20200324 直播总结

动态规划 —— 01 背包问题

#include<iostream>
using namespace std;
const int N = 1050;
int n, m;
int f[N][N], v[N], w[N];

int main()
{
    cin >> n >> m;
    for(int i = 1; i <= n; i ++) cin >> v[i] >> w[i];
    for(int i = 1; i <= n; i++) 
        for(int j = 0; j <= m; j++)
        {
            f[i][j] = f[i-1][j];
            if(j >= v[i]) f[i][j] = max(f[i][j], f[i-1][j-v[i]] + w[i]);
        }
    cout << f[n][m] << endl;
    return 0;
}

#include<iostream>
using namespace std;
const int N = 1050;
int n, m, f[N], v[N], w[N];

int main()
{
    cin >> n >> m;
    for(int i = 1; i <= n; i++) cin >> v[i] >> w[i];
    
    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] << endl;
    return 0;
}

完全背包问题

#include<iostream>
using namespace std;
const int N = 1050;
int f[N][N];
int v[N], w[N];
int n, m;

int main()
{
    cin >> n >> m;
    for(int i = 1; i <= n; i++) cin >> v[i] >> w[i];
    
    for(int i = 1; i <= n; i ++)
        for(int j = 0; j <= m; j++)
        {
            f[i][j] = f[i-1][j];
            if(j >= v[i]) f[i][j] = max(f[i][j], f[i][j-v[i]] + w[i]);
        }
    cout << f[n][m] << endl;
    return 0;
}

优化版

#include<iostream>
using namespace std;
const int N = 1050;
int f[N];
int v[N], w[N];
int n, m;

int main()
{
    cin >> n >> m;
    for(int i = 1; i <= n; i++) cin >> v[i] >> w[i];
    
    for(int i = 1; i <= n; i ++)
        for(int j = v[i]; j <= m; j++)
            f[j] = max(f[j], f[j-v[i]] + w[i]);
    cout << f[m] << endl;
    return 0;
}

#include<iostream>
using namespace std;
const int N = 1010;
int f[N][N];
char A[N], B[N];
int n, m;

int main()
{
    cin >> n >> m >> A+1 >> B+1;
    for(int i= 1; i <= n; i++)
        for(int j = 1; j <= m; j++)
        {
            f[i][j] = max(f[i-1][j], f[i][j-1]);
            if(A[i] == B[j]) f[i][j] = max(f[i][j], f[i-1][j-1]+1);
        }
    cout << f[n][m] << endl;
    return 0;
}