Create #SolutionsOfLinearEqtn.java

Author: 17tanya

DynamicProgramming/#SolutionsOfLinearEqtn.java

@@ -0,0 +1,62 @@
+/*
+https://www.techiedelight.com/total-possible-solutions-linear-equation-k-variables/
+
+Problem is similar to the problem - number of ways to change coin.
+We either include the current coefficient or exlcude it.
+
+Recurrence - 
+count(coeff, k, rhs) = count(coeff, k, rhs-coeff[k]) + count(coeff, k-1, rhs)
+where, count(coeff, k, rhs-coeff[k]) --> including coeff[k]
+       count(coeff, k-1, rhs) --> excluding coeff[k]
+*/
+
+//Recursion
+
+public int count(int coeff[], int index, int rhs){
+    //Base Case: we have considered valid coeff and their summation equals rhs
+    if(rhs == 0) return 1;
+    
+    //Base Case: we have considered invalid coeff and their summation does not equals rhs
+    else if(rhs<0 || index< 0) return 0;
+    
+    //Include the current coeff
+    int includeIndex = count(coeff, index, rhs-coeff[index]);
+    
+    //Exclude the current coeff
+    int excludeIndex = count(coeff, index-1, rhs);
+    
+    return include + exclude;
+}
+
+
+//Memoized Recursion
+public int count(int coeff[], int index, int rhs, HashMap<String, Integer> map){
+
+    //Base Case: we have considered valid coeff and their summation equals rhs
+    if(rhs == 0) return 1;
+    
+    //Base Case: we have considered invalid coeff and their summation does not equals rhs
+    else if(rhs<0 || index< 0) return 0;
+    
+    String key = index + "|" + rhs;
+    
+    if(!map.containsKey(key)){
+        //Include the current coeff
+        int includeIndex = count(coeff, index, rhs-coeff[index]);
+    
+        //Exclude the current coeff
+        int excludeIndex = count(coeff, index-1, rhs);
+        
+        map.put(key, include + exclude);
+    }
+    
+    return map.get(key);
+    
+}
+
+
+/*
+Time Complexity - O(numberOfCoefficients * RHS)
+Pseudo Polynomial
+*/
+