Create building-boxes.cpp

Author: kamyu104

C++/building-boxes.cpp

@@ -0,0 +1,18 @@
+// Time:  O(1)
+// Space: O(1)
+
+class Solution {
+public:
+    int minimumBoxes(int n) {
+        // find max h s.t. sum(k*(k+1)//2 for k in xrange(1, h+1)) <= n
+        // => find max h s.t. h*(h+1)*(h+2)//6 <= n
+        int h = pow(6.0 * n, 1.0 / 3);
+        if (int64_t(h) * (h + 1) * (h + 2) / 6 > n) {
+            // (h-1)*h*(h+1) < h^3 <= 6n < h*(h+1)*(h+2) < (h+1)^3
+            --h;
+        }
+        n -= int64_t(h) * (h + 1) * (h + 2) / 6;
+        int d = ceil((-1 + sqrt(1 + 8 * n)) / 2);  // find min d s.t. d*(d+1)//2 >= n
+        return h * (h + 1) / 2 + d;
+    }
+};