[Leetcode] 631. Design Excel Sum Formula 解题报告

题目：

Your task is to design the basic function of Excel and implement the function of sum formula. Specifically, you need to implement the following functions:

Excel(int H, char W): This is the constructor. The inputs represents the height and width of the Excel form. H is a positive integer, range from 1 to 26. It represents the height. W is a character range from 'A' to 'Z'. It represents that the width is the number of characters from 'A' to W. The Excel form content is represented by a height * width 2D integer array C, it should be initialized to zero. You should assume that the first row of C starts from 1, and the first column of C starts from 'A'.

void Set(int row, char column, int val): Change the value at C(row, column) to be val.

int Get(int row, char column): Return the value at C(row, column).

int Sum(int row, char column, List of Strings : numbers): This function calculate and set the value at C(row, column), where the value should be the sum of cells represented by numbers. This function return the sum result at C(row, column). This sum formula should exist until this cell is overlapped by another value or another sum formula.

numbers is a list of strings that each string represent a cell or a range of cells. If the string represent a single cell, then it has the following format : ColRow. For example, "F7" represents the cell at (7, F).

If the string represent a range of cells, then it has the following format : ColRow1:ColRow2. The range will always be a rectangle, and ColRow1 represent the position of the top-left cell, and ColRow2 represents the position of the bottom-right cell.

Example 1:

Excel(3,"C"); 
// construct a 3*3 2D array with all zero.
//   A B C
// 1 0 0 0
// 2 0 0 0
// 3 0 0 0

Set(1, "A", 2);
// set C(1,"A") to be 2.
//   A B C
// 1 2 0 0
// 2 0 0 0
// 3 0 0 0

Sum(3, "C", ["A1", "A1:B2"]);
// set C(3,"C") to be the sum of value at C(1,"A") and the values sum of the rectangle range whose top-left cell is C(1,"A") and bottom-right cell is C(2,"B"). Return 4. 
//   A B C
// 1 2 0 0
// 2 0 0 0
// 3 0 0 4

Set(2, "B", 2);
// set C(2,"B") to be 2. Note C(3, "C") should also be changed.
//   A B C
// 1 2 0 0
// 2 0 2 0
// 3 0 0 6

Note:

1. You could assume that there won't be any circular sum reference. For example, A1 = sum(B1) and B1 = sum(A1).
2. The test cases are using double-quotes to represent a character.
3. Please remember to RESET your class variables declared in class Excel, as static/class variables are persisted across multiple test cases. Please see here for more details.

思路：

这道题目也是hard模式的，而且难的“名副其实”。我自己写的代码肯定是很长效率很差的，这里翻译一段网上的代码及其相应的解释：

1）当一个cell改变时，所有与之相关的sum都需要做相应的update，所以我们记录一个fward，记录从一个cell到其所影响的所有sum的位置。而由于一个cell对另外一个cell的影响有可能是多次的（例如重合区域），所以我们用unordered_map<cell, unordered_map<cell, weight>>来表示。采用weight可以提高update的效率。

2）当一个cell的值被reset之后，或者被赋予一个新的range之后，所有原来影响它的cell都应该失效，所以我们还需要一个bward，用来建立影响某个cell的所有源cell。

为了方便，我们用row *26 + col来作为Excel表格的key，这样就可以将二维数组完全映射到一维上。

代码：

class Excel {
public:
    Excel(int H, char W) {
        exl = vector<vector<int>>(H + 1, vector<int>(W - 'A' + 1, 0));
        fward.clear();
        bward.clear();
    }
    
    void set(int r, char c, int v) {
        int col = c - 'A';
        int key = r * 26 + col;
        update(r, col, v);          // update its value and all the sum related
        if (bward.count(key)) {     // reset, so break all the forward links if existing
            for (int k : bward[key]) {
                fward[k].erase(key);
            }
            bward[key].clear();
        }
    }
    
    int get(int r, char c) {
        return exl[r][c - 'A'];
    }
    
    int sum(int r, char c, vector<string> strs) {
        int col = c - 'A', key = r * 26 + col, ans = 0;
        if (bward.count(key)) {     // another reset for position (r, c)
            for (int k:bward[key]) {
                fward[k].erase(key);
            }
            bward[key].clear();
        }
        for (string str:strs) {     // get the sum over multiple ranges
            int p = str.find(':'), left, right, top, bot;
            left = str[0] - 'A';
            right = str[p + 1] - 'A';
            if (p == -1) {
                top = stoi(str.substr(1));
            }
            else {
                top = stoi(str.substr(1, p - 1));
            }
            bot = stoi(str.substr(p + 2));
            for (int i = top; i <= bot; ++i) {
                for (int j = left; j <= right; ++j) {
                    ans += exl[i][j];
                    ++fward[i * 26 + j][key];
                    bward[key].insert(i * 26 + j);  
                }
            }
        }
        update(r, col, ans);    // update this cell and all the sum related
        return ans;
    }
private:
    void update(int r, int col, int v) {
        // update a cell and all the sum related, using BFS
        int prev = exl[r][col];
        exl[r][col] = v;
        queue<int> q;           // q is keys for cells in next level
        queue<int> update;      // update is the increment for each cell
        q.push(r * 26 + col);
        update.push(v - prev);
        while (!q.empty()) {
            int key = q.front(), dif = update.front();
            q.pop(), update.pop();
            if(fward.count(key)) {
                for (auto it = fward[key].begin(); it != fward[key].end(); ++it) {
                    int k = it->first;
                    q.push(k);
                    update.push(dif * (it->second));
                    exl[k / 26][k % 26] += dif * (it->second);
                }
            }
        }
    }
    // The key of a cell is defined as 26 * row + col, which is int
    vector<vector<int>> exl;
    // fward links a cell to all the cells which use it for sum, and it may be used for 
    // multiple times due to overlap ranges, so another map is used for its weight 
    unordered_map<int, unordered_map<int, int>> fward;
    // bward links a cell to all the cells that contribute to its sum. When reset its value,
    // or reassign a new sum range to it, we need disconnect the forward link of those cells to it.
    unordered_map<int, unordered_set<int>> bward;
};

/**
 * Your Excel object will be instantiated and called as such:
 * Excel obj = new Excel(H, W);
 * obj.set(r,c,v);
 * int param_2 = obj.get(r,c);
 * int param_3 = obj.sum(r,c,strs);
 */