Added solution for problem 12

Author: Scott Weeden-Moody

12/README.md

@@ -0,0 +1,52 @@
+# Project Euler - Problem #11
+
+## Highly divisible triangluar number
+
+### Problem 12
+
+The sequence of triangle numbers is generated by adding the natural numbers. So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten terms would be:
+
+1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
+
+Let us list the factors of the first seven triangle numbers:
+
+     1: 1
+     3: 1,3
+     6: 1,2,3,6
+    10: 1,2,5,10
+    15: 1,3,5,15
+    21: 1,3,7,21
+    28: 1,2,4,7,14,28
+
+We can see that 28 is the first triangle number to have over five divisors.
+
+What is the value of the first triangle number to have over five hundred divisors?
+
+---------
+
+A very straightforward problem at a high level. For each triangle number starting from the first, find the divisors.
+If the count of the divisor list exceeds 500, you found the number.
+
+Generating triangle numbers iteratively is easy as each subsequent triangle number is the previous one plus
+the next number. Computing divisors can be done by finding prime divisors and multiplying the exponents.
+Alternatively, you can just brute force it and wait ~20 minutes.
+
+Answer: 76576500
+
+---------
+
+--License--
+
+Copyright 2019 Scott Weeden-Moody
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this project except in compliance with the License.
+You may obtain a copy of the License at
+ 
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.

12/build.gradle

@@ -0,0 +1,43 @@
+/*
+ * Copyright 2016 Scott Weeden-Moody
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this project except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+apply plugin: 'kotlin'
+
+buildscript {
+    ext.kotlin_version = '1.3.50'
+    repositories {
+        mavenCentral()
+    }
+    dependencies {
+        classpath "org.jetbrains.kotlin:kotlin-gradle-plugin:$kotlin_version"
+    }
+}
+repositories {
+    mavenCentral()
+}
+dependencies {
+    implementation "org.jetbrains.kotlin:kotlin-stdlib-jdk8:$kotlin_version"
+}
+compileKotlin {
+    kotlinOptions {
+        jvmTarget = "1.8"
+    }
+}
+compileTestKotlin {
+    kotlinOptions {
+        jvmTarget = "1.8"
+    }
+}

12/src/main/kotlin/com/lillicoder/projecteuler/Problem12.kt

@@ -0,0 +1,87 @@
+/*
+ * Copyright 2019 Scott Weeden-Moody
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this project except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.lillicoder.projecteuler
+
+import kotlin.math.ceil
+import kotlin.math.sqrt
+
+/**
+ * Project Euler - Problem #12
+ *
+ * Highly divisible triangular number
+ *
+ * Problem 12
+ *
+ * The sequence of triangle numbers is generated by adding the natural numbers. So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten terms would be:
+ *
+ * 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
+ *
+ * Let us list the factors of the first seven triangle numbers:
+ *
+ * 1: 1
+ * 3: 1,3
+ * 6: 1,2,3,6
+ * 10: 1,2,5,10
+ * 15: 1,3,5,15
+ * 21: 1,3,7,21
+ * 28: 1,2,4,7,14,28
+ *
+ * We can see that 28 is the first triangle number to have over five divisors.
+ *
+ * What is the value of the first triangle number to have over five hundred divisors?
+ */
+
+fun main() {
+    val divisorCount = 500
+    val triangleNumber = Problem12().withDivisorCount(divisorCount)
+    println("The triangle number with more than $divisorCount divisors is: $triangleNumber")
+}
+
+class Problem12 {
+
+    fun withDivisorCount(count: Int): Long {
+        var current = 0L
+        var iteration = 1
+
+        var didFind = false
+        while (!didFind) {
+            current = nextTriangleNumber(current, iteration)
+            val divisors = divisors(current)
+            if (divisors.size > count) didFind = true
+
+            println("[debug] Triangle number: $current, divisorCount: ${divisors.size}, divisors: $divisors")
+            iteration++
+        }
+
+        return current
+    }
+
+    private fun divisors(number: Long): List<Long> {
+        val divisors = mutableListOf(number)
+        val half = number / 2
+        for (divisor in 1..half) {
+            if (number % divisor == 0.toLong()) divisors.add(divisor)
+        }
+
+        return divisors
+    }
+
+    private fun nextTriangleNumber(lastTriangleNumber: Long, iteration: Int): Long {
+        return lastTriangleNumber + iteration;
+    }
+
+}

settings.gradle

@@ -9,3 +9,4 @@ include ":08"
 include ":09"
 include ":10"
 include ":11"
+include ":12"