leetcode(c++)(博弈类dp)

#include <iostream>
#include <vector>
using namespace std;

bool canWin(int n)
{
    vector<bool>dp(max(n+1,4));
    dp[3] = dp[1] = dp[2] = true;
    for(int i = 4; i <= n; ++i)
    {
        dp[i] = !dp[i-1] || !dp[i-2] || !dp[i-3];
    }
    return dp[n];
}

 int dfs(const vector<int>& piles, int i, int j, vector<vector<int>>&memo)
{
    if(i > j) return 0;
    if(memo[i][j] != -1) return memo[i][j]; 
    memo[i][j] = max(piles[i] - dfs(piles,i+1,j,memo),piles[j]-dfs(piles,i,j-1,memo));
    return memo[i][j];
}

bool predictWinner(const vector<int>& piles)
{
    int n = piles.size();
    vector<vector<int>>memo(n,vector<int>(n,-1));
    return dfs(piles,0,n,memo) > 0;
}

bool dfs(int n, vector<int>&memo)
{
    if(1 == n)return false;
    if(memo[n]!=-1)return memo[n];
    bool canWin = false;
    for(int i = 1; i <= n/2; ++i)
    {
        if(n % i == 0 && !dfs(n-i,memo))
        {
            canWin = true;
            break;
        }
    }
    return memo[n] = canWin;
}

bool divisorGame(int n)
{
    vector<int>memo(n+1,-1);
    return dfs(n,memo);
}

bool stonesGame(const vector<int>& stones)
{
    int n = stones.size();
    vector<vector<int>>memo(n,vector<int>(n,-1));
    int max = dfs(stones,0,n-1,memo);
    return memo[0][n-1] > 0;
}

int minmax(const vector<int>& nums, int index, vector<int>&memo)
{
    if(index == nums.size())return 0;
    if(memo[index]!=-1)return memo[index];
    int res = INT_MIN;
    int score = 0;
    for(int i = index; i < index + 3 && i < nums.size(); ++i)
    {
        score += nums[i];
        res = max(res,score - minmax(nums,index + 1,memo));
    }
    return memo[index] = res;

}

int stoneGameIII(const vector<int>& nums)
{
    int n = nums.size();
    vector<int>memo(n,-1);
    return minmax(nums,0,memo);
}

bool winSquareGame(int n)
{
    vector<bool>dp(n+1,false);
    for(int i = 1; i <= n; ++i)
    {
        for(int k = 1; k * k <= i; ++k)
        {
            if(!dp[i-k*k])
            {
                dp[i] = true;
                break;
            }
            
        }
    }
    return dp[n];
}

int main()
{
    //LeetCode292
    cout << canWin(4) << endl;

    //LeetCode486
    vector<int>v{1,5,233,7};
    cout << predictWinner(v) << endl;

    //LeetCode1025
    cout << divisorGame(4) << endl;

    //LeetCode877
    vector<int>stones{5,3,4,5};
    cout << stonesGame(stones) << endl;

    //LeetCode1406
    vector<int>nums{1,2,3,-9};
    cout << stoneGameIII(nums) << endl;

    //LeetCode1510
    int n = 1;
    cout << winSquareGame(n) << endl;
    return 0;
}