37

P1004 [NOIP 2000 提高组] 方格取数

做法1：DFS+剪枝

cpp 复制代码 
#include<bits/stdc++.h>
using namespace std;
int n, a[10][10], maxs, minx = 11, miny = 11, maxx, maxy;
void dfs(int x, int y, int s, int type){
	if(type == 1 && x == minx && y == miny){
		maxs = max(maxs, s);
		return;
	}else if(x < minx || x > maxx || y < miny || y > maxy)return;
	else if(x == maxx && y == maxy)type = 1;
	int z = a[x][y];
	a[x][y] = 0;
	if(type){
		dfs(x - 1, y, s + z, type);
		dfs(x, y - 1, s + z, type);
	}
	else{
		dfs(x + 1, y, s + z, type);
		dfs(x, y + 1, s + z, type); 
	}
	a[x][y] = z;
}
void solve(){
	cin >> n;
	int x, y, v;
	while(cin >> x >> y >> v, x || y || v){
		a[x][y] = v;
		minx = min(minx, x);
		miny = min(miny, y);
		maxx = max(maxx, x);
		maxy = max(maxy, y);
	}
	dfs(minx, miny, 0, 0);
	cout << maxs << endl;
} 
signed main()
{
    ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
    solve();
    
    return 0;
}

做法2：动态规划

四维数组

cpp 复制代码 
#include<bits/stdc++.h>
using namespace std;
int a[12][12], dp[12][12][12][12]; 
int mmax(int a, int b, int c, int d){
	return max(max(a, b), max(c, d));
}
void solve(){
	int n, x, y, s;
	cin >> n;
	while(cin >> x >> y >> s)a[x][y] = s;
	for(int i = 1; i <= n; i++){
		for(int j = 1; j <= n; j++){
			for(int k = 1; k <= n; k++){
				for(int l = 1; l <= n; l++){
					if(i + j == k + l){
						dp[i][j][k][l] = mmax(
						dp[i - 1][j][k - 1][l], dp[i - 1][j][k][l - 1], 
						dp[i][j - 1][k - 1][l], dp[i][j - 1][k][l - 1])
						+ a[i][j] + a[k][l];
						if(i == k && j == l) dp[i][j][k][l] -= a[k][l];
					}
				}
			}
		}
	}
	cout << dp[n][n][n][n] << endl;
}
signed main()
{
    ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
    solve();
    
    return 0;
}

P4933 大师

cpp 复制代码 
#include<bits/stdc++.h>
using namespace std;
#define int long long
const int N = 1010; int mod = 998244353;
int a[N], f[N][N];
int ans;
void solve(){
	int n; cin >> n;
	int flag = 0;
	int temp = 0;
	for(int i = 1; i <= n; i++){
		cin >> a[i];
		if(i == 1)temp = a[i];
		else{
			if(temp != a[i])flag = 1;
		}
	}
	if(flag == 0){
		long long sum = 1;
		for(int i = 1; i <= n; i++){
			sum = (sum * 2) % mod;
		}
		cout << (sum - 1 + mod) % mod << endl;
		return;
	}
	ans += n;
	for(int i = 1; i < n; i++){
		for(int j = i + 1; j <= n; j++){
			f[i][j] = 1;
			int x = a[j] - a[i];
			for(int k = 1; k < i; k++){
				if(x == a[i] - a[k]){
					f[i][j] = (f[i][j] + f[k][i]) % mod;
				}
			}
			ans = (ans + f[i][j]) % mod;
		}
	}
	cout << ans << endl;
} 
signed main()
{
    ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
    solve();
    
