最短编辑距离—区间DP

 

#include <bits/stdc++.h>

#define rep(i, num, e) for (int i = (num); i <= (e); i++)
#define dep(i, num, e) for (int i = (num); i >= (e); i--)
#define endl '\n'
#define int long long
using namespace std;
constexpr int N = 1000 + 10, inf = 0x3f3f3f3f;
int n, m;
char a[N], b[N];
int dp[N][N]; // 表示第一个字符串前i个，
void solve()
{

    cin >> n >> a + 1;
    cin >> m >> b + 1;
    for (int i = 0; i <= m; i++)
    {
        dp[0][i] = i;
    }
    for (int i = 0; i <= n; i++)
    {
        dp[i][0] = i;
    }
    for (int i = 1; i <= n; i++)
    {
        for (int j = 1; j <= m; j++)
        {
            dp[i][j] = min(dp[i - 1][j] + 1, dp[i][j - 1] + 1);
            if (a[i] == b[j])
            {
                dp[i][j] = min(dp[i][j], dp[i - 1][j - 1]);
            }
            else
            {
                dp[i][j] = min(dp[i][j], dp[i - 1][j - 1] + 1);
            }
        }
    }
    cout << dp[n][m];
}

signed main()
{
    ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
    int T = 1;
    while (T--)
    {
        solve();
    }
    return 0;
}