Find longest non-decreasing sequence - algorithm

Question

Given the following question,
Given an array of integers A of length n, find the longest sequence {i_1, ..., i_k} such that i_j < i_(j+1) and A[i_j] <= A[i_(j+1)] for any j in [1, k-1].
Here is my solution, is this correct?
max_start = 0; // store the final result
max_end = 0;
try_start = 0; // store the initial result
try_end = 0;
FOR i=0; i<(A.length-1); i++ DO
if A[i] <= A[i+1]
try_end = i+1; // satisfy the condition so move the ending point
else // now the condition is broken
if (try_end - try_start) > (max_end - max_start) // keep it if it is the maximum
max_end = try_end;
max_start = try_start;
endif
try_start = i+1; // reset the search
try_end = i+1;
endif
ENDFOR
// Checking the boundary conditions based on comments by Jason
if (try_end - try_start) > (max_end - max_start)
max_end = try_end;
max_start = try_start;
endif
Somehow, I don't think this is a correct solution but I cannot find a counter-example that disapprove this solution.
anyone can help?
Thank you

Answer 1

I don't see any backtracking in your algorithm, and it seems to be suited for contiguous blocks of non-decreasing numbers. If I understand correctly, for the following input:
1 2 3 4 10 5 6 7
your algorithm would return 1 2 3 4 10 instead of 1 2 3 4 5 6 7.
Try to find a solution using dynamic programming.

Answer 2

You're missing the case where the condition is not broken at its last iteration:
1, 3, 5, 2, 4, 6, 8, 10
You'll never promote try_start and try_end to max_start and max_end unless your condition is broken. You need to perform the same check at the end of the loop.

Answer 3

Well, it looks like you're finding the start and the end of the sequence, which may be correct but it wasn't what was asked. I'd start by reading http://en.wikipedia.org/wiki/Longest_increasing_subsequence - I believe this is the question that was asked and it's a fairly well-known problem. In general cannot be solved in linear time, and will also require some form of dynamic programming. (There's an easier n^2 variant of the algorithm on Wikipedia as well - just do a linear sweep instead of the binary search.)

Answer 4

#include <algorithm>
#include <vector>
#include <stdio.h>
#include <string.h>
#include <assert.h>
template<class RandIter>
class CompM {
const RandIter X;
typedef typename std::iterator_traits<RandIter>::value_type value_type;
struct elem {
value_type c; // char type
explicit elem(value_type c) : c(c) {}
};
public:
elem operator()(value_type c) const { return elem(c); }
bool operator()(int a, int b) const { return X[a] < X[b]; } // for is_sorted
bool operator()(int a, elem b) const { return X[a] < b.c; } // for find
bool operator()(elem a, int b) const { return a.c < X[b]; } // for find
explicit CompM(const RandIter X) : X(X) {}
};
template<class RandContainer, class Key, class Compare>
int upper(const RandContainer& a, int n, const Key& k, const Compare& comp) {
return std::upper_bound(a.begin(), a.begin() + n, k, comp) - a.begin();
}
template<class RandIter>
std::pair<int,int> lis2(RandIter X, std::vector<int>& P)
{
int n = P.size(); assert(n > 0);
std::vector<int> M(n);
CompM<RandIter> comp(X);
int L = 0;
for (int i = 0; i < n; ++i) {
int j = upper(M, L, comp(X[i]), comp);
P[i] = (j > 0) ? M[j-1] : -1;
if (j == L) L++;
M[j] = i;
}
return std::pair<int,int>(L, M[L-1]);
}
int main(int argc, char** argv)
{
if (argc < 2) {
fprintf(stderr, "usage: %s string\n", argv[0]);
return 3;
}
const char* X = argv[1];
int n = strlen(X);
if (n == 0) {
fprintf(stderr, "param string must not empty\n");
return 3;
}
std::vector<int> P(n), S(n), F(n);
std::pair<int,int> lt = lis2(X, P); // L and tail
int L = lt.first;
printf("Longest_increasing_subsequence:L=%d\n", L);
for (int i = lt.second; i >= 0; --i) {
if (!F[i]) {
int j, k = 0;
for (j = i; j != -1; j = P[j], ++k) {
S[k] = j;
F[j] = 1;
}
std::reverse(S.begin(), S.begin()+k);
for (j = 0; j < k; ++j)
printf("%c", X[S[j]]);
printf("\n");
}
}
return 0;
}