LeetCode: Perfect Squares

原创于 2016-09-14 23:48:49 发布 · 225 阅读

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#LeetCode #dynamic programming #Perfect Squares

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本文介绍了一个算法，用于找出组成给定正整数n所需的最少数量的完全平方数。通过动态规划的方法，该算法有效地解决了这个问题，并提供了具体实例进行说明。

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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.

int numSquares(int n) {
    if (n <= 1) return 1;
    
    int logn = sqrt(n);
    int *res = (int*)malloc((n + 1) * sizeof(int));
    memset(res, 0, (n + 1) * sizeof(int));
    
    for (int i = 0; i <= logn; ++i) res[i * i] = 1;
    
    for (int i = 2; i <= n; ++i)
    {
        if (res[i] != 0) continue;
        
        int tmp = res[i - 1] + 1;
        int logi = sqrt(i);
        for (int j = 2; j <= logi; ++j) {
            if (tmp > res[i - j * j] + 1) tmp = res[i - j * j] + 1;
        }
        res[i] = tmp;
    }
    
    return res[n];
}