买卖股票的最佳时机-每天1LeetCode

题目

给定一个数组 prices ，它的第 i 个元素 prices[i] 表示一支给定股票第 i 天的价格。

你只能选择 某一天 买入这只股票，并选择在 未来的某一个不同的日子 卖出该股票。设计一个算法来计算你所能获取的最大利润。

返回你可以从这笔交易中获取的最大利润。如果你不能获取任何利润，返回 0 。

示例 1：

输入：[7,1,5,3,6,4]
输出：5
解释：在第 2 天（股票价格 = 1）的时候买入，在第 5 天（股票价格 = 6）的时候卖出，最大利润 = 6-1 = 5 。
     注意利润不能是 7-1 = 6, 因为卖出价格需要大于买入价格；同时，你不能在买入前卖出股票。

示例 2：

1 2	输入：prices = [7,6,4,3,1] 输出：0

解释：在这种情况下, 没有交易完成, 所以最大利润为 0。

提示：

1 <= prices.length <= 105
0 <= prices[i] <= 104

解法1 - 两层遍历

#include <vector>
using namespace std;
class Solution {
public:
    int maxProfit(vector<int>& prices) {
        int profit = 0;
        auto it = prices.begin();
        while (it != prices.end() - 1)
        {
            auto it2 = it + 1;
            while (it2 != prices.end())
            {
                profit = max(profit, *it2 - *it);
                it2++;
            }
            it++;
        }
        return profit;
    }
};

这种是最笨但是最直观的方法，两层循环，外层循环遍历所有买入价格，内层循环遍历所有卖出价格，求出最大利润。

但是

因为他非常慢,所以有一个case是无法通过的

prices = 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0,7,645,910,900,421,673,265,632,340,122,413,853,987,920,784,609,721,4,791,247,524,826,997,310,478,38,304,594,924,796,816,764,872,315,323,649,642,419,117,247,529,493,180,88,705,434,618,95,424,851,780,666,937,267,310,980,418,768,568,114,862,535,500,820,473,207,898,76,957,619,656,488,150,724,356,823,924,322,583,145,436,17,418,269,103,750,618,88,361,142,342,700,268,587,492,984,364,782,341,264,672,546,97,989,119,212,399,281,34,383,963,218,987,905,164,651,430,643,624,606,805,572,604,623,508,651,672,268,3,981,781,981,30,890,407,963,496,502,30,507,53,769,526,370,145,663,879,858,249,841,357,273,783,773,710,727,111,945,269,159,656,182,92,76,517,102,561,808,303,140,927,719,519,176,123,998,282,78,586,554,567,686,794,758,328,724,143,571,921,351,520,944,305,290,79,867,751,288,103,184,616,22,36,876,715,967,430,163,705,892,256,608,526,889,200,926,383,929,625,829,665,232,208,657,575,180,11,488,459,266,406,198,658,64,874,339,613,720,885,629,619,33,84,450,351,832,508,259,340,908,274,698,284,958,82,748,822,476,214,684,281,992,90,95,112,184,863,255,876,19,574,297,123,732,675,485,712,700,950,551,148,316,410,316,443,371,457,150,824,88,594,387,807,831,84,433,84,822,322,289,659,921,352,25,711,958,972,730,791,476,435,362,265,439,905,193,975,225,388,990,686,716,615,274,488,80,695,118,324,798,1,492,2,958,285,776,785,750,555,156,436,414,16,870,565,415,388,806,207,411,566,965,350,609,109,492,591,461,192,790,441,179,14,448,689,942,984,396,831,309,245,994,924,104,945,490,850,262,989,598,855,758,934,428,45,931,617,582,398,979,210,467,64,725,966,305,217,741,616,147,579,678,333,286,430,891,970,593,442,369,509,145,467,568,777,408,795,275,1,627,111,465,672,101,896,200,472,561,891,419,795,290,231,302,611,550,367,466,765,943,423,208,211,191,131,222,132,64,379,326,513,469,2,711,646,153,35,583,292,717,737,642,430,995,276,984,878,144,233,30,406,533,134,866,573,143,437,411,777,671,341,174,481,7,454,985,392,228,6,843,379,791,328,967,374,641,48,818,715,427,432,652,472,569,214,66,42,640,922,408,890,180,480,147,602,793,452,396,322,262,104,113,871,642,758,506,571,431,886,315,260,68,413,721,6,727,615,668,72,880,627,403,716,196,121,118,353,204,518,116,578,924,133,858,675,757,905,270,297,681,753,624,27,151,802,42,429,45,494,2,242,811,386,272,325,359,95,921,591,823,274,670,488,750,30,177,40,106,513,639,802,176,248,108,822,94,141,464,736,511,188,516,133,930,886,66,311,218,663,394,52,31,176,108,607,226,622,619,823,181,694,107,138,375,825,309,521,887,402,183,510,705,186,398,677,445,721,185,481,80,96,461,972]

所以这种方法其实是不行的.

解法2 - 直接遍历

在这题中我们不难发现,vector中的索引其实就是天数,你不可能在买入股票之前就将这支股票卖出去,所以可以直接遍历vector,先找最小的数,之后再找最大的数,只有最大的利润才保存下来

#include <vector>
using namespace std;
class Solution {
public:
    int maxProfit(vector<int>& prices) {
        // 提示中提到了输入数据中含有0,所以这里要设置成-1代表没有数据
        int profit = -1;
        int low = -1,high = -1;
        for (int price : prices)
        {
            if (price < low or low == -1) {
                low = price;
                high = -1;
                continue;
            }
            if (price > high or high == -1)
            {
                high = price;
                // 有些时候他会放一些收益低的组合在后面,所以要判断一下是不是最高收益
                profit = max(profit, high - low);
            }
        }
        // 题目要求没有利润返回0
        return max(0,profit);
    }
};

更好的解法(Top Voted Solution)

#include <vector>
using namespace std;
class Solution {
public:
    int maxProfit(vector<int>& prices) {
        int maxPro = 0;
        int minPrice = INT_MAX;
        for(int price : prices){
            minPrice = min(minPrice, price);
            maxPro = max(maxPro, price - minPrice);
        }
        return maxPro;
    }
};

高票解法思路更清晰,找到最小值之后就与最小值最大的差