| /*@ 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; | |
| } | |