From 50d451b5fffa3640dfb198c4c834bbdbac7fd79b Mon Sep 17 00:00:00 2001
From: unknown <purvansh11@gmail.com>
Date: Thu, 1 Oct 2020 00:23:59 +0530
Subject: [PATCH] Add standard dp questions

---
 src/coin change - minimum number of coins.cpp | 51 +++++++++++++++++++
 src/coin change - number of ways.cpp          | 29 +++++++++++
 src/count number of subsets with sum = k.cpp  | 42 +++++++++++++++
 ...inimum subset sum difference iterative.cpp | 40 +++++++++++++++
 ...inimum subset sum difference recursive.cpp | 30 +++++++++++
 ...given score by some numbers distinctly.cpp | 27 ++++++++++
 src/subset sum - dp.cpp                       | 44 ++++++++++++++++
 src/unbounded Knapsack.cpp                    | 32 ++++++++++++
 8 files changed, 295 insertions(+)
 create mode 100644 src/coin change - minimum number of coins.cpp
 create mode 100644 src/coin change - number of ways.cpp
 create mode 100644 src/count number of subsets with sum = k.cpp
 create mode 100644 src/minimum subset sum difference iterative.cpp
 create mode 100644 src/minimum subset sum difference recursive.cpp
 create mode 100644 src/reach a given score by some numbers distinctly.cpp
 create mode 100644 src/subset sum - dp.cpp
 create mode 100644 src/unbounded Knapsack.cpp

diff --git a/src/coin change - minimum number of coins.cpp b/src/coin change - minimum number of coins.cpp
new file mode 100644
index 0000000..612a42f
--- /dev/null
+++ b/src/coin change - minimum number of coins.cpp	
@@ -0,0 +1,51 @@
+//https://practice.geeksforgeeks.org/problems/number-of-coins/0/
+
+//2D dp
+#include<bits/stdc++.h>
+using namespace std;
+int main(){
+    int t;
+    cin>>t;
+    while(t--){
+        int sum,n;
+        cin>>sum>>n;
+        vector<int> v(n);
+        for(auto &itr:v) cin>>itr;
+        int dp[n+1][sum+1];
+        for(int j=0;j<=sum;j++) dp[0][j] = INT_MAX - 1;
+        for(int i=0;i<=n;i++) dp[i][0] = 0;
+        for(int i=1;i<=n;i++){
+            for(int j=1;j<=sum;j++){
+                if(j>=v[i-1]){
+                    dp[i][j] = min(1 + dp[i][j-v[i-1]],dp[i-1][j]);
+                }
+                else dp[i][j] = dp[i-1][j];
+            }
+        }
+        if(dp[n][sum] == INT_MAX - 1) cout<<-1<<endl;
+        else 
+        cout<<dp[n][sum]<<endl;
+    }
+    return 0;
+}
+
+
+//1D dp
+
+ll n,sum;
+cin>>n>>sum;
+vector<ll> v(n);
+for(auto &itr:v) cin>>itr;
+ll dp[sum+1];
+for(ll i=0;i<=sum;i++) dp[i] = INT_MAX-1;
+dp[0]=0;
+
+for(ll i=1;i<=sum;i++){
+    for(ll j=1;j<=n;j++){
+        if(i>=v[j-1])
+        dp[i] = min(1+ dp[i-v[j-1]] , dp[i]);
+    }
+}
+if(dp[sum]==INT_MAX-1) cout<<-1;
+else    
+cout<<dp[sum];
\ No newline at end of file
diff --git a/src/coin change - number of ways.cpp b/src/coin change - number of ways.cpp
new file mode 100644
index 0000000..a25de41
--- /dev/null
+++ b/src/coin change - number of ways.cpp	
@@ -0,0 +1,29 @@
+// https://practice.geeksforgeeks.org/problems/coin-change/0
+
+#include<bits/stdc++.h>
+using namespace std;
+int main(){
+    int t;
+    cin>>t;
+    while(t--){
+        int n;
+        cin>>n;
+        int sum;
+        vector<int> v(n);
+        for(auto &itr:v) cin>>itr;
+        cin>>sum;
+        int dp[n+1][sum+1];
+        for(int j=0;j<=sum;j++) dp[0][j]=0;
+        for(int i=0;i<=n;i++) dp[i][0]=1;
+        for(int i=1;i<=n;i++){
+            for(int j=1;j<=sum;j++){
+                if(j>=v[i-1]){
+                    dp[i][j] = dp[i][j-v[i-1]] + dp[i-1][j];
+                }
+                else dp[i][j] = dp[i-1][j];
