formatting filenames d7af6fdc8c

dynamic_programming/edit_distance.cpp

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+/* Given two strings str1 & str2
+ * and below operations that can
+ * be performed on str1. Find
+ * minimum number of edits
+ * (operations) required to convert
+ * 'str1' into 'str2'/
+ * a. Insert
+ * b. Remove
+ * c. Replace
+ * All of the above operations are 
+ * of equal cost
+ */
+
+#include <iostream>
+#include <string>
+using namespace std;
+
+int min(int x, int y, int z)
+{
+    return min(min(x, y), z);
+}
+
+/* A Naive recursive C++ program to find
+ * minimum number of operations to convert
+ * str1 to str2.
+ * O(3^m)
+ */
+int editDist(string str1, string str2, int m, int n)
+{
+    if (m == 0)
+        return n;
+    if (n == 0)
+        return m;
+
+    //If last characters are same then continue
+    //for the rest of them.
+    if (str1[m - 1] == str2[n - 1])
+        return editDist(str1, str2, m - 1, n - 1);
+
+    //If last not same, then 3 possibilities
+    //a.Insert b.Remove c. Replace
+    //Get min of three and continue for rest.
+    return 1 + min(editDist(str1, str2, m, n - 1),
+                   editDist(str1, str2, m - 1, n),
+                   editDist(str1, str2, m - 1, n - 1));
+}
+
+/* A DP based program
+ * O(m x n)
+ */
+int editDistDP(string str1, string str2, int m, int n)
+{
+
+    //Create Table for SubProblems
+    int dp[m + 1][n + 1];
+
+    //Fill d[][] in bottom up manner
+    for (int i = 0; i <= m; i++)
+    {
+        for (int j = 0; j <= n; j++)
+        {
+            //If str1 empty. Then add all of str2
+            if (i == 0)
+                dp[i][j] = j;
+
+            //If str2 empty. Then add all of str1
+            else if (j == 0)
+                dp[i][j] = i;
+
+            //If character same. Recur for remaining
+            else if (str1[i - 1] == str2[j - 1])
+                dp[i][j] = dp[i - 1][j - 1];
+
+            else
+                dp[i][j] = 1 + min(dp[i][j - 1],    //Insert
+                                   dp[i - 1][j],    //Remove
+                                   dp[i - 1][j - 1] //Replace
+                               );
+        }
+    }
+
+    return dp[m][n];
+}
+
+int main()
+{
+    string str1 = "sunday";
+    string str2 = "saturday";
+
+    cout << editDist(str1, str2, str1.length(), str2.length()) << endl;
+    cout << editDistDP(str1, str2, str1.length(), str2.length()) << endl;
+
+    return 0;
+}