complete 1764.cpp 10816.cpp 25793.kt

storage/zeta/kt/completed/25793.kt

@@ -0,0 +1,36 @@
+import kotlin.math.min
+
+fun chocolatePyramidSum(r: Int, c: Int): Long {
+    val m = min(r, c).toLong()
+    return m * (4 * m * m - 6 * m * (r.toLong() + c.toLong()) + 12 * r.toLong() * c.toLong() - 1) / 3
+}
+
+fun chocolatePyramidDark(r: Int, c: Int): Long {
+    val m = min(r, c).toLong()
+    return m * (2 * m * m - 3 * m * (r.toLong() + c.toLong()) + 6 * r.toLong() * c.toLong() - 2) / 3
+}
+
+fun chocolatePyramid(r: Int, c: Int): Pair<Long, Long> {
+    // W(r, c) = (r * c) + (r-1) * (c-1) + D(r-1, c-1)
+    // D(r, c) = (r - 1) * c + r * (c-1) + W(r-1, c-1)
+    // therefore,
+    // W(r, c) = (r * c) + 2*(r-1)*(c-1) ...(until r-k or c-k is equal to 0)
+    // D(r, c) = (r - 1) * c + r * (c-1) + (r-2) * (c-1) + (r - 1) * (c-2)
+    //(r*c) + (r-1) * c + r * (c-1) + (r-1) * (c-1)
+    // S(r, c) = (2r-1)(2c-1) + S(r-1, c-1)
+
+    val s = chocolatePyramidSum(r, c)
+    val d = chocolatePyramidDark(r, c)
+    return s - d to d
+}
+
+fun main() = with(System.`in`.bufferedReader()) {
+    val t = this.readLine().toInt()
+    repeat(t) {
+        val (r, c) = this.readLine().split(" ").map { it.toInt() }
+
+        println(chocolatePyramid(r, c).let {
+            "${it.first} ${it.second}"
+        })
+    }
+}