Add day 8

Author: MadhavBahl

README.md

@@ -24,6 +24,7 @@ Read [CONTRIBUTING.md](./CONTRIBUTING.md) for contribution guidelines.
 5. [Day 5 -- Pattern Printing Problems](./day5/) -- [http://codetoexpress.tech/dc/day5/](http://codetoexpress.tech/dc/day5/)
 6. [Day 6 -- Sentence Cap + Word Reversal + Anagram](./day6/) -- [http://codetoexpress.tech/dc/day6/](http://codetoexpress.tech/dc/day6/)
 7. [Day 7 -- One Edit Away](./day7/) -- [http://codetoexpress.tech/dc/day7/](http://codetoexpress.tech/dc/day7/)
+8. [Day 8 -- Minimum Edit Distance](./day8/) -- [http://codetoexpress.tech/dc/day8/](http://codetoexpress.tech/dc/day8/)
 
 ## Timeline
 

day7/cover.png

@@ -0,0 +1,50 @@
+/**
+ * @author MadhavBahlMD
+ * @date 31/12/2018
+ */
+
+function minEditDist (str1, str2) {
+    // Initialize the distance matrix with all zeroes
+    let len1 = str1.length,
+        len2 = str2.length,
+        distMatrix = [];
+
+    for (let i=0; i<=len2; i++) {
+        let row = [];
+        for (let j=0; j<=len1; j++) {
+            // Initialie the edit distance matrix by all zeroes
+            row.push(0);
+        }
+        distMatrix.push(row);
+    }
+
+    // Fill the first row
+    for (let i=0; i<=len1; i++) {
+        distMatrix[0][i] = i;
+    }
+
+    // Fill the first column
+    for (let j=0; j<=len2; j++) {
+        distMatrix[j][0] = j;
+    }
+
+    // Fill the edit distance matrix
+    for (let i=1; i<=len2; i++) {
+        for (let j=1; j<=len1; j++) {
+            if (str1[i-1] === str2[j-1]) {
+                distMatrix[i][j] = distMatrix[i-1][j-1];
+            } else {
+                distMatrix [i][j] = 1 + Math.min (
+                                            distMatrix[i-1][j-1],
+                                            distMatrix[i-1][j],
+                                            distMatrix[i][j-1]
+                                          );
+            }
+        }
+    }
+
+    return distMatrix[len2][len1];
+}
+
+console.log(minEditDist ('abcdefgs', 'agced'));
+console.log(minEditDist('kitten', 'sitting'));

day8/JavaScript/sol.js

@@ -0,0 +1,96 @@
+![cover](./cover.png)
+
+# Day 8 - Maximum Edit Distance (Levenshtein Distance)
+
+Given two strings, and operations like replace, delete and add, write a program to determine how many minimum operations would it take to convert one string into another string.
+
+**Hint: Use Lavenshtein Distance**
+
+## Example (source: [Wikipedia](https://en.wikipedia.org/wiki/Levenshtein_distance))
+
+For example, the (Minimum Edit) Levenshtein distance between `kitten` and 
+`sitting` is `3`, since the following three edits change one 
+into the other, and there is no way to do it with fewer than 
+three edits:
+
+1. **k**itten → **s**itten (substitution of "s" for "k")
+2. sitt**e**n → sitt**i**n (substitution of "i" for "e")
+3. sittin → sittin**g** (insertion of "g" at the end).
+
+## Levenshtein distance (source: [Wikipedia](https://en.wikipedia.org/wiki/Levenshtein_distance))
+
+Levenshtein distance between two words is the minimum number of single-character edits (insertions, deletions or substitutions) required to change one word into the other. It is named after the Soviet mathematician Vladimir Levenshtein, who considered this distance in 1965.
+
+### Definition
+
+Mathematically, the Levenshtein distance between two strings `a` and `b` (of length `|a|` and `|b|` respectively) is given by ![lev](https://wikimedia.org/api/rest_v1/media/math/render/svg/4cf357d8f2135035207088d2c7b890fb4b64e410) where,
+
+![def](https://wikimedia.org/api/rest_v1/media/math/render/svg/f0a48ecfc9852c042382fdc33c19e11a16948e85)
+
+where 
+![def](https://wikimedia.org/api/rest_v1/media/math/render/svg/52512ede08444b13838c570ba4a3fc71d54dbce9)
+is the indicator function equal to `0` when
+![def](https://wikimedia.org/api/rest_v1/media/math/render/svg/231fda9ee578f0328c5ca28088d01928bb0aaaec)
+and equal to 1 otherwise, and
+![def](https://wikimedia.org/api/rest_v1/media/math/render/svg/bdc0315678caad28648aafedb6ebafb16bd1655c)
+is the distance between the first `i` characters of `a` and the first 
+`j` characters of `b`.
+
+Therefore, the minimum edit distance between `a` and `b` is the last element in the edit distance matrix
+
+## JavaScript Implementation
+
+### [Solution](./JavaScript/sol.js)
+
+```js
+/**
+ * @author MadhavBahlMD
+ * @date 31/12/2018
+ */
+
+function minEditDist (str1, str2) {
+    // Initialize the distance matrix with all zeroes
+    let len1 = str1.length,
+        len2 = str2.length,
+        distMatrix = [];
+
+    for (let i=0; i<=len2; i++) {
+        let row = [];
+        for (let j=0; j<=len1; j++) {
+            // Initialie the edit distance matrix by all zeroes
+            row.push(0);
+        }
+        distMatrix.push(row);
+    }
+
+    // Fill the first row
+    for (let i=0; i<=len1; i++) {
+        distMatrix[0][i] = i;
+    }
+
+    // Fill the first column
+    for (let j=0; j<=len2; j++) {
+        distMatrix[j][0] = j;
+    }
+
+    // Fill the edit distance matrix
+    for (let i=1; i<=len2; i++) {
+        for (let j=1; j<=len1; j++) {
+            if (str1[i-1] === str2[j-1]) {
+                distMatrix[i][j] = distMatrix[i-1][j-1];
+            } else {
+                distMatrix [i][j] = 1 + Math.min (
+                                            distMatrix[i-1][j-1],
+                                            distMatrix[i-1][j],
+                                            distMatrix[i][j-1]
+                                          );
+            }
+        }
+    }
+
+    return distMatrix[len2][len1];
+}
+
+console.log(minEditDist ('abcdefgs', 'agced'));
+console.log(minEditDist('kitten', 'sitting'));
+```