76 lines
1.9 KiB
C++
76 lines
1.9 KiB
C++
#include <cstdio>
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#include <cstdint>
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// Clang does not accept this constexpr Solver, but MSVC does.
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template<int N>
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struct Solver {
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int bobs[3000];
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int endPosition;
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constexpr Solver() : bobs() {
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int dp[N + 5][2]{{-1, 1}};
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auto f = [&dp](int n, int who, auto&& fr) {
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if (dp[n][who])
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return dp[n][who];
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for (int i = 1; i * i <= n; ++i) {
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if (fr(n - i * i, who ^ 1, fr) == (who ? -1 : 1))
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return dp[n][who] = (who ? -1 : 1);
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}
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return dp[n][who] = (who ? 1 : -1);
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};
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int pos = 0;
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for (int i = 0; i < N + 3; ++i) {
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if (f(i, 0, f) == -1){
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bobs[pos++] = i;
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}
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}
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endPosition = pos;
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}
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};
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/**
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* 1510. Stone Game IV
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* Alice and Bob take turns playing a game, with Alice starting first.
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* Initially, there are n stones in a pile. On each player's turn, that player makes a move consisting of removing any non-zero square number of stones in the pile.
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* Also, if a player cannot make a move, he/she loses the game.
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* Given a positive integer n, return true if and only if Alice wins the game otherwise return false, assuming both players play optimally.
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*/
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class Solution {
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private:
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static constexpr Solver<100005> answer;
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public:
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static bool winnerSquareGame(int n) {
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for (int i = 0; i < answer.endPosition; ++i) {
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if (answer.bobs[i] == n) {
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return false;
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}
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}
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return true;
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}
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};
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class SolutionOld {
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private:
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// 0 -> Unknown, 1 -> Alice, -1 -> Bob
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// dp[n][0] -> Alice to take, [1] -> Bob to take;
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int8_t dp[100005][2]{{-1, 1}};
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int8_t d(int n, int8_t who) {
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if (dp[n][who])
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return dp[n][who];
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for (int i = 1; i * i <= n; ++i) {
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if (d(n - i * i, who ^ 1) == (who ? -1 : 1))
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return dp[n][who] = (who ? -1 : 1);
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}
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return dp[n][who] = (who ? 1 : -1);
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}
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public:
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bool winnerSquareGame(int n) {
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return d(n, 0) == 1;
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}
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};
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int main() {
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SolutionOld solver;
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std::printf("%s\n", Solution::winnerSquareGame(4) ? "true" : "false");
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return 0;
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} |