(Daily algorithm) Leetcode -- Edit Distance (editing Distance)

(Daily algorithm) Leetcode -- Edit Distance (editing Distance)

Simply put, it is the minimum number of steps for converting a string s1 to another string s2 only through insert, delete, and substitute operations. It is easy for people familiar with algorithms to know that this is a dynamic planning problem.

In fact, a replacement operation can be equivalent to a delete + insert operation, so we define the weight as follows:

I (insert): 1

D (delete): 1

S (substitute): 1

Example:

Intention-> execution

Minimal edit distance:

Delete I; n-> e; t-> x; insert c; n-> u sum cost = 5

Edit DistanceUsed to measure the similarity between two strings. Between two strings Minimum edit distanceIt refers to the minimum operand for converting one string to another by editing (including insert, delete, and replace operations. As shown in, d (deletion) indicates the delete operation, s (substitution) indicates the replace operation, and I (insertion) indicates the insert operation. (For the sake of simplicity, Edit Distance is abbreviated as ED.) If the cost (cost) of each operation is 1, then ED = 5.

We define D (I, j) as the first I character of X [1... i] and Y's first j characters Y [1... j], where 0

<喎?http: www.bkjia.com kf ware vc " target="_blank" class="keylink"> VcD4KPHA + yOe5 + 8Tcz + u1vcrHtq/MrLnmu67Oyszivs2yu8TRveK + 9sHLoaM8L3A + large "brush: java;"> class Solution {public: int minDistance (string word1, string word2) {const size_t n = word1.size (); const size_t m = word2.size (); int f [n + 1] [m + 1]; for (size_t I = 0; I <= n; I ++) f [I] [0] = I; for (size_t j = 0; j <= m; j ++) f [0] [j] = j; for (size_t I = 1; I <= n; I ++) {for (size_t j = 1; j <= m; j ++) {if (word1 [I-1] = word2 [j-1]) f [I] [j] = f [I-1] [j-1]; else {int mn = min (f [I-1] [j], f [I] [j-1]); f [I] [j] = min (f [I-1] [j-1], mn) + 1 ;}}return f [n] [m] ;}};
Similarly, for dynamic planning, we do not want to use the space complexity of O (m * n.

The space complexity can be reduced to O (min (m, n) By scrolling an array ))

Reference URL: editing distance-Natural Language Processing editing distance-zhangshen