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Oct 4, 2019
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Dynamic Programming #1

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113 changes: 113 additions & 0 deletions Dynamic Programming/LCS.cpp
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#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <sstream>
#include <queue>
#include <deque>
#include <bitset>
#include <iterator>
#include <list>
#include <stack>
#include <map>
#include <set>
#include <unordered_map>
#include <unordered_set>
#include <functional>
#include <numeric>
#include <utility>
#include <limits>
#include <iomanip>
#include <ctime>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <cassert>
using namespace std;

#define MP make_pair
#define PB push_back
#define ARR_MAX (int)1e5 //Max array length
#define INF (int)1e9 //10^9
#define EPS 1e-9 //10^-9
#define MOD 1000000007 //10^9+7
#define PI 3.1415926535897932384626433832795
typedef long int int32;
typedef unsigned long int uint32;
typedef long long int int64;
typedef unsigned long long int uint64;
typedef pair<int, int> Pii;
typedef vector<int> Vi;
typedef vector<string> Vs;
typedef vector<Pii> VPii;
typedef vector<Vi> VVi;
typedef map<int,int> Mii;
typedef set<int> Si;
typedef multimap<int,int> MMii;
typedef multiset<int> MSi;
typedef unordered_map<int,int> UMii;
typedef unordered_set<int> USi;
typedef unordered_multimap<int,int> UMMii;
typedef unordered_multiset<int> UMSi;
typedef priority_queue<int> PQi;
typedef queue<int> Qi;
typedef deque<int> DQi;


string s1, s2;

int bruteForce(int i, int j){
if(i==s1.size() || j==s2.size()) return 0;
if(s1[i] == s2[j]) return 1+bruteForce(i+1, j+1);
return max(bruteForce(i+1, j), bruteForce(i, j+1));
}

VVi DP;
int dpTopDown(int i, int j){
if(i==s1.size() || j==s2.size()) return 0;
if(DP[i][j] != -1) return DP[i][j];
if(s1[i] == s2[j]) return DP[i][j] = 1+dpTopDown(i+1, j+1);
return DP[i][j] = max(dpTopDown(i+1, j), dpTopDown(i, j+1));
}

int dpBottomUp(){

for (int i = 0; i < s1.size(); i++) DP[i][0] = (int)(s1[i] == s2[0]);
for (int j = 0; j < s2.size(); j++) DP[0][j] = (int)(s1[0] == s2[j]);


for (int i = 1; i < s1.size(); i++)
{
for (int j = 1; j < s2.size(); j++)
{
int val = 0;
if(s1[i] == s2[j]) val = 1;
DP[i][j] = max(DP[i-1][j-1]+val, max(DP[i-1][j], DP[i][j-1]));
}
}

return DP[s1.size()-1][s2.size()-1];
}

void print() {
std::for_each(std::begin(DP), std::end(DP), [](Vi v) {std::for_each(std::begin(v), std::end(v), [](int a) {cout << a << ' ';});cout << endl; });cout << endl;
}
int main (int argc, char const *argv[]) {
s1 = "Hello";
s2 = "World is Hell but hey Hello";

cout << bruteForce(0,0) << endl;

DP = VVi(s1.size(), Vi(s2.size(), -1));
cout << dpTopDown(0,0) << endl;

print();

DP = VVi(s1.size(), Vi(s2.size(), 0));
cout << dpBottomUp() << endl;

print();

return EXIT_SUCCESS;
}
119 changes: 119 additions & 0 deletions Dynamic Programming/LIS.cpp
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// Created on 29-07-2019 16:21:24 by necronomicon
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <sstream>
#include <queue>
#include <deque>
#include <bitset>
#include <iterator>
#include <list>
#include <stack>
#include <map>
#include <set>
#include <unordered_map>
#include <unordered_set>
#include <functional>
#include <numeric>
#include <utility>
#include <limits>
#include <iomanip>
#include <ctime>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <cassert>
using namespace std;

#define MP make_pair
#define PB push_back
#define ARR_MAX (int)1e5 //Max array length
#define INF (int)1e9 //10^9
#define EPS 1e-9 //10^-9
#define MOD 1000000007 //10^9+7
#define PI 3.1415926535897932384626433832795
typedef long int int32;
typedef unsigned long int uint32;
typedef long long int int64;
typedef unsigned long long int uint64;
typedef pair<int, int> Pii;
typedef vector<int> Vi;
typedef vector<string> Vs;
typedef vector<Pii> VPii;
typedef vector<Vi> VVi;
typedef map<int,int> Mii;
typedef set<int> Si;
typedef multimap<int,int> MMii;
typedef multiset<int> MSi;
typedef unordered_map<int,int> UMii;
typedef unordered_set<int> USi;
typedef unordered_multimap<int,int> UMMii;
typedef unordered_multiset<int> UMSi;
typedef priority_queue<int> PQi;
typedef queue<int> Qi;
typedef deque<int> DQi;