+            }
+        }
+        cout<<dp[n][sum]<<endl;
+    }
+    return 0;
+}
\ No newline at end of file
diff --git a/src/count number of subsets with sum = k.cpp b/src/count number of subsets with sum = k.cpp
new file mode 100644
index 0000000..89b0ba5
--- /dev/null
+++ b/src/count number of subsets with sum = k.cpp	
@@ -0,0 +1,42 @@
+#include<bits/stdc++.h>
+using namespace std;
+vector<int> v;
+int n;
+int main(){
+    int t;
+    cin>>t;
+    while(t--){
+        v.clear();
+        cin>>n;
+        for(int i=0;i<n;i++){
+            int temp;
+            cin>>temp;
+            v.push_back(temp);
+        }
+        int k;
+        cin>>k;
+        int sum=k;
+        int dp[n+5][sum+5];
+        
+        for(int j=0;j<=sum;j++) dp[0][j]=0;
+        for(int i=0;i<=n;i++) dp[i][0]=1;
+        int cnt=0;
+        for(int i=1;i<=n;i++){
+            for(int j=1;j<=sum;j++){
+                
+                if((j-v[i-1])>=0){
+                    dp[i][j] = (dp[i-1][j-v[i-1]] + dp[i-1][j]); 
+                    //only change or of subset sum to + here to count the number of subsets
+
+                    
+                }
+                else{
+                    dp[i][j] = dp[i-1][j];
+                }
+            }
+        }
+        cout<<dp[n][sum]<<endl;
+        
+    }
+    return 0;
+}
\ No newline at end of file
diff --git a/src/minimum subset sum difference iterative.cpp b/src/minimum subset sum difference iterative.cpp
new file mode 100644
index 0000000..e2fb17d
--- /dev/null
+++ b/src/minimum subset sum difference iterative.cpp	
@@ -0,0 +1,40 @@
+//https://practice.geeksforgeeks.org/problems/minimum-sum-partition/0
+
+#include<bits/stdc++.h>
+
+using namespace std;
+
+int main(){
+    int t;
+    cin>>t;
+    while(t--){
+        int n;
+        cin>>n;
+        vector<int> v(n);
+        for(auto &itr:v) cin>>itr;
+        int fullsum=0;
+        for(auto ele:v) fullsum+=ele;
+        
+        int sum=fullsum/2;
+        bool dp[n+5][(sum)+5];
+        for(int j=0;j<=sum;j++) dp[0][j]=false;
+        for(int i=0;i<=n;i++) dp[i][0]=true;
+        
+        for(int i=1;i<=n;i++){
+            for(int j=1;j<=sum;j++){
+                if(j-v[i-1]>=0){
+                    dp[i][j] = dp[i-1][j-v[i-1]] or dp[i-1][j];
+                }
+                else dp[i][j] = dp[i-1][j];
+            }
+        }
+        int s1;
+        for(int j=0;j<=sum;j++){
+            if(dp[n][j]) s1=j;
+        }
+        
+        cout<<(fullsum - s1) - s1<<endl; 
+    }
+    return 0;
+
+}
\ No newline at end of file
diff --git a/src/minimum subset sum difference recursive.cpp b/src/minimum subset sum difference recursive.cpp
new file mode 100644
index 0000000..c93ff4a
--- /dev/null
+++ b/src/minimum subset sum difference recursive.cpp	
@@ -0,0 +1,30 @@
+//https://practice.geeksforgeeks.org/problems/minimum-sum-partition/0
+
+#include<bits/stdc++.h>
+
+using namespace std;
+
+int dp[55][10001];
+int arr[200001];
+int solve(int ind,int x,int y,int n){
+    if(ind==n) return abs(x-y);
+    
+    if(dp[ind][y]!=-1) return dp[ind][y];
+    
+    return dp[ind][y]=min(solve(ind+1,x+arr[ind],y,n),solve(ind+1,x,y+arr[ind],n));
+    
+}
+
+
+int main() {
+    int t;
+    cin>>t;
+    while(t--){
+        int n;
+        cin>>n;
+        for(int i=0;i<n;i++) cin>>arr[i];
+        memset(dp,-1,sizeof(dp));
+        cout<<solve(0,0,0,n)<<endl;
+    }
+	return 0;
+}
\ No newline at end of file
