[hdu 1003] Max Sum

跟<算法导论(第三版)>上的一样,抄下来的

30 - 60 ms

标准的分治策略

#include <stdio.h>

int A[100000], Lenght;
const int NegativeInfinity = -1000000;

int gLow, gHigh, gSum;

void FindMaxCrossingSubArray(int low, int mid, int high)
{
    int left_sum = NegativeInfinity;
    int sum = 0;
    int max_left = mid;
    for (int i = mid; low <= i; i--)
    {
        sum += A[i];
        if (sum >= left_sum)
        {
            left_sum = sum;
            max_left = i;
        }
    }

    int right_sum = NegativeInfinity;
    sum = 0;
    int max_right = mid + 1;
    for (int i = mid + 1; i <= high; i++)
    {
        sum = sum + A[i];
        if (sum > right_sum)
        {
            right_sum = sum;
            max_right = i;
        }
    }

    gLow = max_left;
    gHigh = max_right;
    gSum = left_sum + right_sum;
}

void FindMaxSubArray(int low, int high)
{
    if (low == high)
    {
        gLow = low;
        gHigh = high;
        gSum = A[low];
        return;
    }
    
    int mid = (high + low) / 2;
    FindMaxSubArray(low, mid);
    int left_low = gLow, left_high = gHigh, left_sum = gSum;

    FindMaxSubArray(mid + 1, high);
    int right_low = gLow, right_high = gHigh, right_sum = gSum;

    FindMaxCrossingSubArray(low, mid, high);
    int cross_low = gLow, cross_high = gHigh, cross_sum = gSum;

    if (left_sum >= right_sum && left_sum >= cross_sum)
    {
        gLow = left_low;
        gHigh = left_high;
        gSum = left_sum;
    }
    else if (cross_sum >= right_sum && cross_sum >= left_sum)
    {
        gLow = cross_low;
        gHigh = cross_high;
        gSum = cross_sum;
    }
    else
    {
        gLow = right_low;
        gHigh = right_high;
        gSum = right_sum;
    }
}

int main()
{
    int N;
    scanf("%d", &N);

    for (int index = 0; index < N; index++)
    {
        // input
        int number;
        scanf("%d", &number);

        for (int i = 1; i <= number; i++)
        {
            scanf("%d", A + i);
        }

        // find
        FindMaxSubArray(1, number);

        // output
        printf("Case %d:
%d %d %d
", index + 1, gSum, gLow, gHigh);

        if (index != N - 1)
            printf("
");
    }

    return 0;
}

网上大神的

来源: http://acm.hdu.edu.cn/discuss/problem/post/reply.php?postid=23376&messageid=1&deep=0

15 ms 的光景

关键是 最大子数组一定是在一个负号之前

#include <stdio.h>
#include <stdlib.h>


/* run this program using the console pauser or add your own getch, system("pause") or input loop */

int main(int argc, char *argv[]) {
    int length;
    int Num[100000];
    int nums,i,times=1;
    int sum,pre_x,x,pre_y,y,max;
    scanf("%d",&nums);
    while(nums-->0){
        sum=0;max=0;
        pre_x=0;pre_y=0;x=0;y=0;
        scanf("%d",&length);
        for(i=0; i<length; i++){
            scanf("%d",&Num[i]);
        }
        max=Num[0];
        for(i=0; i<length; i++){
            sum+=Num[i];
            
            if(Num[i]>0)y=i;
            if(sum>max){
                pre_x=x;
                pre_y=y;
                max=sum;
            }
            if(sum<0){
                sum=0;x=i+1;y=i+1;
            }
        }
        printf("Case %d:
",times);
        printf("%d %d %d
",max,pre_x+1,pre_y+1);
        if(nums>0)printf("
");
        times++;
    } 
    return 0;
}