C++动态规划计算最大子数组 C++动态规划计算最大子数组

例题
1.求最大的子数组的和
2.求和最大的相应子数组

例题题目：输入一个整形数组，数组里有正数也有负数。数组中连续的一个或多个整数组成一个子数组，每个子数组都有一个和。求所有子数组的和的最大值。要求时间复杂度为O(n)。
例如输入的数组为1, -2, 3, 10, -4, 7, 2, -5，和最大的子数组为3, 10, -4, 7, 2，因此输出为该子数组的和18。

1.求最大的子数组的和代码【C++】

#include using namespace std; /// Find the greatest sum of all sub-arrays// Return value: if the input is valid, return true, otherwise return false/bool FindGreatestSumOfSubArray(int *pData,// an arrayunsigned int nLength, // the length of arrayint &nGreatestSum// the greatest sum of all sub-arrays){// if the input is invalid, return falseif((pData =https://www.it610.com/article/= NULL) || (nLength == 0))return false; int nCurSum = nGreatestSum = 0; for(unsigned int i = 0; i < nLength; ++i){nCurSum += pData[i]; // if the current sum is negative, discard itif(nCurSum < 0)nCurSum = 0; // if a greater sum is found, update the greatest sumif(nCurSum> nGreatestSum)nGreatestSum = nCurSum; }// if all data are negative, find the greatest element in the arrayif(nGreatestSum == 0){nGreatestSum = pData[0]; for(unsigned int i = 1; i < nLength; ++i){if(pData[i] > nGreatestSum)nGreatestSum = pData[i]; }}return true; }int main(){int arr[] = {1, -2, 3, 10, -4, 7, 2, -5}; int iGreatestSum; FindGreatestSumOfSubArray(arr, sizeof(arr)/sizeof(int), iGreatestSum); cout << iGreatestSum << endl; return 0; }

结果

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2.求和最大的相应子数组代码【C++】

#include using namespace std; /// Find the greatest sum of all sub-arrays// Return value: if the input is valid, return true, otherwise return false/bool FindGreatestSumOfSubArray(int *pData,// an arrayunsigned int nLength, // the length of arrayint &nGreatestSum,// the greatest sum of all sub-arraysint &start,// Addedint &end// Added){// if the input is invalid, return falseif((pData =https://www.it610.com/article/= NULL) || (nLength == 0))return false; int nCurSum = nGreatestSum = 0; int curStart = 0, curEnd = 0; // Addedstart = end = 0; // Addedfor(unsigned int i = 0; i < nLength; ++i){nCurSum += pData[i]; curEnd = i; // Added// if the current sum is negative, discard itif(nCurSum < 0){nCurSum = 0; curStart = curEnd = i + 1; // Added}// if a greater sum is found, update the greatest sumif(nCurSum> nGreatestSum){nGreatestSum = nCurSum; start = curStart; // Addedend = curEnd; // Added}}// if all data are negative, find the greatest element in the arrayif(nGreatestSum == 0){nGreatestSum = pData[0]; start = end = 0; // Addedfor(unsigned int i = 1; i < nLength; ++i){if(pData[i] > nGreatestSum){nGreatestSum = pData[i]; start = end = i; // Added}}}return true; }int main(){int arr[] = {1, -2, 3, 10, -4, 7, 2, -5}; int iGreatestSum, start, end; FindGreatestSumOfSubArray(arr, sizeof(arr)/sizeof(int), iGreatestSum, start, end); cout << iGreatestSum << ": "; for(int i = start; i <= end; i++){cout << arr[i] << " "; }return 0; }

结果
【C++动态规划计算最大子数组】