diff --git a/src/reach a given score by some numbers distinctly.cpp b/src/reach a given score by some numbers distinctly.cpp
new file mode 100644
index 0000000..8b532bc
--- /dev/null
+++ b/src/reach a given score by some numbers distinctly.cpp	
@@ -0,0 +1,27 @@
+// https://practice.geeksforgeeks.org/problems/reach-a-given-score/0
+
+#include<bits/stdc++.h>
+using namespace std;
+int dp[1001][10];
+int solve(int arr[],int n,int i){
+    if(i<0 or n<0) return 0;
+    if(n==0) return 1;
+    if(dp[n][i]!=-1) return dp[n][i];
+    
+    return dp[n][i] = solve(arr,n-arr[i],i) + solve(arr,n,i-1);
+    
+}
+
+int main(){
+    int t;
+    cin>>t;
+    while(t--){
+        int n;
+        cin>>n;
+        memset(dp,-1,sizeof(dp));
+        int arr[3] = {3,5,10};
+        cout<<solve(arr,n,2)<<endl;
+    }
+    
+    return 0;
+}
\ No newline at end of file
diff --git a/src/subset sum - dp.cpp b/src/subset sum - dp.cpp
new file mode 100644
index 0000000..afdcf2e
--- /dev/null
+++ b/src/subset sum - dp.cpp	
@@ -0,0 +1,44 @@
+#include<bits/stdc++.h>
+using namespace std;
+vector<int> v;
+int n;
+int main(){
+    int t;
+    cin>>t;
+    while(t--){
+        v.clear();
+        cin>>n;
+        for(int i=0;i<n;i++){
+            int temp;
+            cin>>temp;
+            v.push_back(temp);
+        }
+        int sum=0;
+        for(auto ele:v) sum+=ele;
+        if(sum&1) {
+            cout<<"NO"<<endl;
+            continue;
+        }
+        sum/=2;
+        bool dp[n+5][sum+5];
+        memset(dp,false,sizeof(dp));
+        for(int j=0;j<=sum;j++) dp[0][j]=false;
+        for(int i=0;i<=n;i++) dp[i][0]=false;
+        for(int i=1;i<=n;i++){
+            for(int j=1;j<=sum;j++){
+                if((j-v[i-1])==0) dp[i][j] = true;
+                else if((j-v[i-1])>0){
+                    dp[i][j] = (dp[i-1][j-v[i-1]] | dp[i-1][j]);
+                }
+                else{
+                    dp[i][j] = dp[i-1][j];
+                }
+            }
+        }
+        
+        if(dp[n][sum]) cout<<"YES"<<endl;
+        else cout<<"NO"<<endl;
+        
+    }
+    return 0;
+}
\ No newline at end of file
diff --git a/src/unbounded Knapsack.cpp b/src/unbounded Knapsack.cpp
new file mode 100644
index 0000000..9ab032a
--- /dev/null
+++ b/src/unbounded Knapsack.cpp	
@@ -0,0 +1,32 @@
+#include<bits/stdc++.h>
+using namespace std;
+
+int main(){
+    int t; 
+    cin>>t; 
+    while(t--){
+        int n,w;
+        cin>>n>>w;
+        
+        vector<int> v(n);
+        for(auto &itr:v) cin>>itr;
+        vector<int> wt(n);
+        for(auto &itr:wt) cin>>itr;
+        int dp[n+5][w+5];
+        for(int i=0;i<=n;i++) dp[i][0]=0;
+        for(int j=0;j<=w;j++) dp[0][j]=0;
+        for(int i=1;i<=n;i++){
+            for(int j=1;j<=w;j++){
+                if(j>=wt[i-1]){
+                    //only one change from 0/1 Knapsack which is that if we take the item then we can again take it so v[i-1] + dp[i][j-wt[i-1]] 
+                    // i.e. in 0/1 Knapsack -- if 5,6,4,8 is the value array we can take 8 and move to arr with end 4 so dp[i-1][j-wt[i-1]]
+                    // in Unbounded Knapsack -- if 5,6,4,8 is the value array we can take 8 and stay at arr with end 8 as again we can take 8 so dp[i][j-wt[i-1]]
+                    dp[i][j] = max((v[i-1] + dp[i][j-wt[i-1]]),dp[i-1][j]);
+                }
+                else dp[i][j] = dp[i-1][j];
+            }
+        }
+        cout<<dp[n][w]<<endl;
+    }
+    return 0;
+}
\ No newline at end of file