complete 11057.kt 15835.kt 20411.kt 25345.kt 28242.kt 32628.kt

storage/zeta/kt/completed/28242.kt

@@ -0,0 +1,52 @@
+fun divisors(n: Long): List<Pair<Long, Long>> {
+    val res = mutableListOf<Pair<Long, Long>>()
+
+    var i = 1L
+
+    while (i * i <= n) {
+        if (n % i == 0L) {
+            res.add(i to n / i)
+            if (i != n / i) {
+                res.add(n / i to i)
+            }
+        }
+        i++
+    }
+
+    return res
+}
+
+
+fun main() {
+    val n = readln().toLong()
+
+    // nx^2 + (n+1)x -(n+2)
+    // = (ax+b)(cx+d)
+    // = acx^2 + (ad + bc)x + bd
+
+    // 다음 조건을 만족하는 a > 0, b, c > 0,d를 구하는 프로그램을 작성하시오.
+    // n = a * c
+    // (n+1) = a * d + b * c
+    // b * d = -(n+2)
+
+
+    divisors(n).flatMap { first ->
+        divisors(n + 2).let {
+            it.map {
+                it.first to -it.second
+            } + it.map {
+                -it.first to it.second
+            }
+        }.map {
+            first to it
+        }
+    }.firstOrNull { (first, second) ->
+        val (a, c) = first
+        val (b, d) = second
+        n + 1 == a * d + b * c
+    }?.let { (first, second) ->
+        val (a, c) = first
+        val (b, d) = second
+        println("$a $b $c $d")
+    } ?: println(-1)
+}