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Optimised Space Complexity To O(sum) (#5651)

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* Optimised Space Complexity To O(sum)

* Fixes Clang Format

* Optimised Space Complexity To Use a Single DP Array
This commit is contained in:
Sanketh L Reddy
2024-10-09 19:27:11 +05:30
committed by GitHub
parent 0603accfd4
commit 2d34bc150f
1 changed files with 13 additions and 16 deletions
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29
src/main/java/com/thealgorithms/dynamicprogramming/SubsetSum.java
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@ -9,28 +9,25 @@ public final class SubsetSum {
* *
* @param arr the array containing integers. * @param arr the array containing integers.
* @param sum the target sum of the subset. * @param sum the target sum of the subset.
* @return {@code true} if a subset exists that sums to the given value, otherwise {@code false}. * @return {@code true} if a subset exists that sums to the given value,
* otherwise {@code false}.
*/ */
public static boolean subsetSum(int[] arr, int sum) { public static boolean subsetSum(int[] arr, int sum) {
int n = arr.length; int n = arr.length;
boolean[][] isSum = new boolean[n + 1][sum + 1];
// Initialize the first column to true since a sum of 0 can always be achieved with an empty subset. // Initialize a single array to store the possible sums
for (int i = 0; i <= n; i++) { boolean[] isSum = new boolean[sum + 1];
isSum[i][0] = true;
}
// Fill the subset sum matrix // Mark isSum[0] = true since a sum of 0 is always possible with 0 elements
for (int i = 1; i <= n; i++) { isSum[0] = true;
for (int j = 1; j <= sum; j++) {
if (arr[i - 1] <= j) { // Iterate through each Element in the array
isSum[i][j] = isSum[i - 1][j] || isSum[i - 1][j - arr[i - 1]]; for (int i = 0; i < n; i++) {
} else { // Traverse the isSum array backwards to prevent overwriting values
isSum[i][j] = isSum[i - 1][j]; for (int j = sum; j >= arr[i]; j--) {
} isSum[j] = isSum[j] || isSum[j - arr[i]];
} }
} }
return isSum[sum];
return isSum[n][sum];
} }
} }