Problem_03_CoinsMin

package chapter_4_recursionanddp;

public class Problem_03_CoinsMin {

    public static int minCoins1(int[] arr, int aim) {
        if (arr == null || arr.length == 0 || aim < 0) {
            return -1;
        }
        int n = arr.length;
        int max = Integer.MAX_VALUE;
        int[][] dp = new int[n][aim + 1];
        for (int j = 1; j <= aim; j++) {
            dp[0][j] = max;
            if (j - arr[0] >= 0 && dp[0][j - arr[0]] != max) {
                dp[0][j] = dp[0][j - arr[0]] + 1;
            }
        }
        int left = 0;
        for (int i = 1; i < n; i++) {
            for (int j = 1; j <= aim; j++) {
                left = max;
                if (j - arr[i] >= 0 && dp[i][j - arr[i]] != max) {
                    left = dp[i][j - arr[i]] + 1;
                }
                dp[i][j] = Math.min(left, dp[i - 1][j]);
            }
        }
        return dp[n - 1][aim] != max ? dp[n - 1][aim] : -1;
    }

    public static int minCoins2(int[] arr, int aim) {
        if (arr == null || arr.length == 0 || aim < 0) {
            return -1;
        }
        int n = arr.length;
        int max = Integer.MAX_VALUE;
        int[] dp = new int[aim + 1];
        for (int j = 1; j <= aim; j++) {
            dp[j] = max;
            if (j - arr[0] >= 0 && dp[j - arr[0]] != max) {
                dp[j] = dp[j - arr[0]] + 1;
            }
        }
        int left = 0;
        for (int i = 1; i < n; i++) {
            for (int j = 1; j <= aim; j++) {
                left = max;
                if (j - arr[i] >= 0 && dp[j - arr[i]] != max) {
                    left = dp[j - arr[i]] + 1;
                }
                dp[j] = Math.min(left, dp[j]);
            }
        }
        return dp[aim] != max ? dp[aim] : -1;
    }

    public static int minCoins3(int[] arr, int aim) {
        if (arr == null || arr.length == 0 || aim < 0) {
            return -1;
        }
        int n = arr.length;
        int max = Integer.MAX_VALUE;
        int[][] dp = new int[n][aim + 1];
        for (int j = 1; j <= aim; j++) {
            dp[0][j] = max;
        }
        if (arr[0] <= aim) {
            dp[0][arr[0]] = 1;
        }
        int leftup = 0; // 左上角某个位置的值
        for (int i = 1; i < n; i++) {
            for (int j = 1; j <= aim; j++) {
                leftup = max;
                if (j - arr[i] >= 0 && dp[i - 1][j - arr[i]] != max) {
                    leftup = dp[i - 1][j - arr[i]] + 1;
                }
                dp[i][j] = Math.min(leftup, dp[i - 1][j]);
            }
        }
        return dp[n - 1][aim] != max ? dp[n - 1][aim] : -1;
    }

    public static int minCoins4(int[] arr, int aim) {
        if (arr == null || arr.length == 0 || aim < 0) {
            return -1;
        }
        int n = arr.length;
        int max = Integer.MAX_VALUE;
        int[] dp = new int[aim + 1];
        for (int j = 1; j <= aim; j++) {
            dp[j] = max;
        }
        if (arr[0] <= aim) {
            dp[arr[0]] = 1;
        }
        int leftup = 0; // 左上角某个位置的值
        for (int i = 1; i < n; i++) {
            for (int j = aim; j > 0; j--) {
                leftup = max;
                if (j - arr[i] >= 0 && dp[j - arr[i]] != max) {
                    leftup = dp[j - arr[i]] + 1;
                }
                dp[j] = Math.min(leftup, dp[j]);
            }
        }
        return dp[aim] != max ? dp[aim] : -1;
    }

    public static void main(String[] args) {
        int[] arr1 = { 100, 20, 5, 10, 2, 50, 1 };
        int aim1 = 17019;
        System.out.println(minCoins1(arr1, aim1));
        System.out.println(minCoins2(arr1, aim1));

        int[] arr2 = { 10, 100, 2, 5, 5, 5, 10, 1, 1, 1, 2, 100 };
        int aim2 = 223;
        System.out.println(minCoins3(arr2, aim2));
        System.out.println(minCoins4(arr2, aim2));

    }
}