DP

Author: Skm2000

.gitignore

@@ -1 +1 @@
-./a.out
+a.out

Circular_Kadene.cpp

@@ -0,0 +1,22 @@
+// A very beautiful explalation given in leetcode
+// https://leetcode.com/problems/maximum-sum-circular-subarray/discuss/178422/One-Pass
+#include<bits/stdc++.h>
+using namespace std;
+
+int  maxMoney(int arr[], int num)
+{
+    int max_far=arr[0],max_curr=arr[0],min_far=arr[0],min_curr=arr[0],total=arr[0];
+    for(int i=1;i<num;i++){
+        max_curr=max(max_curr+arr[i],arr[i]);
+        max_far=max(max_curr,max_far);
+        min_curr=min(min_curr+arr[i],arr[i]);
+        min_far=min(min_far,min_curr);
+        total+=arr[i];
+    }
+    if(max_far>0){
+        return max(max_far,total-min_far);
+    }
+    else{
+        return max_far;
+    }
+}

Count_Pallindromic_SubString_Of_String_gfg.cpp

@@ -0,0 +1,33 @@
+#include<bits/stdc++.h>
+using namespace std;
+
+int expandAroundCenter(string s,int left,int right){
+    if(s.length()==0 || left>right) return 0;
+    int ans=0;
+    while(left>=0 && right<s.length() && s[left]==s[right]){
+        ans++;
+        left--;
+        right++;
+    }
+    return ans;
+}
+int CountLPSubstring(string s){
+    if(s.length()==0) return 0;
+    int res=0;
+    for(int i=0;i<s.length();i++){
+        res+=expandAroundCenter(s,i,i);
+        res+=expandAroundCenter(s,i,i+1);
+    }
+    return res;
+}
+int main(){
+    int t;
+    cin>>t;
+    while(t--){
+        int n;
+        cin>>n;
+        string s;
+        cin>>s;
+        cout<<CountLPSubstring(s)-n<<"\n";
+    }
+}

Friends_Pairing_Problem.cpp

@@ -0,0 +1,21 @@
+#include<iostream>
+#define m 1000000007
+using namespace std;
+int main()
+ {
+	int t;
+	cin>>t;
+	while(t--){
+	    int n;
+	    cin>>n;
+	    long long int dp[n+1];
+	    for(int i=0;i<=n;i++){
+	        if(i<=2) dp[i]=i;
+	        else{
+	            dp[i]=((dp[i-1]%m)+((i-1)%m*(dp[i-2]%m))%m)%m;
+	        }
+	    }
+	    cout<<dp[n]<<"\n";
+	}
+	return 0;
+}

GoldMine_Problem.cpp

@@ -0,0 +1,32 @@
+#include<bits/stdc++.h>
+using namespace std;
+int main(){
+    int t;
+    cin>>t;
+    while(t--){
+        int m,n;
+        cin>>n>>m;
+        int gold[n][m];
+        for(int i=0;i<n;i++){
+            for(int j=0;j<m;j++){
+                cin>>gold[i][j];
+            }
+        }
+        int dp[n][m];
+        int right,right_up,right_down;
+        memset(dp,0,sizeof(dp));
+        for(int i=m-1;i>=0;i--){
+            for(int j=0;j<n;j++){
+                right = (i==m-1)?0:dp[j][i+1];
+                right_up=(i==m-1 || j==0)?0:dp[j-1][i+1];
+                right_down=(i==m-1 || j==n-1)?0:dp[j+1][i+1];
+                dp[j][i]=gold[j][i]+max(right,max(right_up,right_down));
+            }
+        }
+        int ans=dp[0][0];
+        for(int i=1;i<n;i++){
+            ans=max(ans,dp[i][0]);
+        }
+        cout<<ans<<"\n";
+    }
+}

Kadane.cpp

@@ -11,7 +11,7 @@ int Kadane(int a[],int size){
 }
 
 int main(){
-    int a[]={4,-1,2,1};
+    int a[]={8 ,-8 ,9 ,-9 ,10 ,-11 ,12};
     int size=sizeof(a)/sizeof(a[0]);
     cout<<Kadane(a,size)<<"\n";
 }

