算法考前一天

0-1背包的动态规划

#include<iostream>
using namespace std;

int w[50], v[50], dp[50][50];

int knapsack(int n, int c)
{
	for (int i = 0; i <= n; i++)
	{
		dp[i][0] = 0;
	}
	for (int j = 0; j <= c; j++)
	{
		dp[0][j] = 0;
	}

	for (int i = 1; i <= n; i++)
	{
		for (int j = 1; j <= c; j++)
		{
			if (j < w[i])
			{
				dp[i][j] = dp[i - 1][j];
			}
			else
			{
				dp[i][j] = max(dp[i-1][j], dp[i - 1][j - w[i]] + v[i]);
			}
		}
	}
	return dp[n][c];
}

int main()
{
	int n, c;
	cout << "请输入物品数量和背包容量";
	cin >> n >> c;
	cout << "请输入每个物品的重量和价值";
	for (int i = 1; i <= n; i++)
	{
		cin >> w[i] >> v[i];
	}

	cout<<knapsack(n, c);
}

最长单调递增子序列

#include<iostream>
using namespace std;

// 定义一个函数来计算最长不下降子序列的长度
int longestNonDecreasingSubsequence(int a[], int n) {
    int b[100] = { 0 };
    int i, j;
    int maxLength = 0;
    for (i = 2; i <= n; i++) {
        int k = 0;
        for (j = 1; j < i; j++)
            if (a[j] <= a[i] && k < b[j])
                k = b[j];
        b[i] = k + 1;
        if (maxLength < b[i])
            maxLength = b[i];
    }
    return maxLength;
}

int main() {
    int a[100];
    int n;
    cout << "请输入序列的长度: ";
    cin >> n;
    cout << "请输入序列的元素: ";
    for (int i = 1; i <= n; i++) {
        cin >> a[i];
    }
    int result = longestNonDecreasingSubsequence(a, n);
    cout << "最长不下降子序列的长度是: " << result << endl;
    return 0;
}