    return 0;
}

P1435 [IOI 2000] 回文字串

cpp 复制代码 
#include<bits/stdc++.h>
using namespace std;
const int N = 1010;
char a[N], b[N];
int f[N][N];
void solve(){
	cin >> a + 1;
	int len = strlen(a + 1);
	for(int i = 1; i <= len; i++){
		b[len - i + 1] = a[i];
	}
	for(int i = 1; i <= len; i++){
		for(int j = 1; j <= len; j++){
			if(a[i] == b[j])f[i][j] = f[i - 1][j - 1] + 1;
			else f[i][j] = max(f[i - 1][j], f[i][j - 1]);
		}
	}
	cout << len - f[len][len] << endl;
}
signed main()
{
    ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
    solve();
    
    return 0;
}

P1439 【模板】最长公共子序列

cpp 复制代码 
#include<bits/stdc++.h>
using namespace std;
const int N = 100010;
int a[N], b[N];
map<int, int> mp;
set<int> se;
void solve(){
	int n; cin >> n;
	for(int i = 1; i <= n; i++){
		cin >> a[i];
		mp[a[i]] = i;
	}
	for(int i = 1; i <= n; i++)cin >> b[i];
	se.insert(mp[b[1]]);
	for(int i = 2; i <= n; i++){
		auto it = se.lower_bound(mp[b[i]]);
		if(it != se.end())se.erase(it);
		se.insert(mp[b[i]]);
	}
	cout << se.size() << endl;
} 
signed main()
{
    ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
    solve();
    
    return 0;
}

下面是手搓二分

cpp 复制代码 
#include<bits/stdc++.h>
using namespace std;
const int N = 100010;
int a[N], b[N], f[N], mp[N];

void solve(){
	int n; cin >> n;
	for(int i = 1; i <= n; i++){
		cin >> a[i];
		mp[a[i]] = i;
	}
	for(int i = 1; i <= n; i++)cin >> b[i];
	f[0] = 0;
	int len = 0;
	for(int i = 1; i <= n; i++){
		if(mp[b[i]] > f[len])f[++len] = mp[b[i]];
		int l = 0, r = len + 1;
		while(l + 1 != r){
			int mid = l + r >> 1;
			if(mp[b[i]] > f[mid])l = mid;
			else r = mid;
		}
		f[r] = min(f[r], mp[b[i]]);
	}
	cout << len << endl;
}
signed main(){
	ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
	solve();
	
	return 0;
}

P2679 [NOIP 2015 提高组] 子串

cpp 复制代码 
#include<bits/stdc++.h>
using namespace std;
#define int long long 
const int mod = 1e9 + 7;
int dp[2][210][210][2];
void solve(){
	int n, m, k; cin >> n >> m >> k;
	string s1, s2; cin >> s1 >> s2;
	s1 = " " + s1, s2 = " " + s2;
	for(int i = 0; i <= 2; i++)dp[i][0][0][0] = 1;
	for(int i = 1; i <= n; i++){
		for(int j = 1; j <= m; j++){
			for(int l = 1; l <= k; l++){
				dp[1][j][l][0] = (dp[0][j][l][0] + dp[0][j][l][1]) % mod;
				if(s1[i] == s2[j]){
					dp[1][j][l][1] = (
					dp[0][j - 1][l][1] + 
					dp[0][j - 1][l - 1][1] + 
					dp[0][j - 1][l - 1][0]) % mod;
				}
				else{
					dp[1][j][l][1] = 0;
				}
			}
		}
		memcpy(dp[0], dp[1], sizeof(dp[1]));
	}
	cout << (dp[1][m][k][0] + dp[1][m][k][1]) % mod << endl;
}
signed main()
{
    ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
    solve();
    