Longest_Pallindromic_Substring.cpp

@@ -1,28 +1,29 @@
 #include<bits/stdc++.h>
 using namespace std;
 
-int LPSubstring(string s){
-    int n=s.length();
-    int dp[n][n],ans=-1;
-    memset(dp,0,sizeof(dp));
-    for(int i=0;i<n;i++){
-        dp[i][i] = 1;
+int expandAroundCenter(string s,int left,int right){
+    if(s.length()==0 || left>right) return 0;
+    while(left>=0 && right<s.length() && s[left]==s[right]){
+        left--;
+        right++;
     }
-    for(int i=n-2;i>=0;i--){
-        for(int j=i+1;j<n;j++){
-            if(s[i] == s[j]){
-                dp[i][j] = 2 + dp[i+1][j-1];
-            }
-            else{
-                dp[i][j] = 0;
-            }
-            ans = max(ans,dp[i][j]);
+    return right-left-1;
+}
+string LPSubstring(string s){
+    if(s.length()==0) return "";
+    int start=0,end=0;
+    for(int i=0;i<s.length();i++){
+        int len1=expandAroundCenter(s,i,i);
+        int len2=expandAroundCenter(s,i,i+1);
+        int len=max(len1,len2);
+        if(len>end-start){
+            start=i-(len-1)/2;
+            end=i+len/2;
         }
     }
-    return ans;
+    return s.substr(start,end-start+1);
 }
-
 int main(){
-    string s = "abcaabaafrg";
+    string s = "helppreanadkada";
     cout<<LPSubstring(s)<<"\n";
 }

Maximize_the_cutting.cpp

@@ -0,0 +1,33 @@
+#include<iostream>
+using namespace std;
+int main()
+ {
+	int t;
+	cin>>t;
+	while(t--){
+	    int n,x,y,z;
+	    cin>>n;
+        cin>>x>>y>>z;
+	    int dp[n+1];
+        for(int i=0;i<=n;i++) dp[i]=-1;
+	    dp[0]=0;
+	    for(int i=0;i<=n;i++){
+            if(dp[i]==-1) continue;
+	        if(i+x<=n){
+	            dp[i+x]=max(dp[i+x],dp[i]+1);
+	        }
+	        if(i+y<=n){
+	            dp[i+y]=max(dp[i+y],dp[i]+1);
+	        }
+	        if(i+z<=n){
+	            dp[i+z]=max(dp[i+z],dp[i]+1);
+	        }
+	    }
+        for(int i=0;i<=n;i++){
+            cout<<dp[i]<<" ";
+        }
+        cout<<"\n";
+	    cout<<dp[n]<<"\n";
+	}
+	return 0;
+}

Path_In_A_Matrix.cpp

@@ -0,0 +1,34 @@
+#include<bits/stdc++.h>
+using namespace std;
+int cost[1000][1000];
+void solve(int n,int cost[][1000]){
+    int dp[n][n];
+    memset(dp,0,sizeof(dp));
+    for(int i=n-1;i>=0;i--){
+        for(int j=n-1;j>=0;j--){
+            int down=(i==n-1)?0:dp[i+1][j];
+            int down_left=(i==n-1 || j==0)?0:dp[i+1][j-1];
+            int down_right=(i==n-1 || j==n-1)?0:dp[i+1][j+1];
+            dp[i][j]= cost[i][j]+max(down,max(down_right,down_left));
+        }
+    }
+    int ans=dp[0][0];
+    for(int i=1;i<n;i++){
+        ans=max(ans,dp[0][i]);
+    }
+    cout<<ans<<"\n";
+}
+int main(){
+    int t;
+    cin>>t;
+    while(t--){
+        int n;
+        cin>>n;
+        for(int i=0;i<n;i++){
+            for(int j=0;j<n;j++){
+                cin>>cost[i][j];
+            }
+        }
+        solve(n,cost);
+    }
+}