2014-10-20 11:23:39 +08:00
|
|
|
// Source : https://oj.leetcode.com/problems/edit-distance/
|
|
|
|
// Author : Hao Chen
|
|
|
|
// Date : 2014-08-22
|
|
|
|
|
2014-10-21 10:49:57 +08:00
|
|
|
/**********************************************************************************
|
|
|
|
*
|
2014-10-21 11:39:53 +08:00
|
|
|
* 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.)
|
2014-10-21 10:49:57 +08:00
|
|
|
*
|
|
|
|
* You have the following 3 operations permitted on a word:
|
|
|
|
*
|
|
|
|
* a) Insert a character
|
|
|
|
* b) Delete a character
|
|
|
|
* c) Replace a character
|
|
|
|
*
|
|
|
|
*
|
|
|
|
**********************************************************************************/
|
|
|
|
|
2014-10-20 11:23:39 +08:00
|
|
|
#include <iostream>
|
|
|
|
#include <string>
|
|
|
|
#include <vector>
|
|
|
|
#include <algorithm>
|
|
|
|
using namespace std;
|
|
|
|
|
2014-10-27 22:43:09 +08:00
|
|
|
|
|
|
|
/*
|
|
|
|
* Dynamic Programming
|
|
|
|
*
|
|
|
|
* Definitaion
|
|
|
|
*
|
|
|
|
* m[i][j] is minimal distance from word1[0..i] to word2[0..j]
|
|
|
|
*
|
|
|
|
* So,
|
|
|
|
*
|
|
|
|
* 1) if word1[i] == word2[j], then m[i][j] == m[i-1][j-1].
|
|
|
|
*
|
|
|
|
* 2) if word1[i] != word2[j], then we need to find which one below is minimal:
|
|
|
|
*
|
|
|
|
* min( m[i-1][j-1], m[i-1][j], m[i][j-1] )
|
|
|
|
*
|
|
|
|
* and +1 - current char need be changed.
|
|
|
|
*
|
|
|
|
* Let's take a look m[1][2] : "a" => "ab"
|
|
|
|
*
|
|
|
|
* +---+ +---+
|
|
|
|
* ''=> a | 1 | | 2 | '' => ab
|
|
|
|
* +---+ +---+
|
|
|
|
*
|
|
|
|
* +---+ +---+
|
|
|
|
* a => a | 0 | | 1 | a => ab
|
|
|
|
* +---+ +---+
|
|
|
|
*
|
|
|
|
* To know the minimal distance `a => ab`, we can get it from one of the following cases:
|
|
|
|
*
|
|
|
|
* 1) delete the last char in word1, minDistance( '' => ab ) + 1
|
|
|
|
* 2) delete the last char in word2, minDistance( a => a ) + 1
|
|
|
|
* 3) change the last char, minDistance( '' => a ) + 1
|
|
|
|
*
|
|
|
|
*
|
|
|
|
* For Example:
|
|
|
|
*
|
|
|
|
* word1="abb", word2="abccb"
|
|
|
|
*
|
|
|
|
* 1) Initialize the DP matrix as below:
|
|
|
|
*
|
|
|
|
* "" a b c c b
|
|
|
|
* "" 0 1 2 3 4 5
|
|
|
|
* a 1
|
|
|
|
* b 2
|
|
|
|
* b 3
|
|
|
|
*
|
|
|
|
* 2) Dynamic Programming
|
|
|
|
*
|
|
|
|
* "" a b c c b
|
|
|
|
* "" 0 1 2 3 4 5
|
|
|
|
* a 1 0 1 2 3 4
|
|
|
|
* b 2 1 0 1 2 3
|
2016-06-14 20:31:43 +08:00
|
|
|
* b 3 2 1 1 2 2
|
2014-10-27 22:43:09 +08:00
|
|
|
*
|
|
|
|
*/
|
|
|
|
int min(int x, int y, int z) {
|
|
|
|
return std::min(x, std::min(y,z));
|
|
|
|
}
|
|
|
|
|
2014-10-20 11:23:39 +08:00
|
|
|
int minDistance(string word1, string word2) {
|
|
|
|
int n1 = word1.size();
|
|
|
|
int n2 = word2.size();
|
|
|
|
if (n1==0) return n2;
|
|
|
|
if (n2==0) return n1;
|
2014-10-27 22:43:09 +08:00
|
|
|
vector< vector<int> > m(n1+1, vector<int>(n2+1));
|
2014-10-20 11:23:39 +08:00
|
|
|
for(int i=0; i<m.size(); i++){
|
2014-10-27 22:43:09 +08:00
|
|
|
m[i][0] = i;
|
2014-10-20 11:23:39 +08:00
|
|
|
}
|
|
|
|
for (int i=0; i<m[0].size(); i++) {
|
|
|
|
m[0][i]=i;
|
|
|
|
}
|
|
|
|
|
|
|
|
//Dynamic Programming
|
2014-10-27 22:43:09 +08:00
|
|
|
int row, col;
|
2014-10-20 11:23:39 +08:00
|
|
|
for (row=1; row<m.size(); row++) {
|
|
|
|
for(col=1; col<m[row].size(); col++){
|
|
|
|
if (word1[row-1] == word2[col-1] ){
|
|
|
|
m[row][col] = m[row-1][col-1];
|
|
|
|
}else{
|
2014-10-27 22:43:09 +08:00
|
|
|
int minValue = min(m[row-1][col-1], m[row-1][col], m[row][col-1]);
|
2014-10-20 11:23:39 +08:00
|
|
|
m[row][col] = minValue + 1;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
return m[row-1][col-1];
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
int main(int argc, char**argv)
|
|
|
|
{
|
|
|
|
string word1="abb", word2="abccb";
|
|
|
|
if (argc>2){
|
|
|
|
word1 = argv[1];
|
|
|
|
word2 = argv[2];
|
|
|
|
}
|
|
|
|
|
|
|
|
int steps = minDistance(word1, word2);
|
|
|
|
|
|
|
|
cout << word1 << ", " << word2 << " : " << steps << endl;
|
|
|
|
return 0;
|
|
|
|
}
|