cpp-algo-cases/chapter_dynamic_programming/edit_distance.cpp

/**
 * File: edit_distance.cpp
 * Created Time: 2023-07-13
 * Author: krahets (krahets@163.com)
 */

#include "../utils/common.hpp"

/* <20>༭<EFBFBD><E0BCAD><EFBFBD>룺<EFBFBD><EBA3BA><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> */
int editDistanceDFS(string s, string t, int i, int j) {
    // <20><> s <20><> t <20><>Ϊ<EFBFBD>գ<EFBFBD><D5A3>򷵻<EFBFBD> 0
    if (i == 0 && j == 0)
        return 0;
    // <20><> s Ϊ<>գ<EFBFBD><D5A3>򷵻<EFBFBD> t <20><><EFBFBD><EFBFBD>
    if (i == 0)
        return j;
    // <20><> t Ϊ<>գ<EFBFBD><D5A3>򷵻<EFBFBD> s <20><><EFBFBD><EFBFBD>
    if (j == 0)
        return i;
    // <20><><EFBFBD><EFBFBD><EFBFBD>ַ<EFBFBD><D6B7><EFBFBD><EFBFBD>ȣ<EFBFBD><C8A3><EFBFBD>ֱ<EFBFBD><D6B1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ַ<EFBFBD>
    if (s[i - 1] == t[j - 1])
        return editDistanceDFS(s, t, i - 1, j - 1);
    // <20><><EFBFBD>ٱ༭<D9B1><E0BCAD><EFBFBD><EFBFBD> = <20><><EFBFBD>롢ɾ<EBA1A2><C9BE><EFBFBD><EFBFBD><EFBFBD>滻<EFBFBD><E6BBBB><EFBFBD><EFBFBD><EFBFBD>ֲ<EFBFBD><D6B2><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ٱ༭<D9B1><E0BCAD><EFBFBD><EFBFBD> + 1
    int insert = editDistanceDFS(s, t, i, j - 1);
    int del = editDistanceDFS(s, t, i - 1, j);
    int replace = editDistanceDFS(s, t, i - 1, j - 1);
    // <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ٱ༭<D9B1><E0BCAD><EFBFBD><EFBFBD>
    return min(min(insert, del), replace) + 1;
}

/* <20>༭<EFBFBD><E0BCAD><EFBFBD>룺<EFBFBD><EBA3BA><EFBFBD>仯<EFBFBD><E4BBAF><EFBFBD><EFBFBD> */
int editDistanceDFSMem(string s, string t, vector<vector<int>> &mem, int i, int j) {
    // <20><> s <20><> t <20><>Ϊ<EFBFBD>գ<EFBFBD><D5A3>򷵻<EFBFBD> 0
    if (i == 0 && j == 0)
        return 0;
    // <20><> s Ϊ<>գ<EFBFBD><D5A3>򷵻<EFBFBD> t <20><><EFBFBD><EFBFBD>
    if (i == 0)
        return j;
    // <20><> t Ϊ<>գ<EFBFBD><D5A3>򷵻<EFBFBD> s <20><><EFBFBD><EFBFBD>
    if (j == 0)
        return i;
    // <20><><EFBFBD><EFBFBD><EFBFBD>м<EFBFBD>¼<EFBFBD><C2BC><EFBFBD><EFBFBD>ֱ<EFBFBD>ӷ<EFBFBD><D3B7><EFBFBD>֮
    if (mem[i][j] != -1)
        return mem[i][j];
    // <20><><EFBFBD><EFBFBD><EFBFBD>ַ<EFBFBD><D6B7><EFBFBD><EFBFBD>ȣ<EFBFBD><C8A3><EFBFBD>ֱ<EFBFBD><D6B1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ַ<EFBFBD>
    if (s[i - 1] == t[j - 1])
        return editDistanceDFSMem(s, t, mem, i - 1, j - 1);
    // <20><><EFBFBD>ٱ༭<D9B1><E0BCAD><EFBFBD><EFBFBD> = <20><><EFBFBD>롢ɾ<EBA1A2><C9BE><EFBFBD><EFBFBD><EFBFBD>滻<EFBFBD><E6BBBB><EFBFBD><EFBFBD><EFBFBD>ֲ<EFBFBD><D6B2><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ٱ༭<D9B1><E0BCAD><EFBFBD><EFBFBD> + 1
    int insert = editDistanceDFSMem(s, t, mem, i, j - 1);
    int del = editDistanceDFSMem(s, t, mem, i - 1, j);
    int replace = editDistanceDFSMem(s, t, mem, i - 1, j - 1);
    // <20><>¼<EFBFBD><C2BC><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ٱ༭<D9B1><E0BCAD><EFBFBD><EFBFBD>
    mem[i][j] = min(min(insert, del), replace) + 1;
    return mem[i][j];
}

