68 lines
1.4 KiB
C++
68 lines
1.4 KiB
C++
#include <bits/stdc++.h>
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using namespace std;
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/*
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rollMax[i] = n -> at most n dices of value i consecutive
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let dp[i][{1,2,3,4,5,6}] be the number of valid sequences of length i where the last dice was j
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we can extend this in the following way
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for all k such that k != j
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dp[i + 1][k] += dp[i][j]
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dp[i + 2][k] += dp[i][j]
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...
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dp[i + rollMax[k]][k] += dp[i][j]
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dp[0][j] = 1 for all j E {1,2,3,4,5,6}
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answer = sum (dp[N][j]) for all j E {1,2,3,4,5,6}
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*/
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const int MOD = 1e9 + 7;
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int dieSimulator(int n, vector<int> &rollMax)
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{
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vector<vector<long long>> dp(n + 1, vector<long long>(6, 0));
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for (int i = 0; i < 6; i++)
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{
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for (int rolls = 0; rolls <= rollMax[i] && rolls <= n; ++rolls)
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{
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dp[rolls][i] = 1;
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}
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}
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for (int i = 1; i < n; i++)
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{
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for (int j = 0; j < 6; j++)
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{
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if (dp[i][j] == 0)
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continue;
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for (int k = 0; k < 6; k++)
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{
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if (k == j)
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continue;
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for (int m = 1; m <= rollMax[k] && i + m <= n; m++)
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{
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dp[i + m][k] += dp[i][j];
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dp[i + m][k] %= MOD;
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}
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}
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}
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}
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long long ans = 0;
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for (int i = 0; i < 6; i++)
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ans += dp[n][i];
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return ans % MOD;
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}
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int main()
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{
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int n;
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cin >> n;
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vector<int> nums(6);
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for (int i = 0; i < 6; i++)
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cin >> nums[i];
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cout << dieSimulator(n, nums) << endl;
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return 0;
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} |