JavaScript-Data-Structures-and-Alo/DyanmicPrograming.html at master · cqA7/JavaScript-Data-Structures-and-Alo · GitHub

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<!DOCTYPE html>
<html lang="en">
<head>
    <meta charset="UTF-8">
    <title>DP</title>
</head>
<body>
<script>
    //Fibonacci subquence
    //递归版本(复杂度很高O(2^n))
    /*let arr = [];
    function fab(n) {
        if(n<2){
            return 1;
        }
        return fab(n-1) + fab(n-2);
    }
   function sequence(n) {
       for(let i = 0;i<n;i++){
           arr[i] = fab(i);
       }
       console.log(arr);
   }
   sequence(10);*/
    //非递归版本(复杂度为O(n))
    /*let arr = [];
    function fab(n) {
        arr[0] = 1;
        arr[1] = 1;
       if(n>=2){
           for(let i = 2;i<n;i++){
               arr[i] = arr[i-1]+arr[i-2];
           }
       }
       return arr;
    }
   console.log(fab(100));*/


    let task = [
        {
            index: 1, money: 5, time: {
            min: 1,
            max: 4
        }
        },
        {
            index: 2, money: 1, time: {
            min: 3,
            max: 5
        }
        },
        {
            index: 3, money: 8, time: {
            min: 0,
            max: 6
        }
        },
        {
            index: 4, money: 4, time: {
            min: 4,
            max: 7
        }
        },
        {
            index: 5, money: 6, time: {
            min: 3,
            max: 8
        }
        },
        {
            index: 6, money: 3, time: {
            min: 5,
            max: 9
        }
        },
        {
            index: 7, money: 2, time: {
            min: 6,
            max: 10
        }
        },
        {
            index: 8, money: 4, time: {
            min: 8,
            max: 11
        }
        }
    ];

    let prev;

    function genPrev(n) {
        if (n <= 1) return 0;
        let minTime = task[n - 1].time.min;
        for (let i = n - 2; i >= 0; i--) {
            if (task[i].time.max <= minTime) {
                prev = task[i].index;
                return prev;
            }
        }
        prev = 0;
        return prev;
    }

    let opt;

    //递归版本
    function rec_optimal(n) {
        if (n === 0) return 0;
        if (n === 1) {
            opt = task[0].money;
            return opt;
        }
        for (let i = 2; i <= n; i++) {
            let Unselect = rec_optimal(i - 1);
            let Select = task[i - 1].money + rec_optimal(genPrev(i));
            opt = Math.max(Unselect, Select);
        }
        return opt;
    }

    //非递归版本(动态规划)
    function dp_optimal(n) {
        let opt = [];
        opt[0] = task[0].money;
        for (let i = 1; i < n; i++) {
            let Unselect = opt[i - 1];
            let val = genPrev(i + 1) === 0 ? 0 : opt[genPrev(i)];
            let Select = task[i].money + val;
            opt[i] = Math.max(Unselect, Select);
        }
        return opt[n-1];
    }

    console.log(rec_optimal(8));
    console.log(dp_optimal(8));


</script>
</body>
</html>