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935. Knight Dialer.cpp
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935. Knight Dialer.cpp
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//recursion + memorization
//Runtime: 328 ms, faster than 27.43% of C++ online submissions for Knight Dialer.
//Memory Usage: 23.2 MB, less than 57.37% of C++ online submissions for Knight Dialer.
class Solution {
public:
int MOD = 1e9+7;
vector<vector<int>> edges;
vector<vector<int>> memo;
int dfs(int cur, int N){
if(N == 0) return 1;
if(N == 1) return edges[cur].size();
if(memo[cur][N] != -1) return memo[cur][N];
memo[cur][N] = 0;
for(int nei : edges[cur]){
memo[cur][N] = (memo[cur][N] + dfs(nei, N-1)) % MOD;
}
return memo[cur][N];
}
int knightDialer(int N) {
int ans = 0;
edges = vector<vector<int>>(10);
edges[0] = {4,6};
edges[1] = {6,8};
edges[2] = {7,9};
edges[3] = {4,8};
edges[4] = {3,9,0};
edges[5] = {};
edges[6] = {1,7,0};
edges[7] = {2,6};
edges[8] = {1,3};
edges[9] = {2,4};
memo = vector<vector<int>>(10, vector<int>(N, -1));
for(int i = 0; i <= 9; i++){
ans = (ans + dfs(i, N-1)) % MOD;
}
return ans;
}
};
//bottom-up DP
//Runtime: 344 ms, faster than 26.23% of C++ online submissions for Knight Dialer.
//Memory Usage: 21.7 MB, less than 58.60% of C++ online submissions for Knight Dialer.
class Solution {
public:
int MOD = 1e9+7;
vector<vector<int>> edges;
vector<vector<int>> memo;
int knightDialer(int N) {
int ans = 0;
edges = vector<vector<int>>(10);
edges[0] = {4,6};
edges[1] = {6,8};
edges[2] = {7,9};
edges[3] = {4,8};
edges[4] = {3,9,0};
edges[5] = {};
edges[6] = {1,7,0};
edges[7] = {2,6};
edges[8] = {1,3};
edges[9] = {2,4};
vector<vector<int>> dp(10, vector<int>(N, 0));
for(int n = 0; n < N; n++){
for(int cur = 0; cur <= 9; cur++){
if(n == 0){
dp[cur][n] = 1;
}else if(n == 1){
dp[cur][n] = edges[cur].size();
}else{
for(int nei : edges[cur]){
dp[cur][n] = (dp[cur][n] + dp[nei][n-1]) % MOD;
}
}
// cout << "(" << cur << ", " << n << "): " << dp[cur][n] << endl;
}
}
for(int cur = 0; cur <= 9; cur++){
ans = (ans + dp[cur][N-1]) % MOD;
}
return ans;
}
};
//DP, space optimized
//Runtime: 184 ms, faster than 55.96% of C++ online submissions for Knight Dialer.
//Memory Usage: 6.1 MB, less than 88.12% of C++ online submissions for Knight Dialer.
class Solution {
public:
int MOD = 1e9+7;
vector<vector<int>> edges;
vector<vector<int>> memo;
int knightDialer(int N) {
int ans = 0;
edges = vector<vector<int>>(10);
edges[0] = {4,6};
edges[1] = {6,8};
edges[2] = {7,9};
edges[3] = {4,8};
edges[4] = {3,9,0};
edges[5] = {};
edges[6] = {1,7,0};
edges[7] = {2,6};
edges[8] = {1,3};
edges[9] = {2,4};
vector<vector<int>> dp(2, vector<int>(10, 0));
for(int n = 0; n < N; n++){
for(int cur = 0; cur <= 9; cur++){
if(n == 0){
dp[n%2][cur] = 1;
}else if(n == 1){
dp[n%2][cur] = edges[cur].size();
}else{
dp[n%2][cur] = 0;
for(int nei : edges[cur]){
dp[n%2][cur] = (dp[n%2][cur] + dp[(n-1)%2][nei]) % MOD;
}
}
}
}
for(int cur = 0; cur <= 9; cur++){
ans = (ans + dp[(N-1)%2][cur]) % MOD;
}
return ans;
}
};