Added InterviewBit DP questions

Author: shivanshuraj1333

InterviewBit/DP/flipArray.cpp

@@ -0,0 +1,39 @@
+/*
+given array [15, 10, 6], find min no of elements such that when their sign is fliped total sum is minimized;
+find min elements to achieve sum = sum(Array)/2
+*/
+
+#define ll long long
+int Solution::solve(const vector<int> &A) {
+    int s = 0;
+    for(int i=0;i<A.size();i++)
+        s+=A[i];
+    s=s/2;
+    
+    vector<vector<ll>> dp(A.size()+1, vector<ll> (s+1, INT_MAX));
+    
+    for(int i=0;i<dp.size();i++)
+        dp[i][0]=0;
+        
+    for(int i=1;i<dp.size();i++){
+        for(int j=1;j<=s;j++){
+            if(j>=A[i-1]){
+                if(dp[i-1][j-A[i-1]]!=INT_MAX){
+                    dp[i][j] = min(dp[i-1][j], dp[i-1][j-A[i-1]]+1);
+                }
+                else
+                    dp[i][j] = dp[i-1][j];
+            }
+            else
+                dp[i][j] = dp[i-1][j];
+        }
+    }
+    ll ans=0;
+    for(int i=s;i>=1;i--){
+        if(dp[dp.size()-1][i]!=INT_MAX){
+            ans=dp[dp.size()-1][i];
+            break;
+        }
+    }
+    return ans;
+}

InterviewBit/DP/lls.cpp

@@ -0,0 +1,25 @@
+int Solution::longestSubsequenceLength(const vector<int> &A) {
+    if(A.size()==0)
+        return 0;
+    vector<int> incr(A.size(),1);
+    vector<int> decr(A.size(),1);
+    
+    for(int i=0;i<incr.size();i++){
+        for(int j=0;j<i;j++){
+            if(A[i]>A[j])
+                incr[i]=max(incr[i],incr[j]+1);
+        }
+    }
+    
+    for(int i=A.size()-2;i>=0;i--){
+        for(int j=A.size()-1;j>i;j--){
+            if(A[i]>A[j])
+                decr[i] = max(decr[j]+1,decr[i]);
+        }
+    }
+    int ans = INT_MIN;
+    for(int i=0;i<A.size();i++){
+        ans = max(ans,incr[i]+decr[i]-1);
+    }
+    return ans;
+}

InterviewBit/DP/waysToDecode.cpp

@@ -0,0 +1,22 @@
+int ways(const string& A, int s)
+{
+    if(s == A.size())
+        return 1;
+    else if(A[s] == '0')
+        return 0;
+    else if(A[s] > '2')
+        return ways(A,s+1);
+    else if(s+1 >= A.size())
+        return ways(A,s+1);
+    else if(A[s] == '1' 
+            || (A[s] == '2' && A[s+1] < '7'))
+        return ways(A,s+1) +  ways(A,s+2);
+    else
+        return ways(A,s+1);
+}
+
+
+int Solution::numDecodings(string A) {
+    return ways(A,0);
+}
+