[Leetcode 279] Perfect Squares

[Leetcode 279] Perfect Squares

Given a positive integer n, find the least number of perfect square numbers (for example, 1, 4, 9, 16, ...) which sum to n.

For example, given n = 12, return 3 because 12 = 4 + 4 + 4; given n = 13, return 2 because 13 = 4 + 9.

解法一：动态规划

class Solution {
public:
    int numSquares(int n) {
        int sqrt_n = sqrt(n) + 0.5;
        vector<int> a(sqrt_n + 1);
        for(int i = 1; i <= sqrt_n; ++i)
            a[i] = i * i;
        vector<int> b(n+1, 1000);
        b[0] = 0;
        for(int i = 1; i <= n; ++i){
            for(int j = sqrt(i); j >= 1; --j)
                b[i] = min(b[i], b[i - a[j]] + 1);
        return b[n];
    }
};

解法二：拉格朗日四平方定理

class Solution {
    bool is_sqrt(int n){
        int sqrt_n = sqrt(n);
        return (n == sqrt_n * sqrt_n);
    }
public:
    int numSquares(int n) {
        if(is_sqrt(n)) return 1;
        while((n & 3) == 0) n >>= 2;
        if((n & 7) == 7) return 4;
        if((n & 1) == 0) n >>= 1;
        int sqrt_n = sqrt(n);
        if(sqrt_n & 1 == 0) sqrt_n--;
        for(int i = sqrt_n; i > 0; i -= 2){
            if(is_sqrt(n - i*i)) {
                return 2;
            }
        }
        return 3;
    }
};