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lecture17.cpp
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lecture17.cpp
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#include<algorithm>
#include<vector>
#include<iostream>
using namespace std;
int mcmWithRecursion(vector<int>&arr,int i,int j){
if(i+1==j){
return 0;
}
int ans=1000000000;
for(int cut=i+1;cut<j;cut++){
int left=mcmWithRecursion(arr,i,cut);
int right= mcmWithRecursion(arr,cut,j);
ans=min(ans,left+right+arr[i]*arr[cut]*arr[j]);
}
return ans;
}
int mcmWithMemoization(vector<int>&arr,int i,int j,vector<vector<int>>&dp){
if(i+1==j){
return dp[i][j]= 0;
}
if(dp[i][j]!=0){
return dp[i][j];
}
int ans=1000000000;
for(int cut=i+1;cut<j;cut++){
int left=mcmWithMemoization(arr,i,cut,dp);
int right= mcmWithMemoization(arr,cut,j,dp);
ans=min(ans,left+right+arr[i]*arr[cut]*arr[j]);
}
return dp[i][j]= ans;
}
int mcmWihTabulation(vector<int>&arr,vector<vector<int>>&dp){
for(int gap=1;gap<arr.size();gap++){
for(int i=0,j=gap;j<arr.size();i++,j++){
if(i+1==j){
dp[i][j]= 0;
continue;
}
int ans=1000000000;
for(int cut=i+1;cut<j;cut++){
int left=dp[i][cut];
int right=dp[cut][j];
ans=min(ans,left+right+arr[i]*arr[cut]*arr[j]);
}
dp[i][j]= ans;
}
}
return dp[0][dp[0].size()-1];
}
void mcm(){
vector<int>arr={7,3,5,8,2};
vector<vector<int>>dp(arr.size(),vector<int>(arr.size(),0));
// cout<<mcmWithRecursion(arr,0,arr.size()-1)<<"\n";
// cout<<mcmWithMemoization(arr,0,arr.size()-1,dp)<<"\n";
cout<<mcmWihTabulation(arr,dp)<<"\n";
for(int i=0;i<dp.size();i++){
for(int j=0;j<dp[0].size();j++){
cout<<dp[i][j]<<" ";
}
cout<<"\n";
}
}
int editDistanceWithRecursion(string s1,string s2,int s1Pos,int s2Pos){
if(s1Pos==0){
return s2Pos;
}
if(s2Pos==0){
return s1Pos;
}
if(s1[s1Pos-1]==s2[s2Pos-1]){
return editDistanceWithRecursion(s1,s2,s1Pos-1,s2Pos-1);
}
else{
int a= editDistanceWithRecursion(s1,s2,s1Pos-1,s2Pos);//insert
int b= editDistanceWithRecursion(s1,s2,s1Pos,s2Pos-1);//delete
int c= editDistanceWithRecursion(s1,s2,s1Pos-1,s2Pos-1);//swap
return min(a,min(b,c))+1;
}
}
int editDistanceWithMemoization(string s1,string s2,int s1Pos,int s2Pos,vector<vector<int>>&dp){
if(s1Pos==0){
return dp[s1Pos][s2Pos]= s2Pos;
}
if(s2Pos==0){
return dp[s1Pos][s2Pos]= s1Pos;
}
if(dp[s1Pos][s2Pos]!=0){
return dp[s1Pos][s2Pos];
}
if(s1[s1Pos-1]==s2[s2Pos-1]){
return dp[s1Pos][s2Pos]= editDistanceWithMemoization(s1,s2,s1Pos-1,s2Pos-1,dp);
}
else{
int a= editDistanceWithMemoization(s1,s2,s1Pos-1,s2Pos,dp);//insert
int b= editDistanceWithMemoization(s1,s2,s1Pos,s2Pos-1,dp);//delete
int c= editDistanceWithMemoization(s1,s2,s1Pos-1,s2Pos-1,dp);//swap
return dp[s1Pos][s2Pos]= min(a,min(b,c))+1;
}
}
int editDistanceWithTabulation(string s1,string s2,vector<vector<int>>&dp){
for(int s1Pos=0;s1Pos<=s1.length();s1Pos++){
for(int s2Pos=0;s2Pos<=s2.length();s2Pos++){
if(s1Pos==0){
dp[s1Pos][s2Pos]= s2Pos;
continue;
}
if(s2Pos==0){
dp[s1Pos][s2Pos]= s1Pos;
continue;
}
if(s1[s1Pos-1]==s2[s2Pos-1]){
dp[s1Pos][s2Pos]= dp[s1Pos-1][s2Pos-1];
}
else{
int a= dp[s1Pos-1][s2Pos];//insert
int b= dp[s1Pos][s2Pos-1];//delete
int c= dp[s1Pos-1][s2Pos-1];//swap
dp[s1Pos][s2Pos]= min(a,min(b,c))+1;
}
}
}
return dp[dp.size()-1][dp[0].size()-1];
}
void editDistance(){
string s1="abcd";
string s2="acebd";
// cout<<editDistanceWithRecursion(s1,s2,s1.length(),s2.length())<<"\n";
vector<vector<int>>dp(s1.length()+1,vector<int>(s2.length()+1,0));
// cout<<editDistanceWithMemoization(s1,s2,s1.length(),s2.length(),dp)<<"\n";
cout<<editDistanceWithTabulation(s1,s2,dp)<<"\n";
for(int i=0;i<dp.size();i++){
for(int j=0;j<dp[0].size();j++){
cout<<dp[i][j]<<" ";
}
cout<<"\n";
}
}
int main(){
// mcm();
editDistance();
return 0;
}