Leetcode: edit distance string editing distance

Source: Internet
Author: User

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:

Distance two-dimensional matrix settings,Both the row and column correspond to the string length plus 1

DistanceInitialization of 0 rows and 0 columns, Boundary Condition

Leetcode: edit distance string editing distance

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