CPMagical CP Library

Problem solution · Java

Minimum Sum of Squared Difference

Minimum Sum of Squared Difference: a Java solution using breadth-first search. Learn the idea, check the complexity, and read the full code, with credit to walkccc LeetCode Solutions.

Technique
Breadth-first search
Source
walkccc LeetCode Solutions
Length
57 lines
Start with the idea.

Try the problem first. If you get stuck, read the approach below, then write your own solution. The full code is at the bottom.

Approach

Breadth-first search

For Minimum Sum of Squared Difference, the implementation explores reachable states in layers, which is the standard shape for unweighted shortest paths and minimum-step transitions.

  1. Model each valid configuration as a state and each legal move as an edge.
  2. Seed the queue with the starting state and mark it immediately.
  3. Expand each state once, recording distance or reachability for unseen neighbours.

Code notes

  • 57 lines of Java from the credited upstream file 2333.java.
  • The implementation visibly relies on sequence storage, hash lookup, ordered lookup, work queue.
  • 5 loop blocks detected.

Complexity

Verify that each state and transition is processed only a bounded number of times; that determines the traversal cost.

Check the problem constraints before deciding whether this complexity will pass.

Source

Code and credit

This code comes from walkccc LeetCode Solutions by P.-Y. Chen (walkccc) and is used under the MIT licence.

Open problem ↗Original source ↗
Full codeMinimum Sum of Squared Difference · JavaJava
Use this to learn the idea, then write your own version.
class Solution {  public long minSumSquareDiff(int[] nums1, int[] nums2, int k1, int k2) {    int[] diff = getDiff(nums1, nums2);    int k = k1 + k2;    if (Arrays.stream(diff).asLongStream().sum() <= k)      return 0;     Map<Integer, Integer> count = new HashMap<>();    // (num, freq)    Queue<Pair<Integer, Integer>> maxHeap =        new PriorityQueue<>(Comparator.comparing(Pair::getKey, Comparator.reverseOrder()));     for (final int d : diff)      if (d != 0)        count.merge(d, 1, Integer::sum);     for (Map.Entry<Integer, Integer> entry : count.entrySet())      maxHeap.offer(new Pair<>(entry.getKey(), entry.getValue()));     while (k > 0) {      Pair<Integer, Integer> pair = maxHeap.poll();      final int maxNum = pair.getKey();      final int maxNumFreq = pair.getValue();      // Buck decrease in this turn      final int numDecreased = Math.min(k, maxNumFreq);      k -= numDecreased;      if (maxNumFreq > numDecreased)        maxHeap.offer(new Pair<>(maxNum, maxNumFreq - numDecreased));      if (!maxHeap.isEmpty() && maxHeap.peek().getKey() + 1 == maxNum) {        Pair<Integer, Integer> secondNode = maxHeap.poll();        final int secondMaxNum = secondNode.getKey();        final int secondMaxNumFreq = secondNode.getValue();        maxHeap.offer(new Pair<>(secondMaxNum, secondMaxNumFreq + numDecreased));      } else if (maxNum > 1) {        maxHeap.offer(new Pair<>(maxNum - 1, numDecreased));      }    }     long ans = 0;    while (!maxHeap.isEmpty()) {      Pair<Integer, Integer> pair = maxHeap.poll();      final int num = pair.getKey();      final int freq = pair.getValue();      ans += (long) num * num * freq;    }     return ans;  }   private int[] getDiff(int[] nums1, int[] nums2) {    int[] diff = new int[nums1.length];    for (int i = 0; i < nums1.length; ++i)      diff[i] = Math.abs(nums1[i] - nums2[i]);    return diff;  }}

Keep practising

Did this explanation save you time? I'm a Grade 11 student building this free library to make difficult algorithms easier to understand.

Buy me a coffee ↗