Longest monotonic decreasing subsequence

Problem description: Find the longest descending subsequence of an array, for example, {9, 4, 3, 2}. The longest descending subsequence is {9, 5, 4, 3, 2 }.

Idea: This is a standard dynamic planning problem. When you do not understand the algorithm, you are most likely to use the recursive idea. Actually, it is correct. At last, we will provide a recursive method, after knowing that it is a dynamic planning problem, we need to analyze it. We need an auxiliary array to record information. If the source array is SRC and the auxiliary array is table, the table [I] Array records SRC [0] ~ The SRC [I] sub-array contains the length of the longest monotonous sub-sequence consisting of SRC [I] (Note that table [I] records the decrease composed of SRC [I ]. the longest in the sequence, this is the longest descent sub-sequence ending with SRC [I]). If SRC [I] is greater than all the previous elements, then table [I] = 1.

The final result is: Table [I] = max {table [k] + 1, Src [I]> SRC [k] & 0 <k <I }, this is the table array initialized, so the longest descending subsequence is max {table [I], 0 <I <n }.

However, we need to print the oldest sequence. We have recorded the subscript of max {table [I], 0 <I <n}. Then we know the last element of the oldest sequence, at the same time, we know the length of the eldest son sequence. The following is a recursive call. If we already know that table [k] is the largest, Src [k] is the last in the longest descending subsequence, if table [I] + 1 = table [k] & SRC [I] <Table [K], you need to promise SRC [I].

# Include <stdio. h> # include <stdlib. h> void find (int src [], int N, int table []) {table [0] = 1; int I, j, Maxi = 0; for (I = 0; I <n; I ++) {table [I] = 1; for (j = 0; j <I; j ++) {/* this may be a common error. If (SRC [J]> SRC [I]) {table [I] = table [J] + 1; if (SRC [J]> SRC [I]) Table [I] = table [J] + 1; if (Table [I]> table [Maxi]) maxi = I;} */If (SRC [J]> SRC [I] & table [J] + 1> table [I]) {table [I] = table [J] + 1; // This is used to print the existence. The last array element of the maxi record is if (Table [I]> Table [Maxi]) maxi = I ;}}// printf ("% d \ r \ n", Maxi) ;}void print (INT SRC [], int table [], int Maxi) {int I = maxi-1; for (; I> = 0; I --) {If (Table [Maxi] = table [I] + 1 & SRC [I]> SRC [Maxi]) {print (SRC, table, I ); break ;}} printf ("% d", Src [Maxi]);} void findlongestdscarray2 (int * arr, int N) {int mark [9]; int link [9]; int I = 0; for (I = 0; I <n; I ++) {mark [I] = 0; link [I] =-1;} // link [0] = 1; Int J = 0, maxmark = 0; for (I = 0; I <N; I ++) {Maxmark = 0; For (j = 0; j <I; j ++) {If (ARR [J]> arr [I]) {If (maxmark <mark [J]) {maxmark = mark [J]; Link [I] = J ;}} mark [I] = maxmark + 1 ;} for (I = 0; I <9; I ++) printf ("% d", Mark [I]); printf ("\ r \ n "); for (I = 0; I <9; I ++) printf ("% d", link [I]); printf ("\ r \ n "); /* // print () int node = 0; maxmark = 0; for (I = 0; I <n; I ++) {If (MARK [I]> maxmark) node = I;} while (node! =-1) {printf ("% d", arr [node]); node = link [node];} */} int main () {int SRC [] = {9, 4, 3, 2, 5, 4, 3, 2, 4}; int table [9]; find (SRC, 9, table); findlongestdscarray2 (SRC, 9 ); int I = 0; For (; I <9; I ++) printf ("% d", table [I]); printf ("\ r \ n "); return 0 ;}

Longest monotonic decreasing subsequence