Why does DFS+Cache result in Time Limit Exceeded?

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    class Solution {
        int f(int n, unordered_map<int, int>& cache) {
            if (n == 1) {
                return 1;
            if (n == 0) {
                return 0;
            if (cache.find(n) != cache.end()) {
                return cache[n];
            auto min = 10000000;
            for (auto i = 1; i * i <= n; ++i) {
                auto tmp = f(n - i*i, cache);
                min = (1 + tmp) < min ? (1 + tmp) : min;
            cache[n] = min;
            return min;
        int numSquares(int n) {
            unordered_map<int, int> cache;
            f(n, cache);
            return cache[n];

    AFAIU, this should cost pretty much the same time with the DP solution(both are O(n^2)). Why TLE though?

  • 0

    It really depends on the unordered_map implementation. I'm guessing unordered_map is a hash table. Depends on different collision strategies, it's hard to guarantee O(1) time both accessing and searching a none existing element. Replacing the unordered_map with array will give you an acceptable runtime.

  • 0

    I solved this problem just like you but added one more constraint. I keep tracked what is the min value so far and if I calculated f(n) , will it be more than that or not. It save me sometime and accepted. Though the run time is not that good.

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