Problem_04_CoinsWay

package chapter_4_recursionanddp;

public class Problem_04_CoinsWay {

    public static int coins1(int[] arr, int aim) {
        if (arr == null || arr.length == 0 || aim < 0) {
            return 0;
        }
        return process1(arr, 0, aim);
    }

    public static int process1(int[] arr, int index, int aim) {
        int res = 0;
        if (index == arr.length) {
            res = aim == 0 ? 1 : 0;
        } else {
            for (int i = 0; arr[index] * i <= aim; i++) {
                res += process1(arr, index + 1, aim - arr[index] * i);
            }
        }
        return res;
    }

    public static int coins2(int[] arr, int aim) {
        if (arr == null || arr.length == 0 || aim < 0) {
            return 0;
        }
        int[][] map = new int[arr.length + 1][aim + 1];
        return process2(arr, 0, aim, map);
    }

    public static int process2(int[] arr, int index, int aim, int[][] map) {
        int res = 0;
        if (index == arr.length) {
            res = aim == 0 ? 1 : 0;
        } else {
            int mapValue = 0;
            for (int i = 0; arr[index] * i <= aim; i++) {
                mapValue = map[index + 1][aim - arr[index] * i];
                if (mapValue != 0) {
                    res += mapValue == -1 ? 0 : mapValue;
                } else {
                    res += process2(arr, index + 1, aim - arr[index] * i, map);
                }
            }
        }
        map[index][aim] = res == 0 ? -1 : res;
        return res;
    }

    public static int coins3(int[] arr, int aim) {
        if (arr == null || arr.length == 0 || aim < 0) {
            return 0;
        }
        int[][] dp = new int[arr.length][aim + 1];
        for (int i = 0; i < arr.length; i++) {
            dp[i][0] = 1;
        }
        for (int j = 1; arr[0] * j <= aim; j++) {
            dp[0][arr[0] * j] = 1;
        }
        int num = 0;
        for (int i = 1; i < arr.length; i++) {
            for (int j = 1; j <= aim; j++) {
                num = 0;
                for (int k = 0; j - arr[i] * k >= 0; k++) {
                    num += dp[i - 1][j - arr[i] * k];
                }
                dp[i][j] = num;
            }
        }
        return dp[arr.length - 1][aim];
    }

    public static int coins4(int[] arr, int aim) {
        if (arr == null || arr.length == 0 || aim < 0) {
            return 0;
        }
        int[][] dp = new int[arr.length][aim + 1];
        for (int i = 0; i < arr.length; i++) {
            dp[i][0] = 1;
        }
        for (int j = 1; arr[0] * j <= aim; j++) {
            dp[0][arr[0] * j] = 1;
        }
        for (int i = 1; i < arr.length; i++) {
            for (int j = 1; j <= aim; j++) {
                dp[i][j] = dp[i - 1][j];
                dp[i][j] += j - arr[i] >= 0 ? dp[i][j - arr[i]] : 0;
            }
        }
        return dp[arr.length - 1][aim];
    }

    public static int coins5(int[] arr, int aim) {
        if (arr == null || arr.length == 0 || aim < 0) {
            return 0;
        }
        int[] dp = new int[aim + 1];
        for (int j = 0; arr[0] * j <= aim; j++) {
            dp[arr[0] * j] = 1;
        }
        for (int i = 1; i < arr.length; i++) {
            for (int j = 1; j <= aim; j++) {
                dp[j] += j - arr[i] >= 0 ? dp[j - arr[i]] : 0;
            }
        }
        return dp[aim];
    }

    public static void main(String[] args) {
        int[] coins = { 10, 5, 1, 25 };
        int aim = 2000;

        long start = 0;
        long end = 0;
        System.out.println("===========暴力递归的方法===========");
        start = System.currentTimeMillis();
        System.out.println(coins1(coins, aim));
        end = System.currentTimeMillis();
        System.out.println("cost time : " + (end - start) + "(ms)");

        aim = 20000;

        System.out.println("===========记忆搜索的方法===========");
        start = System.currentTimeMillis();
        System.out.println(coins2(coins, aim));
        end = System.currentTimeMillis();
        System.out.println("cost time : " + (end - start) + "(ms)");

        System.out.println("=====动态规划O(N*(aim^2))的方法=====");
        start = System.currentTimeMillis();
        System.out.println(coins3(coins, aim));
        end = System.currentTimeMillis();
        System.out.println("cost time : " + (end - start) + "(ms)");

        System.out.println("=======动态规划O(N*aim)的方法=======");
        start = System.currentTimeMillis();
        System.out.println(coins4(coins, aim));
        end = System.currentTimeMillis();
        System.out.println("cost time : " + (end - start) + "(ms)");

        System.out.println("====动态规划O(N*aim)的方法+空间压缩===");
        start = System.currentTimeMillis();
        System.out.println(coins5(coins, aim));
        end = System.currentTimeMillis();
        System.out.println("cost time : " + (end - start) + "(ms)");

    }

}