Create minimum-cost-to-cut-a-stick.cpp

Author: kamyu104

C++/minimum-cost-to-cut-a-stick.cpp

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+// Time:  O(n^3)
+// Space: O(n^2)
+
+class Solution {
+public:
+    int minCost(int n, vector<int>& cuts) {
+        vector<int> sorted_cuts(cbegin(cuts), cend(cuts));
+        sorted_cuts.emplace_back(0);
+        sorted_cuts.emplace_back(n);
+        sort(begin(sorted_cuts), end(sorted_cuts));
+
+        vector<vector<int>> dp(sorted_cuts.size(), vector<int>(sorted_cuts.size()));
+        for (int l = 2; l < sorted_cuts.size(); ++l) {
+            for (int i = 0; i + l < sorted_cuts.size(); ++i) {
+                dp[i][i + l]  = numeric_limits<int>::max();
+                for (int j = i + 1; j < i + l; ++j) {
+                    dp[i][i + l]  = min(dp[i][i + l], dp[i][j] + dp[j][i + l] +
+                                    sorted_cuts[i + l] - sorted_cuts[i]);
+                }
+            }
+        }
+        return dp[0][sorted_cuts.size() - 1];
+    }
+};