279. Perfect Squares

• Difficulty: Medium

• Topics: Math, Dynamic Programming, Breadth-first Search

• Similar Questions:

  • Count Primes

  • Ugly Number II

Problem:

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

Example 1:

Input: n = 12
Output: 3 
Explanation: 12 = 4 + 4 + 4.

Example 2:

Input: n = 13
Output: 2
Explanation: 13 = 4 + 9.

Solutions:

class Solution {
public:
    int numSquares(int n) {
        queue<int> q;
        unordered_set<int> visited;

        q.push(n);
        visited.insert(n);
        int level = 0;
        while(true) {
            ++level;
            int size = q.size();
            for (int i = 0; i < size; ++i) {
                int sum = q.front(); q.pop();
                for (int sqrt = 1; sqrt <= sum/sqrt; ++sqrt) {
                    if (sum == sqrt * sqrt) return level;
                    int remaining = sum - sqrt * sqrt;
                    if (visited.count(remaining) > 0)   continue;
                    visited.insert(remaining);
                    q.push(remaining);
                }
            }
        }

        return -1;
    }
};