LeetCode 322. 零钱兑换 多种思路

自下而上动态规划

    public int coinChange(int[] coins, int amount) {
        int[] dp = new int[amount + 1];
        // 初始化数组
        for(int i = 1;i< dp.length;i++){
            dp[i] = amount + 1;
        }
        for(int i = 1;i < dp.length;i++){
            for(int j = 0;j < coins.length; j++){
                if(i >= coins[j]) 
                    dp[i] = Math.min(dp[i - coins[j]] + 1,dp[i]);
            }
        }
        return dp[amount] > amount ? -1 : dp[amount];
    }

自上而下动态规划递归

	public int coinChange(int[] coins, int amount) {
        if (amount < 1) {
            return 0;
        }
        return coinChange(coins, amount, new int[amount]);
    }

	private int coinChange(int[] coins, int amount, int[] dp) {
        if (amount < 0) {
            return -1;
        }
        if (amount == 0) {
            return 0;
        }
        if (dp[amount - 1] != 0) {
            return dp[amount - 1];
        }
        int min = Integer.MAX_VALUE;
        for (int coin : coins) {
            int res = coinChange(coins, amount - coin, dp);
            if (res >= 0 && res < min) {
                min = 1 + res;
            }
        }
        dp[amount - 1] = (min == Integer.MAX_VALUE) ? -1 : min;
        return dp[amount - 1];
    }

贪心法+dfs+剪枝

	int ans = Integer.MAX_VALUE;
    public int coinChange(int[] coins, int amount) {
        if (amount == 0) return 0;
        //排序，从大到小排序
        int index,max,temp;
        for (int i = 0; i < coins.length; i++) {
            index = i;
            max = Integer.MIN_VALUE;
            for (int j = i; j < coins.length; j++) {
                if (coins[j] > max){
                    max = coins[j];
                    index = j;
                }
            }
            temp = coins[i];
            coins[i] = max;
            coins[index] = temp;
        }

        coinChange(coins, amount, 0, 0);
        return ans == Integer.MAX_VALUE ? -1 : ans;
    }

    private void coinChange(int[] coins, int amount, int index, int count) {
        if (amount == 0) {
            ans = Math.min(ans, count);
            return;
        }
        if (index == coins.length) return;
        for (int k = amount / coins[index]; k >= 0 && k + count < ans; k--) {
            coinChange(coins, amount - k * coins[index], index + 1, count + k);
        }
    }