Edit DIstance Added

Author: zarif98sjs

Dynamic Programming/04 Levenshtein or Edit Distance.cpp

@@ -0,0 +1,128 @@
+
+/**
+
+Problem : Levenshtein /Edit Distance
+The Levenshtein distance between two words is the minimum number of single-character edits
+(i.e. insertions, deletions or substitutions) required to change one word into the other.
+Each of these operations has unit cost.
+
+**/
+
+/**Which of the favors of your Lord will you deny ?**/
+
+#include<bits/stdc++.h>
+using namespace std;
+
+#define LL long long
+#define PII pair<int,int>
+#define PLL pair<LL,LL>
+#define MP make_pair
+#define F first
+#define S second
+#define INF INT_MAX
+
+#define ALL(x) (x).begin(), (x).end()
+#define DBG(x) cerr << __LINE__ << " says: " << #x << " = " << (x) << endl
+
+#include <ext/pb_ds/assoc_container.hpp>
+#include <ext/pb_ds/tree_policy.hpp>
+using namespace __gnu_pbds;
+
+template<class TIn>
+using indexed_set = tree<
+                    TIn, null_type, less<TIn>,
+                    rb_tree_tag, tree_order_statistics_node_update>;
+
+/*
+PBDS
+-------------------------------------------------
+1) insert(value)
+2) erase(value)
+3) order_of_key(value) // 0 based indexing
+4) *find_by_order(position) // 0 based indexing
+
+*/
+
+inline void optimizeIO()
+{
+    ios_base::sync_with_stdio(false);
+    cin.tie(NULL);
+}
+
+const int nmax = 2e5+7;
+const LL LINF = 1e17;
+
+string to_str(LL x)
+{
+    stringstream ss;
+    ss<<x;
+    return ss.str();
+}
+
+//bool cmp(const PII &A,const PII &B)
+//{
+//
+//}
+
+unordered_map<string,int>dp;
+
+int e_length(string X,string Y,int m,int n)
+{
+    if(m==0 || n==0)
+        return max(m,n); /** the one which is not 0 **/
+
+    string key  = to_str(m) + "|" + to_str(n);
+
+    if(dp.find(key)!=dp.end())
+        return dp[key];
+
+    if(X[m-1]==Y[n-1])
+        dp[key] = e_length(X,Y,m-1,n-1);
+    else
+        dp[key] = 1 + min(e_length(X,Y,m-1,n-1),min(e_length(X,Y,m,n-1),e_length(X,Y,m-1,n)));
+
+    return dp[key];
+}
+
+string e_print(string X,string Y,int m,int n)
+{
+    if(m==0 && n==0) return "";
+    if(m==0) return "+("+Y.substr(0,n)+")"; /** Add the part of Y which is left **/
+    if(n==0) return "-("+X.substr(0,m)+")"; /** Delete the part of X which is left **/
+
+    if(X[m-1]==Y[n-1])
+        return e_print(X,Y,m-1,n-1) + X.substr(m-1,1);
+
+    string key1  = to_str(m-1) + "|" + to_str(n-1);
+    string key2  = to_str(m-1) + "|" + to_str(n);
+    string key3  = to_str(m) + "|" + to_str(n-1);
+
+    int val1 = dp[key1] , val2 = dp[key2] , val3 = dp[key3];
+    int minn = min(val1,min(val2,val3));
+
+    if(minn==val1) return e_print(X,Y,m-1,n-1) + "(-"+X.substr(m-1,1)+"+"+Y.substr(n-1,1)+")"; /** Substitution **/
+    if(minn==val2) return e_print(X,Y,m-1,n) + "-"+X.substr(m-1,1); /** Deletion **/
+    if(minn==val3) return e_print(X,Y,m,n-1) + "+"+Y.substr(n-1,1); /** Addition **/
+
+}
+
+int main()
+{
+    optimizeIO();
+
+    string X = "kitten";
+    string Y = "sitting";
+
+//    string X = "kiy";
+//    string Y = "sitting";
+
+    cout<<"X : "<<X<<endl;
+    cout<<"Y : "<<Y<<endl;
+
+    cout<<"Edit Distance : "<<e_length(X,Y,X.size(),Y.size())<<endl;
+    cout<<"Edit String : "<<e_print(X,Y,X.size(),Y.size())<<endl;
+
+    return 0;
+}
+
+