动态规划的基本模型

有数字三角形模型、LIS、LCS、走网格、最大子矩阵

1258 【例9.2】数字金字塔

数字三角形模型

#include <iostream>
#include <algorithm>
using namespace std;
const int N = 1005;

int a[N][N], dp[N][N];

int main(void)
{
	int r;
	cin >> r;
	for (int i = 1; i <= r; i++)
		for (int j = 1; j <= i; j++)
			cin >> a[i][j];
	for (int i = 1; i <= r; i++) 
		dp[i][1] = dp[i - 1][1] + a[i][1];
	
	for (int i = 1; i <= r; i++)
		dp[i][i] = dp[i - 1][i - 1] + a[i][i];
	
	for (int i = 3; i <= r; i++)
		for (int j = 2; j < i; j++)
			dp[i][j] = max(dp[i - 1][j - 1], dp[i - 1][j]) + a[i][j];
	
	int res = 0;
	for (int j = 1; j <= r; j++)
		res = max(res, dp[r][j]);
	cout << res << endl;
		
	return 0;
}
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1259：【例9.3】求最长不下降序列

因为需要记录路径，我的办法是用一个数组来记录前驱，存入一个栈

#include <bits/stdc++.h>
using namespace std;
const int N = 205;

int arr[N], dp[N], pri[N]; // pri记录前驱 

int main(void)
{
	int n;
	cin >> n;
	for (int i = 1; i <= n; i++) {
		cin >> arr[i];
		dp[i] = 1;
	}
	for (int i = 1; i <= n; i++) {
		for (int j = 1; j < i; j++) {
			// 记录前驱 
			if (arr[i] >= arr[j] && dp[i] < dp[j] + 1) {
				pri[i] = j;
				dp[i] = max(dp[i], dp[j] + 1);
			}
		}
	}
	int res = 0, st;
	for (int i = 1; i <= n; i++) {
		if (res < dp[i]) {
			st = i;
		}
		res = max(res, dp[i]);
	}
	cout << "max=" << res << endl;
	
	stack<int> stk;
	for (int i = st; i != 0; i = pri[i]) {
		stk.push(arr[i]);
	}
	while (stk.size()) {
		cout << stk.top() << " ";
		stk.pop();
	}
	cout << endl;
	
	return 0;
}
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1260：【例9.4】拦截导弹(Noip1999)

注意最后会读入一个EOF，所以 n 需要减1

贪心的思路，一开始没想到