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| 1 | +/// Source : https://leetcode.com/problems/selling-pieces-of-wood/ |
| 2 | +/// Author : liuyubobobo |
| 3 | +/// Time : 2022-06-21 |
| 4 | + |
| 5 | +#include <iostream> |
| 6 | +#include <vector> |
| 7 | +#include <map> |
| 8 | + |
| 9 | +using namespace std; |
| 10 | + |
| 11 | + |
| 12 | +/// DP |
| 13 | +/// Time Complexity: O(m * n * (m + n)) |
| 14 | +/// Space Complexity: O(m * n) |
| 15 | +class Solution { |
| 16 | +public: |
| 17 | + long long sellingWood(int m, int n, vector<vector<int>>& prices) { |
| 18 | + |
| 19 | + vector<vector<long long>> dp(m + 1, vector<long long>(n + 1, 0)); |
| 20 | + vector<vector<bool>> visited(m + 1, vector<bool>(n + 1, false)); |
| 21 | + |
| 22 | + for(const vector<int>& price: prices){ |
| 23 | + int h = price[0], w = price[1], p = price[2]; |
| 24 | + dp[h][w] = max(dp[h][w], 1ll * p); |
| 25 | + } |
| 26 | + |
| 27 | + return dfs(m, n, dp, visited); |
| 28 | + } |
| 29 | + |
| 30 | +private: |
| 31 | + long long dfs(int m, int n, vector<vector<long long>>& dp, vector<vector<bool>>& visited){ |
| 32 | + |
| 33 | + if(visited[m][n]) return dp[m][n]; |
| 34 | + |
| 35 | + long long res = dp[m][n]; |
| 36 | + for(int top = 1; top <= m - 1; top ++) |
| 37 | + res = max(res, dfs(top, n, dp, visited) + dfs(m - top, n, dp, visited)); |
| 38 | + for(int left = 1; left <= n - 1; left ++) |
| 39 | + res = max(res, dfs(m, left, dp, visited) + dfs(m, n - left, dp, visited)); |
| 40 | + |
| 41 | + visited[m][n] = true; |
| 42 | + return dp[m][n] = res; |
| 43 | + } |
| 44 | +}; |
| 45 | + |
| 46 | + |
| 47 | +int main() { |
| 48 | + |
| 49 | + vector<vector<int>> prices1 = {{1, 4, 2}, {2, 2, 7}, {2, 1, 3}}; |
| 50 | + cout << Solution().sellingWood(3, 5, prices1) << '\n'; |
| 51 | + // 19 |
| 52 | + |
| 53 | + vector<vector<int>> prices2 = {{3, 2, 10}, {1, 4, 2}, {4, 1, 3}}; |
| 54 | + cout << Solution().sellingWood(4, 6, prices2) << '\n'; |
| 55 | + // 32 |
| 56 | + |
| 57 | + vector<vector<int>> prices3 = {{4, 1, 18}, {4, 2, 5}, {1, 1, 20}, {3, 1, 21}}; |
| 58 | + cout << Solution().sellingWood(4, 2, prices3) << '\n'; |
| 59 | + // 160 |
| 60 | + |
| 61 | + return 0; |
| 62 | +} |
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