## Problem

Problem ID: 631

Title: Design Excel Sum Formula

Difficulty: Hard

Description: Design the basic function of Excel and implement the function of the sum formula.

## Thoughts

At first glance, this question seem very complicated but once you can identify that the transitive property of sum means that we would need to perform some sort of search to traverse all connected neighbours. The tricky part of this question is in the implementation.

## Solution

The general idea to this problem is to maintain 2 separate board, one for keep tracking of the values that was set and another one for keeping track the grids that it is a sum of.

Data Structures:

• vector<vector<int>> m_sheets: Represents an excel spreadsheet where m_sheets[i][j] stores the value set at row = i+1 and column = 'A' + j
• When m_sheets[i][j] = NullVal this means that the grid’s value is a sum of other grids and should be looked up on m_sums instead.
• vector<vector<vector<pair<int,int>>>> m_sums: Represents the sum data. m_sums[i][j] is a list of other grids [<i1,j1>, <i2,j2>,...] that it is a sum of.

Handling:

• get: We will set the provided grid as our source and perform bfs. We will continue searching till m_sheets[i][j] != NullVal.
• sum: We will use the provided data to updated m_sums. For range of cells, we will iterate deconstruct the range into individual cells.
• We will set the grid on m_sheets to NullVal to indicate that the grid does not have any values.
• set: We will update the m_sheets and clear the data in the corresponding m_sums as it would override the previous sum formula.

### Implementation

class Excel {
private:
// [i][j] = val
vector<vector<int>> m_sheets;
// [i][j] = [<i1,j1>, ...]
vector<vector<vector<pair<int,int>>>> m_sums;
int m_n;
int m_m;
int NullVal = INT_MAX;

inline const pair<int,int> ExtractGrid(const string& grid) {
assert(2 <= grid.length() && grid.length() <= 3);

int row = 0;
for (int row_i = 1; row_i < grid.size(); row_i++) {
assert(isdigit(grid[row_i]));
row *=10;
row += (grid[row_i] - '0');
}
return {GetI(row),GetJ(grid[0])};
}

inline const vector<pair<int,int>> ExtractRange(string range) {
assert(5 <= range.length() && range.length() <= 7);

size_t colon_pos = range.find(':');
string start_grid_s = range.substr(0, colon_pos);
range.erase(0, colon_pos +1);
string end_grid_s = move(range);
const auto [s_i, s_j] = ExtractGrid(start_grid_s);
const auto [t_i, t_j] = ExtractGrid(end_grid_s);
vector<pair<int,int>> ret;
for (int i = s_i; i <= t_i; i++) {
for (int j = s_j; j <= t_j; j++) {
ret.emplace_back(i,j);
}
}
return ret;
}

constexpr inline int GetI(int row) {
return row - 1;
}
constexpr inline int GetJ(char column) {
return column - 'A';
}

constexpr inline bool IsRange(const string& grid) {
return grid.find(':') != std::string::npos;
}

inline vector<pair<int,int>> GetSumOf(const vector<string>& numbers) {
vector<pair<int,int>> v_grids;
for (const string& num : numbers) {
if (IsRange(num)) {
vector<pair<int,int>> curr_v_grids = ExtractRange(num);
v_grids.insert(v_grids.end(), curr_v_grids.begin(), curr_v_grids.end());
} else {
v_grids.push_back(ExtractGrid(num));
}
}
return v_grids;
}

public:
Excel(int height, char width) {
int m_n = height;
int m_m = width - 'A'  +1;
m_sheets = vector<vector<int>>(m_n, vector<int>(m_m, 0));
m_sums = vector<vector<vector<pair<int,int>>>>(m_n, vector<vector<pair<int,int>>>(m_m));
}

void set(int row, char column, int val) {
int i = GetI(row);
int j = GetJ(column);
m_sums[i][j].clear();
m_sheets[i][j] = val;
}

int Get(int s_i, int s_j) {
int sum = 0;
queue<pair<int,int>> q;
q.push({s_i,s_j});
while(!q.empty()) {
auto [i,j] = q.front();
q.pop();
if (m_sheets[i][j] == NullVal) {
for (const auto [v_i, v_j] : m_sums[i][j]) {
q.push({v_i, v_j});
}
} else {
sum += m_sheets[i][j];
}
}
return sum;
}

int get(int row, char column) {
return Get(GetI(row), GetJ(column));
}

int sum(int row, char column, vector<string> numbers) {
vector<pair<int,int>> v_grids = GetSumOf(numbers);
int i = GetI(row);
int j = GetJ(column);
m_sheets[i][j] = NullVal;
m_sums[i][j] = v_grids;
return get(row, column);
}
};