diff --git a/src/main/java/com/thealgorithms/dynamicprogramming/SubsetCount.java b/src/main/java/com/thealgorithms/dynamicprogramming/SubsetCount.java new file mode 100644 index 00000000..2d36f5ad --- /dev/null +++ b/src/main/java/com/thealgorithms/dynamicprogramming/SubsetCount.java @@ -0,0 +1,69 @@ +package com.thealgorithms.dynamicprogramming; + +/** + * Find the number of subsets present in the given array with a sum equal to target. + * Based on Solution discussed on StackOverflow(https://stackoverflow.com/questions/22891076/count-number-of-subsets-with-sum-equal-to-k) + * @author Samrat Podder(https://github.com/samratpodder) + */ +public class SubsetCount { + + + /** + * Dynamic Programming Implementation. + * Method to find out the number of subsets present in the given array with a sum equal to target. + * Time Complexity is O(n*target) and Space Complexity is O(n*target) + * @param arr is the input array on which subsets are to searched + * @param target is the sum of each element of the subset taken together + * + */ + public int getCount(int[] arr, int target){ + /** + * Base Cases - If target becomes zero, we have reached the required sum for the subset + * If we reach the end of the array arr then, either if target==arr[end], then we add one to the final count + * Otherwise we add 0 to the final count + */ + int n = arr.length; + int[][] dp = new int[n][target+1]; + for (int i = 0; i < n; i++) { + dp[i][0] = 1; + } + if(arr[0]<=target) dp[0][arr[0]] = 1; + for(int t=1;t<=target;t++){ + for (int idx = 1; idx < n; idx++) { + int notpick = dp[idx-1][t]; + int pick =0; + if(arr[idx]<=t) pick+=dp[idx-1][target-t]; + dp[idx][target] = pick+notpick; + } + } + return dp[n-1][target]; + } + + + /** + * This Method is a Space Optimized version of the getCount(int[], int) method and solves the same problem + * This approach is a bit better in terms of Space Used + * Time Complexity is O(n*target) and Space Complexity is O(target) + * @param arr is the input array on which subsets are to searched + * @param target is the sum of each element of the subset taken together + */ + public int getCountSO(int[] arr, int target){ + int n = arr.length; + int prev[]=new int[target+1]; + prev[0] =1; + if(arr[0]<=target) prev[arr[0]] = 1; + for(int ind = 1; ind