动态规划（17）

原题：

/** * Created by gouthamvidyapradhan on 19/08/2017. * Initially on a notepad only one character 'A' is present. You can perform two operations on this notepad for each step: * <p> * Copy All: You can copy all the characters present on the notepad (partial copy is not allowed). * Paste: You can paste the characters which are copied last time. * Given a number n. You have to get exactly n 'A' on the notepad by performing the minimum number of steps permitted. Output the minimum number of steps to get n 'A'. * <p> * Example 1: * Input: 3 * Output: 3 * Explanation: * Intitally, we have one character 'A'. * In step 1, we use Copy All operation. * In step 2, we use Paste operation to get 'AA'. * In step 3, we use Paste operation to get 'AAA'. * <p> * Note: * The n will be in the range [1, 1000]. */

答案：

public class TwoKeysKeyboard {    /**     * Main method     *     * @param args     * @throws Exception     */    public static void main(String[] args) throws Exception {        System.out.println(new TwoKeysKeyboard().minSteps(8));    }    public int minSteps(int n) {        int[] DP = new int[n + 1];        for (int i = 2; i <= n; i++) {            DP[i] = i;            for (int j = 2; j < i; j++) {                if ((i % j) == 0) {                    DP[i] = Math.min(DP[i], DP[j] + (i / j));                }            }        }        return DP[n];    }}