动态规划day05

377. 组合总和 Ⅳ

class Solution {
    public int combinationSum4(int[] nums, int target) {
        int[] dp = new int[target + 1];
        //求排列 每一层求得是所有物品刚好凑满i的排列数 每个物品无限使用
        dp[0] = 1;
        for (int i = 0; i <= target; i++) { //背包
            for (int j = 0; j < nums.length; j++) { //物品
                if (i >= nums[j]) {
                    dp[i] += dp[i - nums[j]];
                }
            }
        }
        return dp[target];
    }
}

70. 爬楼梯

//进阶 完全背包
class Solution {
    public int climbStairs(int n) {
        int[] dp = new int[n + 1];
        //排列问题 [0, 1]无限用 凑i
        dp[0] = 1;
        for (int i = 0; i <= n; i++) {
            for (int j = 1; j <= 2; j++) {
                if (i >= j) dp[i] += dp[i - j];
            }
        }
        return dp[n];
    }
}

322. 零钱兑换

class Solution {
    public int coinChange(int[] coins, int amount) {
        if (amount == 0) return 0;
        int[] dp = new int[amount + 1];
        Arrays.fill(dp, Integer.MAX_VALUE);
        //0金额需要0硬币
        dp[0] = 0;
        for (int i = 0; i < coins.length; i++) {
            for (int j = coins[i]; j <= amount; j++) {
                //保证前面有解
                if (dp[j - coins[i]] == Integer.MAX_VALUE) continue;
                dp[j] = Math.min(dp[j], dp[j - coins[i]] + 1);
            }
        }
        return dp[amount] == Integer.MAX_VALUE ? -1 : dp[amount];
    }
}

279. 完全平方数

class Solution {
    public int numSquares(int n) {
        int[] dp = new int[n + 1];
        Arrays.fill(dp, Integer.MAX_VALUE);
        dp[0] = 0;
        for (int i = 1; i * i <= n; i++) {  //物品
            for (int j = i * i; j <= n; j++) {  //背包
                //保证前面是有有解的
                if (dp[j - i * i] == Integer.MAX_VALUE) continue;
                dp[j] = Math.min(dp[j], dp[j - i * i] + 1);
            }
        }
        return dp[n];
    }
}

参考：programmercarl.com