Leetcode: edit distance string editing distance

Original question stamp me

Given two words word1 and word2, find the minimum number of steps required to convert word1 to word2. (each operation is counted as 1 step.)You have the following 3 operations permitted on a word:a) Insert a characterb) Delete a characterc) Replace a character

 

Resolution:

Typical dynamic planning questions.

Set distance [I, j] to indicate the editing distance between word1 [I] And word2 [J ].

1. When word1 [I] = word2 [J], distance [I, j] = distance [I-1, J-1]

2. When word1 [I] is not equal to word2 [J], three operations are involved:

Word1 inserts one character, that is, distance [I, j] = distance [I, j-1] + 1word1 deletes one character, that is, distance [I, j] = distance [I-1, J] + 1word1 replace 1 character, that is, distance [I, j] = distance [I-1, J-1] + 1

 

class Solution {public:    int minDistance(string word1, string word2) {        if (word1.size() == 0) return word2.size();        if (word2.size() == 0) return word1.size();                int rowNum = word1.size() + 1;        int colNum = word2.size() + 1;        std::vector<std::vector<int>> distance(rowNum, std::vector<int>(colNum, 0));        for (int i = 0; i < rowNum; ++i) {            distance.at(i).at(0) = i;        }        for (int j = 0; j < colNum; ++j) {            distance.at(0).at(j) = j;        }                for (int i = 1; i < rowNum; ++i) {            for (int j = 1; j < colNum; ++j) {                if (word1.at(i - 1) == word2.at(j - 1)) {                    distance.at(i).at(j) = distance.at(i - 1).at(j - 1);                } else {                    int deleteCost = distance.at(i - 1).at(j) + 1;                    int insertCost = distance.at(i).at(j - 1) + 1;                    int replaceCost = distance.at(i - 1).at(j - 1) + 1;                    distance.at(i).at(j) = std::min(deleteCost, std::min(insertCost, replaceCost));                }            }        }        return distance.at(word1.size()).at(word2.size());    }};

 

Note:

Set the distance two-dimensional matrix. The row and column are both corresponding to the string length plus 1.

Initialization of 0 rows and 0 columns of the distance two-dimensional matrix, Boundary Condition

Leetcode: edit distance string editing distance