算法-leetCode-01

***砍竹子I：

动态规划：

public int cuttingBamboo(int bamboo_len) {
        int[] dp=new int[bamboo_len+1];
        dp[0]=0;
        dp[1]=1;
        for (int i = 2; i <=bamboo_len ; i++) {
            int max=0;
            for (int j = 1; j < i; j++) {
                max=Math.max(max,Math.max(j*(i-j),j*dp[i-j]));
            }
            dp[i]=max;
        }
        return dp[bamboo_len];
    }

数学解法：

public int cuttingBamboo2(int bamboo_len) {
        if (bamboo_len<=3){
            return bamboo_len-1;
        }
        int a=bamboo_len/3;
        int b=bamboo_len%3;
        if (b==0){
            return (int) Math.pow(3,a);
        }else if(b==1){
            return (int) Math.pow(3,(a-1))*4;
        }else{
            return (int) Math.pow(3,a)*2;
        }
    }

***砍竹子II:

***零钱兑换：

. - 力扣（LeetCode）

public int coinChange(int[] coins, int amount) {
        int[] dp = new int[amount + 1];
        Arrays.fill(dp,amount+1);
        dp[0]=0;
        for (int coin : coins) {
            for (int i = coin; i <=amount; i++) {
                dp[i]=Math.min(dp[i],1+dp[i-coin]);
            }
        }
        return dp[amount]>amount?-1:dp[amount];
    }

**完全平方数：

. - 力扣（LeetCode）

public int numSquares(int n) {
        int[] dp=new int[n+1];
        Arrays.fill(dp,n+1);
        int d =(int)Math.sqrt(n);
        int[] a=new int[d];
        for (int i=1; i <=d; i++) {
            a[i-1]=i*i;
        }
        dp[0]=0;
        for (int i : a) {
            for (int j = i; j <=n; j++) {
                dp[j]=Math.min(dp[j],1+dp[j-i]);
            }
        }
        return dp[n];
    }

**打家劫舍II:

. - 力扣（LeetCode）

public int rob(int[] nums) {
        if (nums.length==1){
            return nums[0];
        }
        if (nums.length==2){
            return Math.max(nums[0],nums[1]);
        }
        return Math.max(robRange(0,nums.length-2,nums),robRange(1,nums.length-1,nums));
    }
    public int robRange(int start,int end,int nums[]){
        int first=nums[start],second=Math.max(nums[start],nums[start+1]);
        for (int i = start+2; i <=end; i++) {
            int temp=second;
            second=Math.max(first+nums[i],second);
            first=temp;
        }
        return second;
    }

*******比特位计数：
. - 力扣（LeetCode）

public int[] countBits(int n) {
        int[] dp=new int[n+1];
        for (int i = 1; i <=n; i++) {
            dp[i]=dp[i&(i-1)]+1;
        }
        return dp;
    }

public int[] countBits2(int n) {
        int[] dp=new int[n+1];
        for (int i = 1; i <=n; i++) {
            dp[i]=dp[i>>1]+(i&1);
        }
        return dp;
    }

**砝码称重：
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public class Main {
    public static void main(String[] args) {
        Scanner scanner=new Scanner(System.in);
        int n=scanner.nextInt();
        int[] w=new int[n];
        Set<Integer> set=new HashSet<>();
        for (int i = 0; i < n; i++) {
            w[i]=scanner.nextInt();
        }
        set.add(w[0]);
        set.add(0);
        Set<Integer> tempSet=new HashSet<>();
        for (int i = 1; i < n; i++) {
            for (Integer num : set) {
                tempSet.add(num+w[i]);
                tempSet.add(Math.abs(num-w[i]));
            }
            set.addAll(tempSet);
        }
        System.out.println(set.size()-1);
    }
}