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Problem solution · C++

Earliest Second to Mark Indices II

Earliest Second to Mark Indices II: a C++ solution using sliding window or two pointers. Learn the idea, check the complexity, and read the full code, with credit to walkccc LeetCode Solutions.

Technique
Sliding window or two pointers
Source
walkccc LeetCode Solutions
Length
87 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

Sliding window or two pointers

For Earliest Second to Mark Indices II, the implementation maintains a moving interval and updates only the information that enters or leaves the window.

  1. Choose the invariant that makes a window valid or useful.
  2. Advance the right boundary and add the new element.
  3. Move the left boundary only as needed while maintaining the invariant and updating the answer.

Code notes

  • 87 lines of C++ from the credited upstream file 3049.cpp.
  • The implementation visibly relies on sequence storage, hash lookup, work queue.
  • 5 loop blocks detected.

Complexity

Confirm that neither pointer moves backwards; if so, the scan is usually linear apart from the window’s data-structure operations.

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 codeEarliest Second to Mark Indices II · C++C++
Use this to learn the idea, then write your own version.
class Solution { public:  int earliestSecondToMarkIndices(vector<int>& nums,                                  vector<int>& changeIndices) {    const long numsSum = accumulate(nums.begin(), nums.end(), 0L);    // {the second: the index of nums can be zeroed at the current second}    const unordered_map<int, int> secondToIndex =        getSecondToIndex(nums, changeIndices);    int l = 0;    int r = changeIndices.size() + 1;     while (l < r) {      const int m = (l + r) / 2;      if (canMark(nums, secondToIndex, m, numsSum))        r = m;      else        l = m + 1;    }     return l <= changeIndices.size() ? l : -1;  }  private:  // Returns true if all indices of `nums` can be marked within `maxSecond`.  bool canMark(const vector<int>& nums,               const unordered_map<int, int>& secondToIndex, int maxSecond,               const long numsSum) {    // Use a min-heap to greedily pop out the minimum number, which yields the    // least saving.    priority_queue<int, vector<int>, greater<int>> minHeap;    int marks = 0;     for (int second = maxSecond - 1; second >= 0; --second) {      if (const auto it = secondToIndex.find(second);          it != secondToIndex.end()) {        // The number mapped by the index is a candidate to be zeroed out.        const int index = it->second;        minHeap.push(nums[index]);        if (marks == 0) {          // Running out of marks, so need to pop out the minimum number.          // So, the current second will be used to mark an index.          minHeap.pop();          ++marks;        } else {          // There're enough marks.          // So, the current second will be used to zero out a number.          --marks;        }      } else {        // There's no candidate to be zeroed out.        // So, the current second will be used to mark an index.        ++marks;      }    }     const int heapSize = minHeap.size();    const long decrementAndMarkCost =        numsSum - getHeapSum(minHeap) + (nums.size() - heapSize);    const long zeroAndMarkCost = heapSize + heapSize;    return decrementAndMarkCost + zeroAndMarkCost <= maxSecond;  }   long getHeapSum(priority_queue<int, vector<int>, greater<int>>& heap) {    long heapSum = 0;    while (!heap.empty())      heapSum += heap.top(), heap.pop();    return heapSum;  }   unordered_map<int, int> getSecondToIndex(const vector<int>& nums,                                           const vector<int>& changeIndices) {    // {the `index` of nums: the earliest second to zero out nums[index]}    unordered_map<int, int> indexToFirstSecond;    unordered_map<int, int> secondToIndex;    for (int zeroIndexedSecond = 0; zeroIndexedSecond < changeIndices.size();         ++zeroIndexedSecond) {      // Convert to 0-indexed.      const int index = changeIndices[zeroIndexedSecond] - 1;      if (nums[index] > 0 && !indexToFirstSecond.contains(index))        indexToFirstSecond[index] = zeroIndexedSecond;    }    for (const auto& [index, second] : indexToFirstSecond)      secondToIndex[second] = index;    return secondToIndex;  }};

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