最大子段和

最大子段和

#include<vector>#include<algorithm>#include<iostream>using namespace std;typedef struct BestNode{int l, r;//和最大子段的最左指针和最右指针int maxs;}Best;class MAXSum{public:MAXSum(){cin >> n;num.assign(n + 1, 0);for (int i = 1; i <= n; i++){int in;cin >> in;num[i] = in;}b0 = { 0 };}//朴素法,简洁易懂O(n^2)void MaxSum1(){for (int i = 1; i <= n; i++){  int sum = 0;for (int j = i; j <= n; j++){sum += num[j];if (sum > b0.maxs){b0 = { i , j , sum };}}}}//分治法 O(nlogn)void  MaxSum2(int i , int j , Best& b){if (i != j){int mid = (i + j) / 2;Best b1 = { 0 };Best b2 = { 0 };Best b3 = { 0 };MaxSum2(i, mid , b1);MaxSum2(mid+1, j , b2);int temp = 0;b3.l = mid + 1;for(int k = mid; k >= i; k--){temp += num[k];if (temp > b3.maxs){b3.maxs = temp;b3.l = k;}}temp = b3.maxs;b3.r = mid + 1;for (int k = mid + 1; k <= j; k++){temp += num[k];if (temp > b3.maxs){b3.maxs = temp;b3.r = k;}}if (b3.maxs == 0){b3.l = b3.r = 0;}//求b1 , b2 , b3中的最大值if (b3.maxs < b1.maxs){b3 = b1;}if (b3.maxs < b2.maxs){b3 = b2;}b = b3;}else{if (num[i] > 0){b = { i , i , num[i] };}else{b = { 0 };}}}//动态规划法O(n)void MaxSum3(){Best b = { 0, 0,0 };Best temp = b;for (int i = 1; i <= n; i++){//以i结尾的所有连续子段中和最大的那个b.r = i;if (b.maxs > 0){b.maxs += num[i];}else{b.maxs = num[i];b.l = i;if (num[i] < 0){b.l = b.r = 0;}}if (temp.maxs < b.maxs){temp = b;}}b0 = temp;}void print(){cout << "最大子段和：" << b0.maxs << endl;;cout << "{ ";for (int i = b0.l; i < b0.r; i++){cout << num[i] << ",";}cout << num[b0.r]<<" }"<< endl;}public:vector<int> num;int n;Best b0;};MAXSum MS;int main(){//MS.MaxSum1();//MS.MaxSum2(1, MS.n, MS.b0);MS.MaxSum3();MS.print();return 0;}