int N;
Vi numbers;
Vi DP;

int bruteForce(int k){
Vi res;
for (int i = 0; i < k; i++)
{
if(numbers[i] < numbers[k]) res.push_back(bruteForce(i));
}
if(res.size() == 0) return 1;
return 1+(*max_element(res.begin(), res.end()));
}

int dpTopDown(int k){
if(k>=0 && DP[k]!=0) return DP[k];
Vi res;
for (int i = 0; i < k; i++)
{
if(numbers[i] < numbers[k]) res.push_back(dpTopDown(i));
}
if(res.size() == 0) return 1;
return DP[k] = 1+(*max_element(res.begin(), res.end()));
}

int dpBottomUp(){
for (int i = 0; i < N+1; i++)
{
int m = 0;
for (int j = 0; j < i; j++)
{
if(numbers[j] < numbers[i]) m = max(m, DP[j]);
}
m++;
DP[i] = m;
}
return (*DP.rbegin())-1;
}

int main (int argc, char const *argv[]) {
N = 9;
numbers = {-7, 10, 9, 2, 3, 8, 8, 1, 10};
numbers.push_back(INF); // adding extra element cuz otherwise we have to run func for every pos 0->N
cout << "Brute-Force: " << bruteForce(N)-1 << endl;

// Top Down
DP.clear();
DP = Vi(N+1, 0);
cout << "Top-Down: " << dpTopDown(N)-1 << endl;
for(int x: DP) cout << x << ' ';
cout << endl;

// Bottom Up
DP.clear();
DP = Vi(N+1, 0);
cout << "Bottom-Up: " << dpBottomUp() << endl;
for(int x: DP) cout << x << ' ';
cout << endl;

return EXIT_SUCCESS;
}
117 changes: 117 additions & 0 deletions Dynamic Programming/coinChange.cpp
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// Created on 29-07-2019 16:21:24 by necronomicon
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <sstream>
#include <queue>
#include <deque>
#include <bitset>
#include <iterator>
#include <list>
#include <stack>
#include <map>
#include <set>
#include <unordered_map>
#include <unordered_set>
#include <functional>
#include <numeric>
#include <utility>
#include <limits>
#include <iomanip>
#include <ctime>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <cassert>
using namespace std;

#define MP make_pair
#define PB push_back
#define ARR_MAX (int)1e5 //Max array length
#define INF (int)1e9 //10^9
#define EPS 1e-9 //10^-9
#define MOD 1000000007 //10^9+7
#define PI 3.1415926535897932384626433832795
typedef long int int32;
typedef unsigned long int uint32;
typedef long long int int64;
typedef unsigned long long int uint64;
typedef pair<int, int> Pii;
typedef vector<int> Vi;
typedef vector<string> Vs;
typedef vector<Pii> VPii;
typedef vector<Vi> VVi;
typedef map<int,int> Mii;
typedef set<int> Si;
typedef multimap<int,int> MMii;
typedef multiset<int> MSi;
typedef unordered_map<int,int> UMii;
typedef unordered_set<int> USi;
typedef unordered_multimap<int,int> UMMii;
typedef unordered_multiset<int> UMSi;
typedef priority_queue<int> PQi;
typedef queue<int> Qi;
typedef deque<int> DQi;


int N, targetSum;
Vi coinValue;
Vi DP;

int bruteForce(int s){
if(s == 0) return 0;
Vi res;
for(int coin: coinValue){
if(s >= coin) res.push_back(1+bruteForce(s-coin));
}
return *min_element(res.begin(), res.end());
}

int dpTopDown(int s){
if(s == 0) return 0;
if(DP[s] != -1) return DP[s];
Vi res;
for(int coin: coinValue){
if(s >= coin) res.push_back(1+dpTopDown(s-coin));
}
return DP[s] = *min_element(res.begin(), res.end());
}

int dpBottomUp(){
DP[0] = 0;
for (int i = 0; i <= targetSum; i++)
{
for(int coin: coinValue){
if(i >= coin){
DP[i] = 1 + min(DP[i], DP[i-coin]);
}
}
}
return DP[targetSum];
}

int main (int argc, char const *argv[]) {
N = 2;
targetSum = 10;
coinValue = {1, 5};

cout << "Brute-Force: " << bruteForce(targetSum) << endl;

// Top Down
DP.clear();
DP = Vi(targetSum+1, -1);
cout << "Top-Down: " << dpTopDown(targetSum) << endl;
for(int x: DP) cout << x << ' ';
cout << endl;

// Bottom Up
DP.clear();
DP = Vi(targetSum+1, INF);
cout << "Bottom-Up: " << dpBottomUp() << endl;
for(int x: DP) cout << x << ' ';
cout << endl;

return EXIT_SUCCESS;
}