UVaLive 4727 Jump (递推)

题意：约瑟夫环，求最后三个数。

析：f[i] = (f[i-1] + k) % i 这是求最后一个数时候，我们倒着推到第一个数时，只有一个数，所以当只有两个数时，就是另一数，

同理，我们可以求得第三个数。

代码如下：

#pragma comment(linker, "/STACK:1024000000,1024000000")
#include <cstdio>
#include <string>
#include <cstdlib>
#include <cmath>
#include <iostream>
#include <cstring>
#include <set>
#include <queue>
#include <algorithm>
#include <vector>
#include <map>
#include <cctype>
#include <cmath>
#include <stack>
#include <unordered_map>
#include <unordered_set>
#define debug() puts("++++");
#define freopenr freopen("in.txt", "r", stdin)
#define freopenw freopen("out.txt", "w", stdout)
using namespace std;

typedef long long LL;
typedef pair<int, int> P;
const int INF = 0x3f3f3f3f;
const double inf = 0x3f3f3f3f3f3f;
const double PI = acos(-1.0);
const double eps = 1e-8;
const int maxn = 5e5 + 5;
const int mod = 2000;
const int dr[] = {-1, 1, 0, 0};
const int dc[] = {0, 0, 1, -1};
const char *de[] = {"0000", "0001", "0010", "0011", "0100", "0101", "0110", "0111", "1000", "1001", "1010", "1011", "1100", "1101", "1110", "1111"};
int n, m;
const int mon[] = {0, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};
const int monn[] = {0, 31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};
inline bool is_in(int r, int c){
    return r >= 0 && r < n && c >= 0 && c < m;
}
int dp[maxn][3];

int main(){
    int T;  cin >> T;
    while(T--){
        cin >> n >> m;
        dp[1][0] = 0;
        dp[2][0] = (dp[1][0] + m) % 2;
        dp[2][1] = 1 - dp[2][0];
        dp[3][0] = (dp[2][0] + m) % 3;
        dp[3][1] = (dp[2][1] + m) % 3;
        dp[3][2] = 3 - dp[3][1] - dp[3][0];
        for(int i = 4; i <= n; ++i)
            for(int j = 0; j < 3; ++j)
                dp[i][j] = (dp[i-1][j] + m) % i;
        for(int i = 0; i < 3; ++i)  ++dp[n][i];
        cout << dp[n][2] << " " << dp[n][1] << " " << dp[n][0] << endl;
    }
    return 0;
}