Create #PathsInMatrixWithGivenCost.java

Author: 17tanya

DynamicProgramming/#PathsInMatrixWithGivenCost.java

@@ -0,0 +1,75 @@
+/*
+https://www.techiedelight.com/counting-paths-on-grid-to-reach-destination-cell/
+https://www.geeksforgeeks.org/number-of-paths-with-exactly-k-coins/
+
+
+pathCount(m, n, k):   Number of paths to reach mat[m][n] from mat[0][0] 
+                      when cost = k
+
+If (m == 0 and n == 0)
+   return 1 if mat[0][0] == k else return 0
+Else:
+    pathCount(m, n, k) = pathCount(m-1, n, k - mat[m][n]) + 
+                         pathCount(m, n-1, k - mat[m][n])
+                         
+Normal Recursion
+*/
+
+public int pathCount(int A[][], int row, int col, int cost){
+    //Base Case
+    if(cost<0) return 0;
+    //Base Case --> Valid path
+    else if(row==0 && col==0 && cost == A[0][0]) return 1;
+    //Base Case
+    else if(row==0 && col==0 && cost != A[0][0]) return 0;
+    
+    //First row --> Only one move --> Go left
+    else if(row == 0) return pathCount(A, row, col-1, cost-A[row][col]);
+    
+    //First col --> Only one move --> Go up
+    else if(col == 0) return pathCount(A, row-1, col, cost-A[row][col]);
+    
+    //Cosider both --> up and left
+    else return pathCount(A, row-1, col, cost-A[row][col]) + pathCount(A, row, col-1, cost-A[row][col]);
+}
+
+//Memoized Recursion - using a hashmap
+
+public int pathCount(int A[][], int row, int count, int cost, HashMap<String, Integer> map){
+    if(cost<0) return 0;
+    
+    else if(row==0 && col==0 && cost == A[0][0]) return 1;
+    
+    else if(row==0 && col==0 && cost != A[0][0]) return 0;
+    
+    String key = row+"|"+col+"|"+cost;
+    
+    if(!map.containsKey(key)){
+        else if(row == 0) map.put(key, pathCount(A, row, col-1, cost-A[row][col]));
+        
+        else if(col == 0) map.put(key, pathCount(A, row-1, col, cost-A[row][col]));
+        
+        else map.put(key, pathCount(A, row-1, col, cost-A[row][col]) + pathCount(A, row, col-1, cost-A[row][col]));
+    }
+    return map.get(key);
+}
+
+//Memoized recursion - using an 3d array
+
+public int pathCount(int A[][], int row, int col, int cost, int dp[][]){
+    if(cost<0) return 0;
+    
+    else if(row==0 && col==0 && cost == A[0][0]) return 1;
+    
+    else if(row==0 && col==0 && cost != A[0][0]) return 0;
+    
+    else if(dp[row][col][cost] != -1) return dp[row][col][cost];
+    else{
+        dp[row][col][cost] = pathCount(A, row-1, col, cost-A[row][col]) + pathCount(A, row, col-1, cost-A[row][col]);
+        
+        return dp[row][col][cost];
+    }
+}
+
+//Time Complexity of DP solution - O(n*m*cost)
+//This is Psedo-Polynomial Time