背包笔记

01背包

朴素版01背包

cin >> n >> m;
f[0][0] = 0;
for(int i = 1; i <= n; i ++)
{
	for(int j = 0; j <= m; j ++)
	{
		f[i][j] = f[i - 1][j];//第i个物品不选
		if(j - v[i] >= 0)
		{
			f[i][j] = max(f[i][j], f[i - 1][j - v[i]] + w[i]);//选第i个物品
		}
	}
}

cout << f[n][m];

一维

cin >> n >> m;
for(int i = 1; i <= n; i ++)cin >> v[i] >> w[i];
//初始化
//一维的要f[0~m]都是0
//如果要恰好背包容量是m的话,要f[0] = 0, f[1~m] = 负无穷
for(int i = 1; i <= n; i ++)
{
	for(int j = m; j >= v[i]; j --)
	{
		f[j] = max(f[j], f[j - v[i]] + w[i]);
	}
}

cout << f[m];