*[hackerrank]Volleyball Match
https://www.hackerrank.com/contests/w1/challenges/volleyball-match
此题不错,首先可以看出是DP,S(x, y)= S(x - 1, y) + S(x, y - 1)。然后比赛结束状态需要认真判断。三来,最后数据量很大(接近10^9)远超一般DP的数据量,分配数组都不行,里面是有规律的。下面是大数据失败的代码:
#include <vector> #include <iostream> #include <cstdlib> #include <cmath> using namespace std; vector<vector<int> > ma; int MOD = 1000000007; bool validEnd(int a, int b) { // a >= b if (a < 25) return false; if (a == 25) { return ((a - b) >= 2); } else { return ((a - b) == 2); } } bool valid(int a, int b) { // a >= b if (a < 0 || b < 0) return false; if (a <= 25 && b <= 25) return true; else return ((a - b) <= 2); } int getCount(int a, int b, bool first) { if (!valid(a, b)) { return 0; } if (!first && validEnd(a, b)) { return 0; } if (ma[a][b] != -1) { return ma[a][b]; } ma[a][b] = (getCount(a - 1, b, false) + getCount(a, b - 1, false)) % MOD; return ma[a][b]; } int main() { int a, b; cin >> a >> b; if (a < b) swap(a, b); if (!validEnd(a, b)) { cout << 0 << endl; return 0; } ma.resize(a + 1); for (int i = 0; i < ma.size(); i++) { ma[i].resize(b + 1, -1); } ma[0][0] = 1; int r = getCount(a, b, true); cout << r << endl; }
正确做法是观察到,大于25的比赛结束状态都是由24:24经由一个一个平局过来的,没经过一次增加一倍。这样只要改写main函数基本就行了,主要pow由于次数太高,会远超long的值域,需要改写每次都MOD一下。
int pw(int k) { if (k == 0) return 1; if (k == 1) return 2; int q = pw(k / 2); q = (1LL * q * q) % MOD; if (k % 2 == 1) return (q + q) % MOD; else return q; } int main() { int a, b; cin >> a >> b; if (a < b) swap(a, b); if (!validEnd(a, b)) { cout << 0 << endl; return 0; } ma.resize(26); for (int i = 0; i < ma.size(); i++) { ma[i].resize(26, -1); } ma[0][0] = 1; int r = 0; if (a == 25) { r = getCount(a, b, true); } else { r = getCount(24, 24, true); r = ((int64_t) r * pw(b - 24)) % MOD; } cout << r << endl; }