Leetcode 1146: Snapshot Array

https://leetcode.com/problems/snapshot-array/description/

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Implement a SnapshotArray that supports the following interface:

• SnapshotArray(int length) initializes an array-like data structure with the given length.  Initially, each element equals 0.
• void set(index, val) sets the element at the given index to be equal to val.
• int snap() takes a snapshot of the array and returns the snap_id: the total number of times we called snap() minus 1.
• int get(index, snap_id) returns the value at the given index, at the time we took the snapshot with the given snap_id

Example 1:

Input: ["SnapshotArray","set","snap","set","get"]
[[3],[0,5],[],[0,6],[0,0]]
Output: [null,null,0,null,5]
Explanation: 
SnapshotArray snapshotArr = new SnapshotArray(3); // set the length to be 3
snapshotArr.set(0,5);  // Set array[0] = 5
snapshotArr.snap();  // Take a snapshot, return snap_id = 0
snapshotArr.set(0,6);
snapshotArr.get(0,0);  // Get the value of array[0] with snap_id = 0, return 5

Constraints:

• 1 <= length <= 50000
• At most 50000 calls will be made to set, snap, and get.
• 0 <= index < length
• 0 <= snap_id < (the total number of times we call snap())
• 0 <= val <= 10^9

Notes:

The size of the array can be very large, and the query number can also be very large. Thus, updating the entire array for every snapshot is not a good idea.

Instead, we just need to update the element that is changed. And we can store this information in a sorted order relative to the snap_id. And the snap_id is monotonically increases.

After storing this information, for getting the value at a specific snap_id, we just need to do a binary search at that index, since the snap_id is sorted.

To this question, we need to find the upper boundary of the snap_id first, then -1 if it is not 0. The reason to do the upper boundary searching is that, we did not update the snap_id for every element, and only update the one when it is changed.

See the code below:

class SnapshotArray {
public:
    SnapshotArray(int length) {
        //initialization
        ct = 0;
        for(int i=0; i<length; ++i) {
            ns.push_back(vector<pair<int, int>>{{ct, 0}});
        }
    }

    void set(int index, int val) {
        ns[index].push_back({ct, val});
    }

    int snap() {
        return ct++;
    }

    int get(int index, int snap_id) {
        int ps = help(ns, index, snap_id);
        if(ps>0) --ps;
        return ns[index][ps].second;
    }

private:
    vector<vector<pair<int, int>>> ns;
    int ct;
    int help(vector<vector<pair<int, int>>> &ns, int i, int id) {
        int left = 0, right = ns[i].size();
        while(left < right) {
            int mid = left + (right - left) /2;
            if(ns[i][mid].first <= id) left = mid + 1;
            else right = mid;
        }
        return left;
    }
};

/**
 * Your SnapshotArray object will be instantiated and called as such:
 * SnapshotArray* obj = new SnapshotArray(length);
 * obj->set(index,val);
 * int param_2 = obj->snap();
 * int param_3 = obj->get(index,snap_id);
 */