72. Edit Distance

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 character

b) Delete a character

c) Replace a character

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题意：计算编辑距离
思路：dp[i][j]表示转换word1[0, i]到word2[0, j]所需的最小步数，则dp[i][j] = min{ dp[i-1][j-1] + carry, dp[i-1][j]+1, dp[i][j-1]+1} carry=0 if word1[i]==word2[j], else carry=1;

class Solution {
public:
int minDistance(string word1, string word2) {
int m = word1.size();
int n = word2.size();
if (m == 0 || n == 0)
return m | n;
vector<vector<int> > dp(m + 1, vector<int>(n + 1, 0));
for (int i = 0; i < n + 1; i++){
dp[0][i] = i;
}
for (int i = 0; i < m + 1; i++){
dp[i][0] = i;
}

for (int i = 1; i < m + 1; i++){
for (int j = 1; j < n + 1; j++){
if (word1[i - 1] == word2[j - 1])
dp[i][j] = dp[i - 1][j - 1];
else
dp[i][j] = min(dp[i - 1][j - 1], min(dp[i - 1][j], dp[i][j - 1])) + 1;
}
}
return dp[m]
;
}
};