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279-完全平方数

LeetCode

发布日期: 2021-11-29

LeetCode 279. Perfect Squares

Given an integer n, return the least number of perfect square numbers that sum to n.

A perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 1, 4, 9, and 16 are perfect squares while 3 and 11 are not.

Example 1:

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

Example 2:

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

method: 完全背包

dp[i]：组成整数i需要的最少的完全平方数个数为dp[i]
物品：完全平方数

因为要最小，所以初始化为INT_MAX
来一个j，就可以考虑把整数i拆成j*j和i-j*j两部分

求最少数量
递推公式：dp[i] = min(dp[i], dp[i-j*j]+1)

int numSquares(int n) {
    vector<int> dp(n + 1, INT_MAX);
    dp[0] = 0;
    for (int i = 1; i <= n; i++) {          // 遍历背包（整数x）
        for (int j = 1; j * j <= i; j++) {  // 遍历物品（平方数），必须小于等于
            dp[i] = min(dp[i], dp[i - j * j] + 1);
        }
    }
    return dp[n];
}