[LeetCode]312. 戳氣球

• DP
• f[i][j]=max { f[i][k-1] + f[k+1][j] + nums[i-1] * nums[k] * nums[j+1] }
• 戳破 i~j 的氣球，最後一個戳破的氣球是 k

312. 戳氣球

class Solution {
public:
    int maxCoins(vector<int>& nums) {
        int n=nums.size();
        if (n==0) return 0;
        //初始化
        int f[n+5][n+5];
        for (int i=0;i<n;i++)
            for (int j=0;j<n;j++) f[i][j]=0;
        for (int i=0;i<n;i++){
            if (i==0 && i==n-1) return nums[0];
            if (i==0) f[i][i]=nums[i+1]*nums[i];
            else if (i==n-1) f[i][i]=nums[i-1]*nums[i];
            else f[i][i]=nums[i-1]*nums[i]*nums[i+1];
        }
        
        for (int p=2;p<=n;p++)
            for (int i=0;i+p-1<n;i++){
                int j=i+p-1;
                //k表示最後一次被紮破的氣球
                for (int k=i;k<=j;k++){
                    int help=0;
                    if (i==0){
                        if (j==n-1) help=1;
                        else help=nums[j+1];
                    }
                    else if (j==n-1){
                        help=nums[i-1];
                    }
                    else help=nums[i-1]*nums[j+1];
                    if (k==i){
                        f[i][j]=max(f[k+1][j]+nums[k]*help,f[i][j]);
                        continue;
                    }
                    if (k==j){
                        f[i][j]=max(f[i][k-1]+nums[k]*help,f[i][j]);
                        continue;
                    }
                    f[i][j]=max(f[i][k-1]+f[k+1][j]+help*nums[k],f[i][j]);
                }
            }
        return f[0][n-1];
    }
};