# C++ Simple Solution with Explanation

• two rules:

1. The sum of rectangles' area must equal to the final rectangle
2. No overlap (Edge points exist 1 times)
``````class Solution {
public:
bool isRectangleCover(vector<vector<int>>& rectangles) {
int area = 0, bot_x = INT_MAX, bot_y = INT_MAX, top_x = INT_MIN, top_y = INT_MIN;
unordered_map<int, unordered_map<int, int>> mp;
for (auto& rec : rectangles) {
int x1 = rec[0], y1 = rec[1], x2 = rec[2], y2 = rec[3];
area += (y2 - y1) * (x2 - x1);
mp[x1][y1]++;
mp[x2][y2]++;
mp[x1][y2]++;
mp[x2][y1]++;
bot_x = min(bot_x, x1);
bot_y = min(bot_y, y1);
top_x = max(top_x, x2);
top_y = max(top_y, y2);
}
if ((top_x - bot_x) * (top_y - bot_y) != area) { // area judge
return false;
}
for (auto& i : mp) {
for (auto& j : i.second) {
if ((i.first == bot_x || i.first == top_x) && (j.first == bot_y || j.first == top_y) && j.second != 1)
return false; // edge points can only exist 1 times
if (j.second & 1) { // points which exist even times must be edge points
if ((i.first == bot_x || i.first == top_x) && (j.first == bot_y || j.first == top_y))
continue;
return false;
}
}
}
return true;
}
};
``````

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