贪心算法

贪心选择性质

在求解一个最优化的问题中,我们使用贪心的方式选择了一组内容后不会影响剩余子问题的求解。

如果无法使用贪心算法,举出反例即可。

如果无法举出反例,如何证明贪心算法的正确性?

1.数学归纳法 有一个变量n在一直变化

2.反证法,是否存在最优解。

leetcode435

题目地址:https://leetcode.com/problems/non-overlapping-intervals/description/

动态规划

import org.junit.Test;import java.util.Arrays;import java.util.Comparator;public class Main {    public class Interval {        int start;        int end;        Interval() {            start = 0;            end = 0;        }        Interval(int s, int e) {            start = s;            end = e;        }    }       public int eraseOverlapIntervals(Interval[] intervals) {        if (intervals==null||intervals.length==0)            return 0;        int length=intervals.length;        //排序        Arrays.sort(intervals, new Comparator<Interval>() {            @Override            public int compare(Interval o1, Interval o2) {            //比较要怎么比较,有疑问,是用例有问题吗                return o1.start-o2.start;            }        });        int dp[] = new int[length];        //置数        Arrays.fill(dp,1);        int max=1;        //类似最长递增子序列        for (int i = 1; i < length; i++) {            for (int j=0;j<i;j++)                if (intervals[i].start>=intervals[j].end)                    dp[i]=Math.max(dp[i],dp[j]+1);            if (dp[i]>max)                max=dp[i];        }        //找出最大值        return length-max;    }    @Test    public void main(){        System.out.println(eraseOverlapIntervals(new Interval[]{new Interval(1,2),new Interval(2,3)}));    }}

贪心法

import org.junit.Test;import java.util.Arrays;import java.util.Comparator;public class Main {    public class Interval {        int start;        int end;        Interval() {            start = 0;            end = 0;        }        Interval(int s, int e) {            start = s;            end = e;        }    }    public int eraseOverlapIntervals(Interval[] intervals) {        if (intervals==null||intervals.length==0)            return 0;        int length=intervals.length;        Arrays.sort(intervals, new Comparator<Interval>() {            @Override            public int compare(Interval o1, Interval o2) {             return o1.end-o2.end;            }        });        int max=1;        //记录刚开始的坐标        int pre=0;        for (int i = 1; i < length; i++) {            if (intervals[i].start>=intervals[pre].end){                max++;                pre=i;            }        }        //找出最大值        return length-max;    }    @Test    public void main() {        System.out.println(eraseOverlapIntervals(new Interval[]{                new Interval(-100,-87),new Interval(-99,-44),new Interval(-98,-19),new Interval(-97,-33),new Interval(-96,-60),new Interval(-95,-17),new Interval(-94,-44),new Interval(-93,-9),new Interval(-92,-63),new Interval(-91,-76),new Interval(-90,-44),new Interval(-89,-18),new Interval(-88,10),new Interval(-87,-39),new Interval(-86,7),new Interval(-85,-76),new Interval(-84,-51),new Interval(-83,-48),new Interval(-82,-36),new Interval(-81,-63),new Interval(-80,-71),new Interval(-79,-4),new Interval(-78,-63),new Interval(-77,-14),new Interval(-76,-10),new Interval(-75,-36),new Interval(-74,31),new Interval(-73,11),new Interval(-72,-50),new Interval(-71,-30),new Interval(-70,33),new Interval(-69,-37),new Interval(-68,-50),new Interval(-67,6),new Interval(-66,-50),new Interval(-65,-26),new Interval(-64,21),new Interval(-63,-8),new Interval(-62,23),new Interval(-61,-34),new Interval(-60,13),new Interval(-59,19),new Interval(-58,41),new Interval(-57,-15),new Interval(-56,35),new Interval(-55,-4),new Interval(-54,-20),new Interval(-53,44),new Interval(-52,48),new Interval(-51,12),new Interval(-50,-43),new Interval(-49,10),new Interval(-48,-34),new Interval(-47,3),new Interval(-46,28),new Interval(-45,51),new Interval(-44,-14),new Interval(-43,59),new Interval(-42,-6),new Interval(-41,-32),new Interval(-40,-12),new Interval(-39,33),new Interval(-38,17),new Interval(-37,-7),new Interval(-36,-29),new Interval(-35,24),new Interval(-34,49),new Interval(-33,-19),new Interval(-32,2),new Interval(-31,8),new Interval(-30,74),new Interval(-29,58),new Interval(-28,13),new Interval(-27,-8),new Interval(-26,45),new Interval(-25,-5),new Interval(-24,45),new Interval(-23,19),new Interval(-22,9),new Interval(-21,54),new Interval(-20,1),new Interval(-19,81),new Interval(-18,17),new Interval(-17,-10),new Interval(-16,7),new Interval(-15,86),new Interval(-14,-3),new Interval(-13,-3),new Interval(-12,45),new Interval(-11,93),new Interval(-10,84),new Interval(-9,20),new Interval(-8,3),new Interval(-7,81),new Interval(-6,52),new Interval(-5,67),new Interval(-4,18),new Interval(-3,40),new Interval(-2,42),new Interval(-1,49),new Interval(0,7),new Interval(1,104),new Interval(2,79),new Interval(3,37),new Interval(4,47),new Interval(5,69),new Interval(6,89),new Interval(7,110),new Interval(8,108),new Interval(9,19),new Interval(10,25),new Interval(11,48),new Interval(12,63),new Interval(13,94),new Interval(14,55),new Interval(15,119),new Interval(16,64),new Interval(17,122),new Interval(18,92),new Interval(19,37),new Interval(20,86),new Interval(21,84),new Interval(22,122),new Interval(23,37),new Interval(24,125),new Interval(25,99),new Interval(26,45),new Interval(27,63),new Interval(28,40),new Interval(29,97),new Interval(30,78),new Interval(31,102),new Interval(32,120),new Interval(33,91),new Interval(34,107),new Interval(35,62),new Interval(36,137),new Interval(37,55),new Interval(38,115),new Interval(39,46),new Interval(40,136),new Interval(41,78),new Interval(42,86),new Interval(43,106),new Interval(44,66),new Interval(45,141),new Interval(46,92),new Interval(47,132),new Interval(48,89),new Interval(49,61),new Interval(50,128),new Interval(51,155),new Interval(52,153),new Interval(53,78),new Interval(54,114),new Interval(55,84),new Interval(56,151),new Interval(57,123),new Interval(58,69),new Interval(59,91),new Interval(60,89),new Interval(61,73),new Interval(62,81),new Interval(63,139),new Interval(64,108),new Interval(65,165),new Interval(66,92),new Interval(67,117),new Interval(68,140),new Interval(69,109),new Interval(70,102),new Interval(71,171),new Interval(72,141),new Interval(73,117),new Interval(74,124),new Interval(75,171),new Interval(76,132),new Interval(77,142),new Interval(78,107),new Interval(79,132),new Interval(80,171),new Interval(81,104),new Interval(82,160),new Interval(83,128),new Interval(84,137),new Interval(85,176),new Interval(86,188),new Interval(87,178),new Interval(88,117),new Interval(89,115),new Interval(90,140),new Interval(91,165),new Interval(92,133),new Interval(93,114)                ,new Interval(94,125),new Interval(95,135),new Interval(96,144),new Interval(97,114),                new Interval(98,183),new Interval(99,157)}));        }    }