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HTML

              
                <!DOCTYPE html>
<html lang="en">
<head>
    <meta charset="UTF-8">
    <meta name="viewport" content="width=device-width, initial-scale=1.0">
    <meta http-equiv="X-UA-Compatible" content="ie=edge">
    <title>dynamic programming</title>
</head>
<body>
    <script>
        // 递归求斐波拉契数列
        function recurFib (n) {
            if (2 > n) return n;
            return recurFib(n - 1) + recurFib(n - 2);
        }
        console.group('递归')
        var time = Date.now();
        console.log(recurFib(30));
        console.log(Date.now() - time);
        console.groupEnd()

        // 动态规划
        function dpFib (n) {
            var arr = [0, 1]
            if (n < 2) return arr[n]
            for (var i = 2; i <= n; i++) {
                arr[i] = arr[i - 1] + arr[i - 2];
            }
            return arr[n];
        }
        console.group('动态规划')
        var time2 = Date.now();
        console.log(dpFib(30));
        console.log(Date.now() - time2);
        console.groupEnd()
        
        // 迭代
        function iterFib (n) {
            if (2 > n) return n;
            var last = 1;
            var lastLast = 0;
            var now;
            for (var i = 2; i <= n; i++) {
                now = last + lastLast;
                lastLast = last;
                last = now;
            }
            return now;
        }
        console.group('迭代')
        var time2 = Date.now();
        console.log(iterFib(30));
        console.log(Date.now() - time2);
        console.groupEnd()

        // 寻找最长公共子串,暴力解法
        function longCompareStr(s1, s2) {
            var index = 0; // 索引位置
            var long = 0; // 总长度

            var tempIndex = 0; // 临时索引位置
            var tempLong = 0; // 临时长度

            for(var i = 0; i < s1.length; i++) {
                for(var j = 0; j < s2.length; j++) {
                    if (s1[i] == s2[j]) { // 找到第一次相同的位置
                        tempIndex = i; // 记录当前的索引位置
                        tempLong++; // 长度加 1
                        for(var k = 1; k < s1.length - i; k++) { // 再往下比对
                            if (s1[i+k] == s2[j+k]) {
                                tempLong++;
                            } else {
                                break;
                            }
                        }

                        if (tempLong > long) {
                            index = tempIndex;
                            long = tempLong;
                        }
                        tempLong = 0;
                    }
                }
            }
            return s1.slice(index, index + long);
        }
        console.group('寻找最长公共子串');
        console.log(longCompareStr('bccaqwerty', 'bbccqwerty2'));
        console.groupEnd();

        // 使用动态规划
        function dpLongCompareStr (s1, s2) {
            var index = 0; // 索引值位置
            var long = 0; // 最长相等的字符数

            var arr = [];
            for (var i = 0; i < s1.length; i++) {
                arr[i] = []
                for (var j = 0; j < s2.length; j++) {
                    arr[i][j] = 0;
                }
            } // 以上代码初始化二维数组

            for (var i = 0; i < s1.length; i++) {
                for (var j = 0; j < s2.length; j++) {
                    if (s1[i] == s2[j]) {
                        if (i > 0 && j > 0) {
                            arr[i][j] = arr[i - 1][j - 1] + 1 // 核心代码
                        } else {
                            arr[i][j] = 1
                        }
                    }
                    
                    if (arr[i][j] > long) {
                        long = arr[i][j];
                        index = i - long + 1; // 为什么要 +1,因为当 i = 0;long = 1;时,index = -1 不合理
                    }
                }
            }
            console.log(arr)
            return s1.slice(index, index + long) || null;
        }

        console.group('寻找最长公共子串 --- 动态规划');
        console.log(dpLongCompareStr('adfsfdfsd', 'adfsfsdfsdf'));
        console.groupEnd();

        // 背包问题,递归求解
        function max (a, b) {
            return a > b ? a : b;
        }
        function recurBackpack (capacity, sizes, value, n) {
            if (capacity == 0 || n == 0) return 0
            
            if (sizes[n - 1] > capacity) {
                return recurBackpack(capacity, sizes, value, n - 1)
            } else {
                return max(
                    value[n - 1] + recurBackpack(capacity - sizes[n - 1], sizes, value, n - 1),
                    recurBackpack(capacity, sizes, value, n - 1)
                ) // 对于当前这个选项,选或者不选,挑选一个最优解
            }
        }
        var value = [13, 4, 5, 10, 11];
        var sizes = [3, 4, 7, 8, 9];
        var capacity = 16;
        console.group('背包问题');
        console.log(recurBackpack(capacity, sizes, value, sizes.length));
        console.groupEnd();

        // 背包问题,动态规划
        function dpBackpack (capacity, sizes, value, n) {
            var arr = [];
            for (var i = 0; i <= n; i++) {
                arr[i] = []
            } // 初始化一个二维数组

            for (var i = 0; i <= n; i++) {
                for (var j = 0; j <= capacity; j++) {
                    if (i == 0 || j == 0) {
                        arr[i][j] = 0;
                    } else if (j >= sizes[i-1]) {
                        arr[i][j] = max(
                            value[i-1] + arr[i-1][j-sizes[i-1]],
                            arr[i-1][j]
                        )
                    } else {
                        arr[i][j] = arr[i-1][j]
                    }
                }
            }
            console.log(arr)
            return arr[n][capacity]
        }

        console.group('背包问题---动态规划');
        console.log(dpBackpack(capacity, sizes, value, sizes.length));
        console.groupEnd();
    </script>
</body>
</html>
              
            
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