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/*@ Extern Coq
(Forall : {A} -> (A -> Prop) -> list A -> Prop)
(Z::le : Z -> Z -> Prop)
(Z::ge : Z -> Z -> Prop)
(LISLength : list Z -> Z -> Prop)
(LISDPTablePrefix : list Z -> list Z -> Z -> Prop)
(LISInnerProgress : list Z -> list Z -> Z -> Z -> Prop)
(LISBestSoFar : list Z -> Z -> Z -> Prop)
*/
/*@ Import Coq Require Import PVbench.Algorithms.longest_increasing_subsequence.rocq.spec_lib */
/*@ Import Coq Require Import PVbench.Algorithms.longest_increasing_subsequence.rocq.helper_lib */
int lengthOfLIS(int *nums, int numsSize)
/*@ With (l : list Z)
Require
1 <= numsSize && numsSize <= 100000 &&
Zlength(l) == numsSize &&
Forall(Z::le(-10000), l) && Forall(Z::ge(10000), l) &&
IntArray::full(nums, numsSize, l)
Ensure
LISLength(l, __return) &&
IntArray::full(nums, numsSize, l)
*/
{
int dp[100000];
int ans = 1;
/*@ Inv Assert
exists d,
nums == nums@pre && numsSize == numsSize@pre &&
1 <= numsSize@pre && numsSize@pre <= 100000 &&
Zlength(l) == numsSize@pre &&
0 <= i && i <= numsSize@pre &&
1 <= ans && ans <= numsSize@pre &&
Zlength(d) == i &&
(forall (k : Z), (0 <= k && k < i) => (1 <= d[k] && d[k] <= k + 1)) &&
LISDPTablePrefix(l, d, i) &&
LISBestSoFar(l, i, ans) &&
IntArray::full(nums, numsSize@pre, l) *
IntArray::seg(dp, 0, i, d) *
IntArray::undef_seg(dp, i, 100000)
*/
for (int i = 0; i < numsSize; ++i) {
dp[i] = 1;
/*@ Inv Assert
exists d,
nums == nums@pre && numsSize == numsSize@pre &&
1 <= numsSize@pre && numsSize@pre <= 100000 &&
Zlength(l) == numsSize@pre &&
0 <= i && i < numsSize@pre &&
0 <= j && j <= i &&
1 <= ans && ans <= numsSize@pre &&
LISBestSoFar(l, i, ans) &&
Zlength(d) == i + 1 &&
(forall (k : Z), (0 <= k && k < i + 1) => (1 <= d[k] && d[k] <= k + 1)) &&
LISInnerProgress(l, d, i, j) &&
IntArray::full(nums, numsSize@pre, l) *
IntArray::seg(dp, 0, i + 1, d) *
IntArray::undef_seg(dp, i + 1, 100000)
*/
for (int j = 0; j < i; ++j) {
if (nums[j] < nums[i]) {
int candidate = dp[j] + 1;
if (candidate > dp[i]) {
dp[i] = candidate;
}
}
}
/*@ Assert
exists d,
nums == nums@pre && numsSize == numsSize@pre &&
1 <= numsSize@pre && numsSize@pre <= 100000 &&
Zlength(l) == numsSize@pre &&
0 <= i && i < numsSize@pre &&
1 <= ans && ans <= numsSize@pre &&
LISBestSoFar(l, i, ans) &&
Zlength(d) == i + 1 &&
(forall (k : Z), (0 <= k && k < i + 1) => (1 <= d[k] && d[k] <= k + 1)) &&
LISDPTablePrefix(l, d, i + 1) &&
IntArray::full(nums, numsSize@pre, l) *
IntArray::seg(dp, 0, i + 1, d) *
IntArray::undef_seg(dp, i + 1, 100000)
*/
if (dp[i] > ans) {
ans = dp[i];
}
}
/*@ Assert
nums == nums@pre && numsSize == numsSize@pre &&
LISLength(l, ans) &&
IntArray::full(nums, numsSize@pre, l) *
IntArray::undef_full(dp, 100000)
*/
return ans;
}
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