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a2
1 parent 20c370f commit 2fe5945

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‎2022/a2/back/d-american.cpp‎

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#include <bits/stdc++.h>
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using namespace std;
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typedef long long ll;
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typedef pair<int, int> pii;
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template<typename T>
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void printv(vector<T> &v) {
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for(int i = 0; i < v.size(); i++) {
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cout << v[i];
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if(i < v.size() - 1)
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cout << " ";
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}
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cout << endl;
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}
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ll dijkstra(
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vector<vector<ll>> &cost,
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vector<vector<ll>> &adj,
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int j, int k, int mask
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) {
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// dijkstra j => k
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priority_queue<
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pair<ll, int>, // cost, node
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vector<pair<ll, int>>,
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greater<pair<ll, int>>
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> q;
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int u, v, i;
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ll d;
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q.emplace(0, j);
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while(!q.empty()) {
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tie(d, u) = q.top(); q.pop();
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if(u == k) return d;
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if(!((mask >> u) & 1)) continue;
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mask = mask ^ (1 << u);
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for(int v : adj[u]) {
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if(!((mask >> v) & 1)) continue;
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q.emplace(d + cost[u][v], v);
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}
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}
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throw runtime_error("dijkstra: cannot find path j => k");
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}
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/*
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g++ -std=c++11 d-american.cpp -o k
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18 < 32 == 2^5
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2^18 = 262,144
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*/
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int main() {
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ios_base::sync_with_stdio(0); cin.tie(0);
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int n, m;
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int i, j, k, l;
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int u, v, s;
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int mask;
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ll d;
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cin >> n >> m;
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vector<vector<ll>> cost(n, vector<ll>(n, numeric_limits<ll>::max())); // adj-mtx
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vector<vector<ll>> adj(n); // adj-list
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for(i = 0; i < m; i++) {
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cin >> u >> v >> d;
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u -= 1; v -= 1;
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cost[u][v] = d;
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cost[v][u] = d;
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adj[u].push_back(v);
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adj[v].push_back(u);
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}
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cin >> s;
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vector<ll> memo(1 << n);
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for(i = 0; i < n; i++) {
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j = (1 << i); // 1 = 2^0
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cost[j][j] = 0;
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j = (i << 18) + (1 << i); // f({i}, i) = 0;
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memo[j] = cost[s][i];
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}
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int key;
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for(i = 2; i < (1 << n); i++) {
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// iterate over subsets X where bitmasks equal i
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if((i >> s) & 1)
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// X contains s
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continue;
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for(j = 0; j < n; j++) {
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// compute f(X, j)
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if(!((i >> j) & 1))
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// node j is not in X
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continue;
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l = (i ^ (1 << j)); // X \ {j}
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if(!l)
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// X \ {j} == {} empty set
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continue;
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key = (j << 18) + i;
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for(k = 0; k < n; k++) {
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// consider subset X \ {j}
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// where last visited node is k
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if(!((l >> k) & 1))
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// node k is not in the set
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continue;
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// do dijkstra between k, j using nodes in X + {s}
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// f(X \ {j}, k) + dijkstra(k, j)
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mask = (i | (1 << s));
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d = dijkstra(cost, adj, j, k, mask);
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// compute f(X \ {j}, k) + d(k, j)
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d = memo[(k << 18) + l] + d;
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// memoize f(X, j) = f(X \ {j}, k) + d(k, j)
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memo[key] = min(memo[key], d);
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}
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}
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}
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ll o = numeric_limits<ll>::max();
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mask = (1 << n) - 1;
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for(i = 0; i < n; i++) {
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d = dijkstra(cost, adj, i, s, mask);
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key = (1 << n) - 1 + (i << 18);
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d = memo[key] + d;
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o = min(d, o);
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}
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cout << o << endl;
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return 0;
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}
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‎2022/a2/back/f-star.cpp‎

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#include <bits/stdc++.h>
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using namespace std;
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typedef long long ll;
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typedef pair<int, int> pii;
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bool DEBUG = false;
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ll MODVAL = 1000000000 + 7;
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//vector<ll> FACTORIAL(1001);
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vector<vector<ll>> CHOOSE(1001, vector<ll>(1001));
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inline ll modmul(ll a, ll b) {
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return (a * b) % MODVAL;
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}
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inline ll modadd(ll a, ll b) {
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return (a + b) % MODVAL;
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}
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/*
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2D DP of divide and conquer
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g++ -std=c++11 f-star.cpp -o k
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This works! Creating another clean version for submission.
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*/
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void main(int argc, char *argv[]) {
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int i, j;
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int n, k;
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int N, K;
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int min_nK;
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ll c, d;
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//FACTORIAL[0] = 1;
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//for(n = 1; n <= 1000; n++)
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// FACTORIAL[n] = (FACTORIAL[n - 1] * n) % MODVAL;
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for(n = 1; n <= 1000; n++) {
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CHOOSE[n][0] = 1;
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for(k = 1; k < n; k++) {
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CHOOSE[n][k] = modadd(CHOOSE[n-1][k-1], CHOOSE[n-1][k]);
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}
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CHOOSE[n][n] = 1;
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}
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cin >> N >> K;
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vector<vector<ll>> memo(N + 1, vector<ll>(K + 1, 0));
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memo[1][0] = 1;
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memo[2][0] = 2;
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for(n = 3; n <= N; n++) {
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min_nK = min(n / 2, K);
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for(k = 0; k <= min_nK; k++) {
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// memoize f(n, k)
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c = 0;
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if(DEBUG) printf("(n=%d, k=%d) \n", n, k);
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for(i = 1; i <= n - 2; i++) {
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for(j = 0; j <= k - 1; j++) {
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if(DEBUG) printf(" f(%d, %d) = %lld = f(i, j) \n", i, j, memo[i][j]);
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if(DEBUG) printf(" f(%d, %d) = %lld = f(n-i-1, k-1-j) \n", n - i - 1, k - 1 - j, memo[n - i - 1][k - 1 - j]);
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if(DEBUG) printf(" choose(%d, %d) = %lld = choose(n-1, i) \n", n-1, i, CHOOSE[n - 1][i]);
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d = modmul(
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modmul(memo[i][j], CHOOSE[n - 1][i]),
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memo[n - i - 1][k - 1 - j]
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);
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if(DEBUG) printf(" sum = %lld \n", d);
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c = modadd(c, d);
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}
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}
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// edge subproblems
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if(DEBUG) printf("f(%d, %d) = %lld = f(n-1, k) \n", n-1, k, memo[n - 1][k]);
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c = modadd(c, modmul(2, memo[n - 1][k]));
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memo[n][k] = c;
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if(DEBUG) printf("f(n=%d, k=%d)=%lld \n", n, k, memo[n][k]);
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}
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}
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cout << memo[N][K] << endl;
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return 0;
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}
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int main(int argc, char *argv[]) {
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ios_base::sync_with_stdio(0); cin.tie(0);
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if (argc > 1) {
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string arg = argv[1];
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DEBUG = arg == "debug";
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}
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int i, j;
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int n, k;
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int N, K;
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int min_nK;
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ll c, d;
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//FACTORIAL[0] = 1;
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//for(n = 1; n <= 1000; n++)
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// FACTORIAL[n] = (FACTORIAL[n - 1] * n) % MODVAL;
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for(n = 1; n <= 1000; n++) {
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CHOOSE[n][0] = 1;
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for(k = 1; k < n; k++) {
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CHOOSE[n][k] = modadd(CHOOSE[n-1][k-1], CHOOSE[n-1][k]);
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}
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CHOOSE[n][n] = 1;
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}
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return 0;
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}
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