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Problem solution · Java

Maximum Score of Non-overlapping Intervals

Maximum Score of Non-overlapping Intervals: a Java solution using dynamic programming. Learn the idea, check the complexity, and read the full code, with credit to walkccc LeetCode Solutions.

Technique
Dynamic programming
Source
walkccc LeetCode Solutions
Length
65 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

Dynamic programming

For Maximum Score of Non-overlapping Intervals, the implementation records answers for smaller states and reuses them to build the requested result without repeating work.

  1. Define precisely what one DP state represents.
  2. Establish the base cases before transitions are evaluated.
  3. Process states in dependency order and combine only already-known values.

Code notes

  • 65 lines of Java from the credited upstream file 3414.java.
  • The implementation visibly relies on sequence storage, cached states.
  • 3 loop blocks detected.

Complexity

Multiply the number of reachable states by the work performed for each transition, then include the stored state table in memory usage.

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 codeMaximum Score of Non-overlapping Intervals · JavaJava
Use this to learn the idea, then write your own version.
class Solution {  public int[] maximumWeight(List<List<Integer>> intervals) {    // Convert input to Interval objects    List<Interval> indexedIntervals = new ArrayList<>();    for (int i = 0; i < intervals.size(); ++i) {      List<Integer> interval = intervals.get(i);      indexedIntervals.add(new Interval(interval.get(0), interval.get(1), interval.get(2), i));    }    indexedIntervals.sort(Comparator.comparingInt(Interval::left));    T[][] memo = new T[indexedIntervals.size()][5];    return dp(indexedIntervals, memo, 0, 4).selected.stream().mapToInt(Integer::intValue).toArray();  }   private record T(long weight, List<Integer> selected) {}  private record Interval(int left, int right, int weight, int originalIndex) {}   private T dp(List<Interval> intervals, T[][] memo, int i, int quota) {    if (i == intervals.size() || quota == 0)      return new T(0, List.of());    if (memo[i][quota] != null)      return memo[i][quota];     T skip = dp(intervals, memo, i + 1, quota);     Interval interval = intervals.get(i);    final int j = findFirstGreater(intervals, i + 1, interval.right);    T nextRes = dp(intervals, memo, j, quota - 1);     List<Integer> newSelected = new ArrayList<>(nextRes.selected);    newSelected.add(interval.originalIndex);    Collections.sort(newSelected);    T pick = new T(interval.weight + nextRes.weight, newSelected);    return memo[i][quota] =               (pick.weight > skip.weight ||                (pick.weight == skip.weight && compareLists(pick.selected, skip.selected) < 0))                   ? pick                   : skip;  }   // Binary searches the first interval that starts after `rightBoundary`.  private int findFirstGreater(List<Interval> intervals, int startFrom, int rightBoundary) {    int l = startFrom;    int r = intervals.size();    while (l < r) {      final int m = (l + r) / 2;      if (intervals.get(m).left > rightBoundary)        r = m;      else        l = m + 1;    }    return l;  }   // Compares two lists of integers lexicographically.  private int compareLists(List<Integer> list1, List<Integer> list2) {    final int minSize = Math.min(list1.size(), list2.size());    for (int i = 0; i < minSize; ++i) {      final int comparison = Integer.compare(list1.get(i), list2.get(i));      if (comparison != 0)        return comparison;    }    return Integer.compare(list1.size(), list2.size());  }}

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