/* <20>༭<EFBFBD><E0BCAD><EFBFBD>룺<EFBFBD><EBA3BA>̬<EFBFBD>滮 */
int editDistanceDP(string s, string t) {
    int n = s.length(), m = t.length();
    vector<vector<int>> dp(n + 1, vector<int>(m + 1, 0));
    // ״̬ת<CCAC>ƣ<EFBFBD><C6A3><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
    for (int i = 1; i <= n; i++) {
        dp[i][0] = i;
    }
    for (int j = 1; j <= m; j++) {
        dp[0][j] = j;
    }
    // ״̬ת<CCAC>ƣ<EFBFBD><C6A3><EFBFBD><EFBFBD><EFBFBD><EFBFBD>к<EFBFBD><D0BA><EFBFBD>
    for (int i = 1; i <= n; i++) {
        for (int j = 1; j <= m; j++) {
            if (s[i - 1] == t[j - 1]) {
                // <20><><EFBFBD><EFBFBD><EFBFBD>ַ<EFBFBD><D6B7><EFBFBD><EFBFBD>ȣ<EFBFBD><C8A3><EFBFBD>ֱ<EFBFBD><D6B1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ַ<EFBFBD>
                dp[i][j] = dp[i - 1][j - 1];
            } else {
                // <20><><EFBFBD>ٱ༭<D9B1><E0BCAD><EFBFBD><EFBFBD> = <20><><EFBFBD>롢ɾ<EBA1A2><C9BE><EFBFBD><EFBFBD><EFBFBD>滻<EFBFBD><E6BBBB><EFBFBD><EFBFBD><EFBFBD>ֲ<EFBFBD><D6B2><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ٱ༭<D9B1><E0BCAD><EFBFBD><EFBFBD> + 1
                dp[i][j] = min(min(dp[i][j - 1], dp[i - 1][j]), dp[i - 1][j - 1]) + 1;
            }
        }
    }
    return dp[n][m];
}

/* <20>༭<EFBFBD><E0BCAD><EFBFBD>룺<EFBFBD>ռ<EFBFBD><D5BC>Ż<EFBFBD><C5BB><EFBFBD><EFBFBD>Ķ<EFBFBD>̬<EFBFBD>滮 */
int editDistanceDPComp(string s, string t) {
    int n = s.length(), m = t.length();
    vector<int> dp(m + 1, 0);
    // ״̬ת<CCAC>ƣ<EFBFBD><C6A3><EFBFBD><EFBFBD><EFBFBD>
    for (int j = 1; j <= m; j++) {
        dp[j] = j;
    }
    // ״̬ת<CCAC>ƣ<EFBFBD><C6A3><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
    for (int i = 1; i <= n; i++) {
        // ״̬ת<CCAC>ƣ<EFBFBD><C6A3><EFBFBD><EFBFBD><EFBFBD>
        int leftup = dp[0]; // <20>ݴ<EFBFBD> dp[i-1, j-1]
        dp[0] = i;
        // ״̬ת<CCAC>ƣ<EFBFBD><C6A3><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
        for (int j = 1; j <= m; j++) {
            int temp = dp[j];
            if (s[i - 1] == t[j - 1]) {
                // <20><><EFBFBD><EFBFBD><EFBFBD>ַ<EFBFBD><D6B7><EFBFBD><EFBFBD>ȣ<EFBFBD><C8A3><EFBFBD>ֱ<EFBFBD><D6B1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ַ<EFBFBD>
                dp[j] = leftup;
            } else {
                // <20><><EFBFBD>ٱ༭<D9B1><E0BCAD><EFBFBD><EFBFBD> = <20><><EFBFBD>롢ɾ<EBA1A2><C9BE><EFBFBD><EFBFBD><EFBFBD>滻<EFBFBD><E6BBBB><EFBFBD><EFBFBD><EFBFBD>ֲ<EFBFBD><D6B2><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ٱ༭<D9B1><E0BCAD><EFBFBD><EFBFBD> + 1
                dp[j] = min(min(dp[j - 1], dp[j]), leftup) + 1;
            }
            leftup = temp; // <20><><EFBFBD><EFBFBD>Ϊ<EFBFBD><CEAA>һ<EFBFBD>ֵ<EFBFBD> dp[i-1, j-1]
        }
    }
    return dp[m];
}

/* Driver Code */
int main() {
    string s = "bag";
    string t = "pack";
    int n = s.length(), m = t.length();

    // <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
    int res = editDistanceDFS(s, t, n, m);
    cout << "<EFBFBD><EFBFBD> " << s << " <20><><EFBFBD><EFBFBD>Ϊ " << t << " <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ҫ<EFBFBD>༭ " << res << " <20><>\n";

    // <20><><EFBFBD>仯<EFBFBD><E4BBAF><EFBFBD><EFBFBD>
    vector<vector<int>> mem(n + 1, vector<int>(m + 1, -1));
    res = editDistanceDFSMem(s, t, mem, n, m);
    cout << "<EFBFBD><EFBFBD> " << s << " <20><><EFBFBD><EFBFBD>Ϊ " << t << " <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ҫ<EFBFBD>༭ " << res << " <20><>\n";

    // <20><>̬<EFBFBD>滮
    res = editDistanceDP(s, t);
    cout << "<EFBFBD><EFBFBD> " << s << " <20><><EFBFBD><EFBFBD>Ϊ " << t << " <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ҫ<EFBFBD>༭ " << res << " <20><>\n";

    // <20>ռ<EFBFBD><D5BC>Ż<EFBFBD><C5BB><EFBFBD><EFBFBD>Ķ<EFBFBD>̬<EFBFBD>滮
    res = editDistanceDPComp(s, t);
    cout << "<EFBFBD><EFBFBD> " << s << " <20><><EFBFBD><EFBFBD>Ϊ " << t << " <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ҫ<EFBFBD>༭ " << res << " <20><>\n";

    return 0;
}