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131 lines
4.5 KiB
131 lines
4.5 KiB
/*
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* File: edit_distance.rs
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* Created Time: 2023-07-09
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* Author: codingonion (coderonion@gmail.com)
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*/
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/* 编辑距离：暴力搜索 */
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fn edit_distance_dfs(s: &str, t: &str, i: usize, j: usize) -> i32 {
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// 若 s 和 t 都为空，则返回 0
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if i == 0 && j == 0 { return 0; }
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// 若 s 为空，则返回 t 长度
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if i == 0 { return j as i32; }
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// 若 t 为空，则返回 s 长度
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if j == 0 {return i as i32; }
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// 若两字符相等，则直接跳过此两字符
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if s.chars().nth(i - 1) == t.chars().nth(j - 1) {
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return edit_distance_dfs(s, t, i - 1, j - 1);
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}
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// 最少编辑步数 = 插入、删除、替换这三种操作的最少编辑步数 + 1
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let insert = edit_distance_dfs(s, t, i, j - 1);
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let delete = edit_distance_dfs(s, t, i - 1, j);
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let replace = edit_distance_dfs(s, t, i - 1, j - 1);
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// 返回最少编辑步数
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std::cmp::min(std::cmp::min(insert, delete), replace) + 1
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}
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/* 编辑距离：记忆化搜索 */
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fn edit_distance_dfs_mem(s: &str, t: &str, mem: &mut Vec<Vec<i32>>, i: usize, j: usize) -> i32 {
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// 若 s 和 t 都为空，则返回 0
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if i == 0 && j == 0 { return 0; }
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// 若 s 为空，则返回 t 长度
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if i == 0 { return j as i32; }
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// 若 t 为空，则返回 s 长度
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if j == 0 {return i as i32; }
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// 若已有记录，则直接返回之
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if mem[i][j] != -1 { return mem[i][j]; }
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// 若两字符相等，则直接跳过此两字符
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if s.chars().nth(i - 1) == t.chars().nth(j - 1) {
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return edit_distance_dfs_mem(s, t, mem, i - 1, j - 1);
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}
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// 最少编辑步数 = 插入、删除、替换这三种操作的最少编辑步数 + 1
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let insert = edit_distance_dfs_mem(s, t, mem, i, j - 1);
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let delete = edit_distance_dfs_mem(s, t, mem, i - 1, j);
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let replace = edit_distance_dfs_mem(s, t, mem, i - 1, j - 1);
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// 记录并返回最少编辑步数
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mem[i][j] = std::cmp::min(std::cmp::min(insert, delete), replace) + 1;
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mem[i][j]
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}
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/* 编辑距离：动态规划 */
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fn edit_distance_dp(s: &str, t: &str) -> i32 {
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let (n, m) = (s.len(), t.len());
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let mut dp = vec![vec![0; m + 1]; n + 1];
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// 状态转移：首行首列
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for i in 1..= n {
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dp[i][0] = i as i32;
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}
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for j in 1..m {
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dp[0][j] = j as i32;
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}
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// 状态转移：其余行和列
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for i in 1..=n {
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for j in 1..=m {
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if s.chars().nth(i - 1) == t.chars().nth(j - 1) {
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// 若两字符相等，则直接跳过此两字符
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dp[i][j] = dp[i - 1][j - 1];
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} else {
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// 最少编辑步数 = 插入、删除、替换这三种操作的最少编辑步数 + 1
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dp[i][j] = std::cmp::min(std::cmp::min(dp[i][j - 1], dp[i - 1][j]), dp[i - 1][j - 1]) + 1;
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}
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}
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}
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dp[n][m]
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}
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/* 编辑距离：空间优化后的动态规划 */
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fn edit_distance_dp_comp(s: &str, t: &str) -> i32 {
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let (n, m) = (s.len(), t.len());
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let mut dp = vec![0; m + 1];
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// 状态转移：首行
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for j in 1..m {
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dp[j] = j as i32;
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}
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// 状态转移：其余行
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for i in 1..=n {
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// 状态转移：首列
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let mut leftup = dp[0]; // 暂存 dp[i-1, j-1]
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dp[0] = i as i32;
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// 状态转移：其余列
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for j in 1..=m {
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let temp = dp[j];
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if s.chars().nth(i - 1) == t.chars().nth(j - 1) {
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// 若两字符相等，则直接跳过此两字符
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dp[j] = leftup;
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} else {
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// 最少编辑步数 = 插入、删除、替换这三种操作的最少编辑步数 + 1
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dp[j] = std::cmp::min(std::cmp::min(dp[j - 1], dp[j]), leftup) + 1;
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}
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leftup = temp; // 更新为下一轮的 dp[i-1, j-1]
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}
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}
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dp[m]
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}
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/* Driver Code */
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pub fn main() {
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let s = "bag";
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let t = "pack";
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let (n, m) = (s.len(), t.len());
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// 暴力搜索
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let res = edit_distance_dfs(s, t, n, m);
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println!("将 {s} 更改为 {t} 最少需要编辑 {res} 步");
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// 记忆搜索
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let mut mem = vec![vec![0; m + 1]; n + 1];
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for row in mem.iter_mut() {
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row.fill(-1);
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}
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let res = edit_distance_dfs_mem(s, t, &mut mem, n, m);
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println!("将 {s} 更改为 {t} 最少需要编辑 {res} 步");
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// 动态规划
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let res = edit_distance_dp(s, t);
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println!("将 {s} 更改为 {t} 最少需要编辑 {res} 步");
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// 空间优化后的动态规划
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let res = edit_distance_dp_comp(s, t);
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println!("将 {s} 更改为 {t} 最少需要编辑 {res} 步");
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}
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