刷题279. Perfect Squares

一、题目说明

题目279. Perfect Squares，给定一个正整数n，找到m个数其平方和刚好是n。求m的最小值，难度是Medium！

二、我的解答

bfs算法：

class Solution{
	public:
		//bfs
		int numSquares(int n){
			queue<int> q;
	        q.push(n);
	        int sum=0;
	        while(1){
	            int l=q.size();
	            for(int i=0;i<l;i++){
	                int f=q.front();
	                if(f==0) return sum;
	                for(int i=1;i*i<=f;i++) {
	                    if(f-i*i==0) return sum+1;
	                    q.push(f-i*i); 
	                };
	                q.pop();
	            }
	            sum++;
	        }
		}
};

性能如下：

Runtime: 132 ms, faster than 42.52% of C++ online submissions for Perfect Squares.
Memory Usage: 53.2 MB, less than 5.77% of C++ online submissions for Perfect Squares.

优化：

class Solution{
	public:
		//bfs
		int numSquares(int n){
        	queue<int> q;
	        q.push(n);
	        int level = 0;
	        vector<bool> visit(n + 1, false);
	        while(!q.empty())
	        {
	            int size = q.size();
	            level++;
	            for(int i = 0; i < size; i++)
	            {
	                int temp = q.front();
	                q.pop();
	                visit[temp] = true;
	                for(int i = 1; i * i <= temp; i++)
	                {
	                    if(temp == i * i) return level;
	                    if(!visit[temp - i * i]) q.push(temp - i * i);
	                }
	            }
	        }
	        return level; 
		}
};

Runtime: 124 ms, faster than 46.86% of C++ online submissions for Perfect Squares.
Memory Usage: 29.7 MB, less than 11.54% of C++ online submissions for Perfect Squares.

三、优化措施

dp：

class Solution{
	public:
		int numSquares(int n){
			vector<int> dp(n+1);
			for(int i=1;i<=n;i++){
				dp[i] = i;
			}
			for(int i=2;i<=n;i++){
				for(int j=1;j*j<=i;j++){
					dp[i] = min(dp[i],dp[i-j*j]+1);
				}
			}
			return dp[n];
		}
};

性能如下：

Runtime: 108 ms, faster than 58.71% of C++ online submissions for Perfect Squares.
Memory Usage: 11.4 MB, less than 61.54% of C++ online submissions for Perfect Squares.