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LIS(nlogn).cpp
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LIS(nlogn).cpp
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/* Longest increasing subsequence O(n log n) */
/* Taken from Topcoder SRM 623 Div 1 - 450 ptr solution */
int LIS(int n, const vector<int> & x)
{
int M[n+1];
int L = 0;
for (int i = 0; i < n; i++) {
// Binary search for the largest positive j ≤ L
// such that X[M[j]] < X[i]
int lo = 1;
int hi = L;
while (lo <= hi) {
int mid = (lo + hi )/2;
if (x[M[mid]] <= x[i]) {
lo = mid+1;
} else {
hi = mid-1;
}
}
// After searching, lo is 1 greater than the
// length of the longest prefix of X[i]
int newL = lo;
if (newL > L) {
// If we found a subsequence longer than any we've
// found yet, update M and L
M[newL] = i;
L = newL;
} else if (x[i] <= x[M[newL]]) {
// If we found a smaller last value for the
// subsequence of length newL, only update M
M[newL] = i;
}
}
return L;
}