    return 0;
}

P1854 花店橱窗布置

cpp 复制代码 
#include<bits/stdc++.h>
using namespace std;
const int N = 110;
int a[N][N][2];
void dfs(int n, int pos){
	if(n == 1)return;
	int x = a[n][pos][1];
	dfs(n - 1, x);
	cout << x << " ";
}
void solve(){
	int n, m; cin >> n >> m;
	for(int i = 1; i <= n; i++){
		for(int j = 1; j <= m; j++){
			cin >> a[i][j][0];
		}
	}
	int maxs, maxpos = 0;
	for(int i = 2; i <= n; i++){
		maxs = -1e9;
		for(int j = i - 1; j <= i - 1 + m - n; j++){
			if(a[i - 1][j][0] > maxs){
				maxs = a[i - 1][j][0];
				maxpos = j;
			}
			a[i][j + 1][0] += maxs;
			a[i][j + 1][1] = maxpos;
		}
	}
	maxs = -1e9;
	for(int i = n; i <= m; i++){
		if(a[n][i][0] > maxs){
			maxs = a[n][i][0];
			maxpos = i;
		}
	}
	cout << maxs << endl;
	dfs(n, maxpos);
	cout << maxpos << endl;
}
signed main()
{
    ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
    solve();
    
    return 0;
}

做法2：DFS

cpp 复制代码 
#include<bits/stdc++.h>
using namespace std;
int n, m;
int a[110][110];
int dp[110][110][2];
int dfs(int x, int pos){
	if(x == n)return a[x][pos];
	if(dp[x][pos][0])return dp[x][pos][0];
	int maxx = -1e9;
	for(int i = pos; i <= m - n + x; i++){
		int t = dfs(x + 1, i + 1);
		if(maxx < t){
			maxx = t;
			dp[x][pos][1] = i + 1;
		}
	}
	maxx += a[x][pos];
	dp[x][pos][0] = maxx;
	return maxx;
}

signed main()
{
    ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
    cin >> n >> m;
    for(int i = 1; i <= n; i++){
    	for(int j = 1; j <= m; j++){
    		cin >> a[i][j];
		}
	}
    cout << dfs(0, 0) << endl;
    int x = 0;
    for(int i = 0; i < n; i++){
    	x = dp[i][x][1];
    	cout << x << " ";
	}
    
    return 0;
}
相关推荐
TsingtaoAI34 分钟前
企业内训｜智能调控系统算法与优化——某汽车厂商
算法·汽车·ai企业内训·自动驾驶企业内训·智驾企业培训
安特尼1 小时前
招行数字金融挑战赛数据分析赛带赛题二
python·算法·机器学习·金融·数据分析
qq_433554541 小时前
C++ string初始化、string赋值操作、string拼接操作
开发语言·c++·算法
理想奋斗中1 小时前
【LeetCode Hot100 | 每日刷题】排序数组
数据结构·算法·leetcode·快速排序
এ᭄画画的北北1 小时前
力扣-2.两数相加
算法·leetcode
不会计算机的捞地1 小时前
【数据结构入门训练DAY-31】组合的输出
数据结构·算法·深度优先
终焉代码1 小时前
C++入门篇——类和对象(下)
开发语言·c++·算法
图灵科竞社资讯组1 小时前
高级数据结构：线段树
数据结构·算法
愚润求学2 小时前
【动态规划】斐波那契数列模型
c++·笔记·算法·leetcode·动态规划
程序猿(雷霆之王)2 小时前
贪心算法专题（Part1）
c++·算法·贪心算法
热门推荐
01【分布式】Hadoop完全分布式的搭建（零基础）02从零安装 LLaMA-Factory 微调 Qwen 大模型成功及所有的坑03KGG转MP3工具|非KGM文件|解密音频04YOLOv8入门 | 重要性能衡量指标、训练结果评价及分析及影响mAP的因素【发论文关注的指标】05【SpeedAI科研小助手】2分钟极速解决知网维普重复率、AIGC率过高，一键全文降！文件格式不变，公式都保留的！06西电B测-计算机网络综合实验(含验收问题)07最新 Kubernetes 集群部署 + flannel 网络插件（保姆级教程，最新 K8S 版本）08苍穹外卖面试总结09DeepSeek各版本说明与优缺点分析10Coze扣子平台完整体验和实践（附国内和国际版对比）