求数组中的最长递增子序列

这里给出解法二的代码：

/** Copyright (c) 2011 alexingcool. All Rights Reserved.*/#include <iostream>#include <iterator>#include <algorithm>#define DEBUG#undef DEBUGusing namespace std;#define INF 65535int array[] = {1, -1, 2, -3, 4, -5, 6, -7};const int size = sizeof array / sizeof *array;int MaxIncrSeq(int (&array)[size]) {int minLast[size + 1];int record[size];int maxLen = 1;for(int i = 0; i < size; i++) {record[i] = 1;}minLast[1] = array[0];for(int i = 1; i < size; i++) {int j;for(j = maxLen; j >= 1; j--) {if(array[i] > minLast[j]) {record[i] = j + 1;break;}}if(record[i] > maxLen) {maxLen = record[i];cout << array[i] << ": " << maxLen << endl;minLast[maxLen] = array[i];}if(minLast[j + 1] > array[i])minLast[j + 1] = array[i];}return maxLen;}void main() {int maxLen = MaxIncrSeq(array);cout << "max incresing len: " << maxLen << endl;}

按照书上解法三的改进，作二分查找，可以将复杂度降低至O(nlogn)

/** Copyright (c) 2011 alexingcool. All Rights Reserved.*/#include <iostream>#include <iterator>#include <algorithm>#define DEBUG#undef DEBUGusing namespace std;#define INF 65535int array[] = {1, -1, 2, -3, 4, -5, 6, -7, -6, -5, -4, -3, -2};const int size = sizeof array / sizeof *array;int BinarySearch(int *array, int size, int data) {int left = 1, right = size;if(data > array[right]) {return right;}if(data < array[left]) {return left - 1;}while(left < right) {int mid = left + (right - left) / 2;if(mid == left)return mid;if(data > array[mid])left = mid;elseright = mid;}}int MaxIncrSeq(int (&array)[size]) {int minLast[size + 1];int record[size];int maxLen = 1;bool flag = false;for(int i = 0; i < size; i++) {record[i] = 1;}minLast[1] = array[0];for(int i = 1; i < size; i++) {int j = BinarySearch(minLast, maxLen, array[i]);record[i] = j + 1;if(record[i] > maxLen) {maxLen = record[i];minLast[maxLen] = array[i];}if(minLast[j + 1] > array[i])minLast[j + 1] = array[i];}return maxLen;}void main() {int maxLen = MaxIncrSeq(array);cout << "max incresing len: " << maxLen << endl;}

/** Copyright (c) 2011 alexingcool. All Rights Reserved.*/#include <iostream>#include <iterator>#include <algorithm>#define DEBUG#undef DEBUGusing namespace std;#define INF 65535int array[] = {3, 2, 1, 2, 3};const int size = sizeof array / sizeof *array;int findLongestIncrement(int *array, int size){if (array == NULL || size <= 0)return -1;int *minValue = new int[size + 1];int maxLen = 1;minValue[1] = *array;for (int i = 1; i < size; i++){int j;for (j = maxLen; j >= 1; j--){if (array[i] < minValue[j]);elsebreak;}if (j == maxLen){maxLen = j + 1;minValue[j + 1] = array[i];}else{if (minValue[j + 1] > array[i])minValue[j + 1] = array[i];}}delete[] minValue;return maxLen;}void main(){int ret = findLongestIncrement(array, size);cout << "ret = " << ret << endl;}